From 2cedfa81f64dfe20426c0f7fa9796947b89a8068 Mon Sep 17 00:00:00 2001 From: moe-ad Date: Fri, 10 Jan 2025 10:51:09 +0100 Subject: [PATCH 01/26] feat: activate mathjax ext and add base rst --- doc/source/conf.py | 1 + .../examples/extended_examples/index.rst | 2 + .../extended_examples/sfem/stochastic_fem.rst | 40 +++++++++++++++++++ 3 files changed, 43 insertions(+) create mode 100644 doc/source/examples/extended_examples/sfem/stochastic_fem.rst diff --git a/doc/source/conf.py b/doc/source/conf.py index d6b87ea0180..13506bc8e48 100755 --- a/doc/source/conf.py +++ b/doc/source/conf.py @@ -103,6 +103,7 @@ "sphinxemoji.sphinxemoji", "sphinx.ext.graphviz", "ansys_sphinx_theme.extension.linkcode", + "sphinx.ext.mathjax", ] # Intersphinx mapping diff --git a/doc/source/examples/extended_examples/index.rst b/doc/source/examples/extended_examples/index.rst index ba788ffc2a4..7261606ce5b 100644 --- a/doc/source/examples/extended_examples/index.rst +++ b/doc/source/examples/extended_examples/index.rst @@ -25,6 +25,8 @@ with other programs, libraries, and features in development. +------------------------------------------------------+--------------------------------------------------------------------------------------------+ | :ref:`hpc_ml_ga_example` | Demonstrates how to use PyMAPDL in a high-performance computing system managed by SLURM. | +------------------------------------------------------+--------------------------------------------------------------------------------------------+ +| :ref:`stochastic_fem_example` | Demonstrates using PyMAPDL for stochastic FEA via the Monte Carlo simulation. | ++------------------------------------------------------+--------------------------------------------------------------------------------------------+ .. toctree:: diff --git a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst new file mode 100644 index 00000000000..949118ee761 --- /dev/null +++ b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst @@ -0,0 +1,40 @@ +.. _stochastic_fem_example: + +Stochastic finite element method with PyMAPDL +============================================= + +This example leverages PyMAPDL for stochastic finite element analysis via the Monte Carlo simulation. +Numerous advantages / workflow possibilities that PyMAPDL affords users is demonstrated through this +extended example. Important concepts are first explained before the example is presented. + +Introduction +------------ +Often in a mechanical system, system parameters (geometry, materials, loads, etc.) and response parameters +(displacement, strain, stress, etc) are taken to be deterministic. This simplification, while sufficient for a +wide range of engineering applications, results in a crude approximation of actual system behaviour. + +To obtain a more accurate representation of a physical system, it is essential to consider the randomness +in system parameters and loading conditions, along with the uncertainty in their estimation and their +spatial variability. The finite element method is undoubtedly the most widely used tool for solving deterministic +physical problems today and to account for randomness and uncertainty in the modeling of engineering systems, +the stochastic finite element method (SFEM) was introduced. + +The stochastic finite element method (SFEM) extends the classical deterministic finite element approach +to a stochastic framework, offering various techniques for calculating response variability. Among these, +the Monte Carlo simulation (MCS) stands out as the most prominent method. Renowned for its versatility and +ease of implementation, MCS can be applied to virtually any type of problem in stochastic analysis. + +Random variables vs stochastic processes +---------------------------------------- +A distinction between random variables and stochastic processes (also called random fields) is attempted in this +section. Explaining these concepts is important since they are used for modelling the system randomness. +Random variables are easier to understand from elementary probability theory, the same cannot be said for stochastic +processes. Readers are advised to consult books on SFEM if the explanation here seems to brief. + +Random variables +~~~~~~~~~~~~~~~~ +Imagine a beam with a concentrated load :math:`P` applied at a specific point on the beam. The value of :math:`P` +is uncertain — it could vary due to manufacturing tolerances, loading conditions, or measurement errors. Mathematically, +:math:`P` is a random variable: + +.. math:: P : \Omega \longrightarrow \mathbb{R} \ No newline at end of file From bd9748ed265f2b1738278f9e3ae3435f6375b04b Mon Sep 17 00:00:00 2001 From: pyansys-ci-bot <92810346+pyansys-ci-bot@users.noreply.github.com> Date: Fri, 10 Jan 2025 09:55:43 +0000 Subject: [PATCH 02/26] chore: adding changelog file 3648.documentation.md [dependabot-skip] --- doc/changelog.d/3648.documentation.md | 1 + 1 file changed, 1 insertion(+) create mode 100644 doc/changelog.d/3648.documentation.md diff --git a/doc/changelog.d/3648.documentation.md b/doc/changelog.d/3648.documentation.md new file mode 100644 index 00000000000..1395630859c --- /dev/null +++ b/doc/changelog.d/3648.documentation.md @@ -0,0 +1 @@ +feat: add stochastic fem example \ No newline at end of file From 28521e4d291b1d7add38fe5db123241672ce5c5a Mon Sep 17 00:00:00 2001 From: moe-ad Date: Sun, 12 Jan 2025 13:59:35 +0100 Subject: [PATCH 03/26] feat: more content --- .../extended_examples/sfem/stochastic_fem.rst | 73 +++++++++++++++++-- 1 file changed, 66 insertions(+), 7 deletions(-) diff --git a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst index 949118ee761..c1fb04ac2d3 100644 --- a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst +++ b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst @@ -26,15 +26,74 @@ ease of implementation, MCS can be applied to virtually any type of problem in s Random variables vs stochastic processes ---------------------------------------- -A distinction between random variables and stochastic processes (also called random fields) is attempted in this -section. Explaining these concepts is important since they are used for modelling the system randomness. -Random variables are easier to understand from elementary probability theory, the same cannot be said for stochastic -processes. Readers are advised to consult books on SFEM if the explanation here seems to brief. +A distinction between random variables and stochastic processes is attempted in this section. Explaining these +concepts is important since they are used for modelling the system randomness. Random variables are easier to +understand from elementary probability theory, the same cannot be said for stochastic processes. Readers are +advised to consult books on SFEM if the explanation here seems too brief. Random variables ~~~~~~~~~~~~~~~~ -Imagine a beam with a concentrated load :math:`P` applied at a specific point on the beam. The value of :math:`P` -is uncertain — it could vary due to manufacturing tolerances, loading conditions, or measurement errors. Mathematically, +**Definition:** A random variable is a rule for assigning to every possible outcome :math:`\theta` of an experiment a +number :math:`X(\theta)`. For notational convenience, the dependence on :math:`\theta` is usually dropped and the +random variable is written as :math:`X`. + +Practical example ++++++++++++++++++ +Imagine a beam with a concentrated load :math:`P` applied at a specific point. The value of :math:`P` +is uncertain—it could vary due to manufacturing tolerances, loading conditions, or measurement errors. Mathematically, :math:`P` is a random variable: -.. math:: P : \Omega \longrightarrow \mathbb{R} \ No newline at end of file +.. math:: P : \Theta \longrightarrow \mathbb{R} + +where :math:`\Theta` is the sample space of all possible loading scenarios, and :math:`\mathbb{R}` represents the set of +possible load magnitudes. For example, :math:`P` could be modeled as a random variable with a probability density +function (PDF) such as: + +.. math:: f_P(p) = \frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{(p-\mu)^2}{2\sigma^2}}, + +where :math:`\mu` is the mean load, and :math:`\sigma^2` is its variance. + +Stochastic processes +~~~~~~~~~~~~~~~~~~~~ +**Definition:** +recall that a random variable is defined as a rule that assigns a number :math:`X(\theta)` to every outcome :math:`\theta` +of an experiment. However, in some applications, the experiment evolves with respect to a deterministic parameter :math:`t`, +which belongs to an interval :math:`I`. For example, this occurs in an engineering system subjected to random dynamic loads +over a time interval :math:`I \subseteq \mathbb{R}^+`. In such cases, the system's response at a specific material point is +described not by a single random variable but by a collection of random variables :math:`\{X(t)\}` indexed by :math:`t \in I`. +This 'infinite' collection of random variables over the interval :math:`I` is called a stochastic process and is denoted as +:math:`\{X(t), t \in I\}` or simply :math:`X`. In this way, a stochastic process generalizes the concept of a random variable, +as it assigns to each outcome :math:`\theta` of the experiment a function :math:`X(t, \theta)`, known as a realization or sample +function. Lastly, if :math:`X` is indexed by some spatial coordinate :math:`s \in D \subseteq \mathbb{R}^n` rather than time :math:`t`, +then :math:`\{X(s), s \in D\}` is called a random field. + +Practical example ++++++++++++++++++ +Now, consider the material property of the beam, such as Young's modulus :math:`E(x)`, which may vary randomly along +the length of the beam :math:`x`. Instead of being a single random value, :math:`E(x)` is a random field—its value +is uncertain at each point along the domain, and it changes continuously across the beam. Mathematically, :math:`E(x)` +random field: + +.. math:: E(x) : x \in [0,L] \longrightarrow \mathbb{R} + +Here: + +* :math:`x` is the spatial coordinate along the length of the beam (:math:`x \in [0,L]`). +* :math:`E(x)` is a random variable at each point :math:`x`, and its randomness is described + by a covariance function or an autocorrelation function. + +For example, :math:`E(x)` could be a Gaussian random field, in which case it has the stationarity +property, making its statistics completely defined by its mean (:math:`\mu_E`), standard deviation +(:math:`\sigma_E`) and covariance function :math:`C_E(x_1,x_2)`. This 'stationarity' simply means +that the mean and standard deviation of every random variable :math:`E(x)` is constant and equal to +:math:`\mu_E` and :math:`\sigma_E` respectively. :math:`C_E(x_1,x_2)` describes how random variables +:math:`E(x_1)` and :math:`E(x_2)` are related. +For a zero-mean Gaussian random field, the covariance function is given by: + +.. math:: C_E(x_1,x_2) = \sigma_E^2e^{-\frac{\lvert x_1-x_2 \rvert}{\ell}} + +where :math:`\sigma_E^2` is the variance, and :math:`\ell` is the correlation length parameter. + +To aid understanding, the figure below is a diagram depicting two equivalent ways of visualizing a +stochastic process / random field, that is, as an infinite collection of random variables or as a +realization/sample function assigned to each outcome of an experiment. \ No newline at end of file From 4fc29e861f5c7d8a79e7ddd1aab8bc10b8ecc429 Mon Sep 17 00:00:00 2001 From: moe-ad Date: Sun, 12 Jan 2025 15:23:17 +0100 Subject: [PATCH 04/26] feat: added realizations figure --- doc/source/conf.py | 2 +- .../examples/extended_examples/sfem/stochastic_fem.rst | 6 +++++- 2 files changed, 6 insertions(+), 2 deletions(-) diff --git a/doc/source/conf.py b/doc/source/conf.py index 13506bc8e48..1c5dddf9032 100755 --- a/doc/source/conf.py +++ b/doc/source/conf.py @@ -99,7 +99,7 @@ "sphinx_design", "sphinx_jinja", "sphinx_copybutton", - "sphinx_gallery.gen_gallery", +# "sphinx_gallery.gen_gallery", "sphinxemoji.sphinxemoji", "sphinx.ext.graphviz", "ansys_sphinx_theme.extension.linkcode", diff --git a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst index c1fb04ac2d3..9d90a85f1d1 100644 --- a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst +++ b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst @@ -96,4 +96,8 @@ where :math:`\sigma_E^2` is the variance, and :math:`\ell` is the correlation le To aid understanding, the figure below is a diagram depicting two equivalent ways of visualizing a stochastic process / random field, that is, as an infinite collection of random variables or as a -realization/sample function assigned to each outcome of an experiment. \ No newline at end of file +realization/sample function assigned to each outcome of an experiment. + +.. figure:: realizations.png + + A random field as a collection of random variables or realizations \ No newline at end of file From 470e3ca2d993d130db1bb8304d2cf212bf29d7d2 Mon Sep 17 00:00:00 2001 From: "pre-commit-ci[bot]" <66853113+pre-commit-ci[bot]@users.noreply.github.com> Date: Sun, 12 Jan 2025 14:23:46 +0000 Subject: [PATCH 05/26] ci: auto fixes from pre-commit.com hooks. for more information, see https://pre-commit.ci --- doc/source/conf.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/doc/source/conf.py b/doc/source/conf.py index 1c5dddf9032..c7fc60490f9 100755 --- a/doc/source/conf.py +++ b/doc/source/conf.py @@ -99,7 +99,7 @@ "sphinx_design", "sphinx_jinja", "sphinx_copybutton", -# "sphinx_gallery.gen_gallery", + # "sphinx_gallery.gen_gallery", "sphinxemoji.sphinxemoji", "sphinx.ext.graphviz", "ansys_sphinx_theme.extension.linkcode", From 9f2758130243e46eaa8cc6b25a31abfccda651de Mon Sep 17 00:00:00 2001 From: moe-ad Date: Tue, 14 Jan 2025 11:16:45 +0100 Subject: [PATCH 06/26] feat: more content --- doc/source/conf.py | 2 +- .../extended_examples/sfem/realizations.png | Bin 0 -> 131959 bytes .../extended_examples/sfem/stochastic_fem.rst | 30 +++++++++++++++--- 3 files changed, 26 insertions(+), 6 deletions(-) create mode 100644 doc/source/examples/extended_examples/sfem/realizations.png diff --git a/doc/source/conf.py b/doc/source/conf.py index c7fc60490f9..13506bc8e48 100755 --- a/doc/source/conf.py +++ b/doc/source/conf.py @@ -99,7 +99,7 @@ "sphinx_design", "sphinx_jinja", "sphinx_copybutton", - # "sphinx_gallery.gen_gallery", + "sphinx_gallery.gen_gallery", "sphinxemoji.sphinxemoji", 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zvji=SlJ?fop+l^de)a{FbOQN6iGwmmJ}B?VG%gO#u2>1&FKYQ|d_3@6`sJDj`)zv( zVK2_4^vyVeOw6G=GASiRU+OL>`@L*zo@bA{k_9`C1vrR&GH8`w>{Wu`oZCE6UjP@^ zWB)SfN`l*6ur4jiVZUtu<4BaTxw-id7@Tl=FIb+-Zvyt90yU7MTwPlCpHLOygOY`W k{PX{<0LXX#FE?H13?t67JBaGLP{5D6ijHy?_Trs?0h`V=a{vGU literal 0 HcmV?d00001 diff --git a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst index 9d90a85f1d1..28c21bf89aa 100644 --- a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst +++ b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst @@ -84,13 +84,13 @@ Here: For example, :math:`E(x)` could be a Gaussian random field, in which case it has the stationarity property, making its statistics completely defined by its mean (:math:`\mu_E`), standard deviation -(:math:`\sigma_E`) and covariance function :math:`C_E(x_1,x_2)`. This 'stationarity' simply means +(:math:`\sigma_E`) and covariance function :math:`C_E(x_i,x_j)`. This 'stationarity' simply means that the mean and standard deviation of every random variable :math:`E(x)` is constant and equal to -:math:`\mu_E` and :math:`\sigma_E` respectively. :math:`C_E(x_1,x_2)` describes how random variables -:math:`E(x_1)` and :math:`E(x_2)` are related. +:math:`\mu_E` and :math:`\sigma_E` respectively. :math:`C_E(x_i,x_j)` describes how random variables +:math:`E(x_i)` and :math:`E(x_j)` are related. For a zero-mean Gaussian random field, the covariance function is given by: -.. math:: C_E(x_1,x_2) = \sigma_E^2e^{-\frac{\lvert x_1-x_2 \rvert}{\ell}} +.. math:: C_E(x_i,x_j) = \sigma_E^2e^{-\frac{\lvert x_i-x_j \rvert}{\ell}} where :math:`\sigma_E^2` is the variance, and :math:`\ell` is the correlation length parameter. @@ -100,4 +100,24 @@ realization/sample function assigned to each outcome of an experiment. .. figure:: realizations.png - A random field as a collection of random variables or realizations \ No newline at end of file + A random field as a collection of random variables or realizations + +.. note:: + The concepts above generalize to more dimensions, for example, a random vector instead of a random + variable, or an :math:`\mathbb{R}^d`-valued stochastic process. The presentation above is however + sufficient for this example. + +Series expansion of stochastic processes +---------------------------------------- +Since a stochastic processes involves an infinite number of random variables, most engineering applications +involving stochastic processes will be mathematically and computationally intractable if there isn't a way of +approximating them with a series of a finite number of random variables. A series expansion method which will +be used in this example is explained next. + +The Karhunen-Loève (K-L) series expansion +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +For a zero-mean stationary gaussian process, :math:`X(t)`, with covariance function +:math:`C_X(t_i,t_j)=\sigma_X^2e^{-\frac{\lvert t_i-t_j \rvert}{b}}` defined on a domain :math:`\mathbb{D}=[-a,a]`, +the K-L series expansion is given by: + +.. math:: X(t) = \sum_{n=1}^\infty \sqrt{\lambda_{n,c}}\cdot\phi_{n,c}(t)\cdot\xi_{n,c} + \sum_{n=1}^\infty \sqrt{\lambda_{n,s}}\cdot\phi_{n,s}(t)\cdot\xi_{n,s},\quad t\in\mathbb{D} \ No newline at end of file From e03e38d28084f9ecd6ffb6edeaffb8446e33e619 Mon Sep 17 00:00:00 2001 From: moe-ad Date: Wed, 15 Jan 2025 13:25:11 +0100 Subject: [PATCH 07/26] feat: toctree entry and more content --- .../examples/extended_examples/index.rst | 1 + .../extended_examples/sfem/stochastic_fem.rst | 37 +++++++++++++++++-- 2 files changed, 34 insertions(+), 4 deletions(-) diff --git a/doc/source/examples/extended_examples/index.rst b/doc/source/examples/extended_examples/index.rst index 7261606ce5b..a0b37325928 100644 --- a/doc/source/examples/extended_examples/index.rst +++ b/doc/source/examples/extended_examples/index.rst @@ -41,4 +41,5 @@ with other programs, libraries, and features in development. executable/executable.rst gui/executable.rst hpc/hpc_ml_ga.rst + sfem/stochastic_fem.rst diff --git a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst index 28c21bf89aa..e112acb77db 100644 --- a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst +++ b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst @@ -114,10 +114,39 @@ involving stochastic processes will be mathematically and computationally intrac approximating them with a series of a finite number of random variables. A series expansion method which will be used in this example is explained next. -The Karhunen-Loève (K-L) series expansion -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +The Karhunen-Loève (K-L) series expansion for a Gaussian process +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +More generally, the K-L expansion of any process is based on a spectral decomposition of its covariance function. Analytical +solutions are possible in a few cases, and such is the case of Gaussian process. + + For a zero-mean stationary gaussian process, :math:`X(t)`, with covariance function -:math:`C_X(t_i,t_j)=\sigma_X^2e^{-\frac{\lvert t_i-t_j \rvert}{b}}` defined on a domain :math:`\mathbb{D}=[-a,a]`, +:math:`C_X(t_i,t_j)=\sigma_X^2e^{-\frac{\lvert t_i-t_j \rvert}{b}}` defined on a symmetric domain :math:`\mathbb{D}=[-a,a]`, the K-L series expansion is given by: -.. math:: X(t) = \sum_{n=1}^\infty \sqrt{\lambda_{n,c}}\cdot\phi_{n,c}(t)\cdot\xi_{n,c} + \sum_{n=1}^\infty \sqrt{\lambda_{n,s}}\cdot\phi_{n,s}(t)\cdot\xi_{n,s},\quad t\in\mathbb{D} \ No newline at end of file +.. math:: X(t) = \sum_{n=1}^\infty \sqrt{\lambda_{c,n}}\cdot\varphi_{c,n}(t)\cdot\xi_{c,n} + \sum_{n=1}^\infty \sqrt{\lambda_{s,n}}\cdot\varphi_{s,n}(t)\cdot\xi_{s,n},\quad t\in\mathbb{D} + +where, + +.. math:: \lambda_{c,n} = \frac{2b}{1+\omega_{c,n}^2\cdot b^2},\quad \varphi_{c,n}(t) = k_{c,n}\cos(\omega_{c,n}\cdot t) +.. math:: k_{c,n} = \frac{1}{\sqrt{a+\frac{\sin(2\omega_{c,n}\cdot a)}{2\omega_{c,n}}}} + +:math:`\omega_{c,n}` is obtained as the solution of + +.. math:: \frac{1}{b} - \omega_{c,n}\cdot\tan(\omega_{c,n}\cdot a) = 0 \quad \text{in the range} \quad \biggl[(n-1)\frac{\pi}{a}, (n-\frac{1}{2})\frac{\pi}{a}\biggr] + +and, + +.. math:: \lambda_{s,n} = \frac{2b}{1+\omega_{s,n}^2\cdot b^2},\quad \varphi_{s,n}(t) = k_{s,n}\sin(\omega_{s,n}\cdot t) +.. math:: k_{s,n} = \frac{1}{\sqrt{a-\frac{\sin(2\omega_{s,n}\cdot a)}{2\omega_{s,n}}}} + +:math:`\omega_{s,n}` is obtained as the solution of + +.. math:: \frac{1}{b}\cdot\tan(\omega_{s,n}\cdot a) + \omega_{s,n} = 0 \quad \text{in the range} \quad \biggl[(n-\frac{1}{2})\frac{\pi}{a}, n\frac{\pi}{a}\biggr] + +The K-L expansion of a gaussian process has the property that :math:`\xi_{c,n}` are independent standard normal variables. For practical +implementation, the infinite series of the K-L expansion above is truncated after a finite number of terms, M, giving the approximation + +.. math:: X(t) \approx \hat{X}(t) = \sum_{n=1}^M \sqrt{\lambda_{c,n}}\cdot\varphi_{c,n}(t)\cdot\xi_{c,n} + \sum_{n=1}^M \sqrt{\lambda_{s,n}}\cdot\varphi_{s,n}(t)\cdot\xi_{s,n},\quad t\in\mathbb{D} + + From 54af6bdfb5fedd831e650785ddd35631bdd0a7d5 Mon Sep 17 00:00:00 2001 From: moe-ad Date: Thu, 16 Jan 2025 10:17:36 +0100 Subject: [PATCH 08/26] feat: more content and new figure --- .../extended_examples/sfem/problem.png | Bin 0 -> 12903 bytes .../extended_examples/sfem/stochastic_fem.rst | 92 +++++++++++++++--- 2 files changed, 79 insertions(+), 13 deletions(-) create mode 100644 doc/source/examples/extended_examples/sfem/problem.png diff --git a/doc/source/examples/extended_examples/sfem/problem.png b/doc/source/examples/extended_examples/sfem/problem.png new file mode 100644 index 0000000000000000000000000000000000000000..82259418131e6c107fe259bda0e88d973bce6a27 GIT binary patch literal 12903 zcmch81yEd3mnMV+2oAwDK!D&9T!XvQKyY`bku>gZ!GkuE;1ZnR1PSgC+}+)oN9LcY z-JSibX0~Rht0=nPd-vXR@6qp^^TL!ABvFwFkzin8P^G2BRA69Ukifve(j&qHS0Kf# zeZW6hXB9~in6e?_9pJ}Hb76U57?{c!j4i*qR<+q*?jukH#kzfCa3VbU;8zzqfDk@Nxsd=1)7Tp%#Lf58Mw8C*o%q9ya z#Uk-p31y7m1;(cQ*)tnXOMl{_k&Ln`z3i12JZc##zPb?{Zr+Nmzj7Y_Jj4U>M-&4- zPi$TrPk+DA1*1_=P^i2TMZmw%s4uH-q29+ zEat%ZnSX8u$^N4zVO#E>2zQSi!SrFZU`!Ak3W=B)uYAPnyw3W@9rR#(6rYhP0KqLV ze#eaAb29>bGz2wmI0-63Ab-xy3d}hP6CCWFa=Vdyt)i2}s2ve1@4;#=2U8Y&)PCzi zUawY$@(vRDysFjPGkEW9UW50LM%|AciBg*kP85}H= zy3J|?P+jC#{feO8Nf7sS1L}(U60*yF0$NT_D6qQ%_=1uFiHY_A?)OZ0t_K~8$VrA9 zn^Nm{ZXdrdt2@+kq^vlkE%gxRGzFDj> z%mX;oB67>4?#G8aR@Z&afpnfXJuze&kWerlu!1s&nwD00eLXji=la$bB_*Zk4*8hw z^J0@~;^IN4p#^6DQ8fNHa{luY^-qS0C}PmYfE+LPKk2l162$z_5)~D7_weZK>5(i1 zB!}Vi=g%p8ZcKu=+m!C^?gmpOpYVB{^2TKI($vsNC?z7>e#g@!PIZn>PfIE(Vc;_B zm8b!7gd2=j6b3v13kw?>9j&f~&dkk?56Hbt1h6H;?d-3i&cMn16O#T{-QW;0oPCwf zLlRU_P_!{|!Jq%#3^Ncb?^j00pLNgt9KL6EOZDKqWxaJP(LIO#)+$7x`duM0In23L z6zo*VCgHY0mDxS&tP!i9lQ@?+OMh+WiN{}eK3ewqg8NzD;uQLu8xfWUQljOl9#}oP zT=)M}A*`&dq-^;RdaNQPC^ymznoxHS>&M8Zii2JW(6jH{qd+)ZO04!U0#Ye9D(R9K zKKWNyv*%wN&o3;nLe4Gn#l`Y|A|WAFxE<;J>gsBroW$ww?tah6C~ji%4vmx_k&llL zyfY@=QlGOvmM`lhKtqEN9UXmIN^Vt7O#EQSRBL*-Qd1{EQ2|9o`BjveNjm@HE;q;v zDcW8jI^hR4FD}d_gu9ptXekk?{&QnnhY}eCMD#LYefjiv^Gv-!j+LAa zyn!WxB;T@@34TWh`s%i$WyX!eYj8--{X53fab^lO@P`h{{OQTIky)(SKq;H0ADDMc z*d2Ld0oQCEFWC#wKjiY`H(qy^XC_|HJ6V)vwL=eD4URB(T;3?#nIa${$l^m`@Gk8- zcv4ozhSMtecHa$kZFP)wir!cC(W~PCdNFG3dVOrzbhYR)Q)`<>{8p>hCM-NW{AY0V z%#0?3PCW)PE<;

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2 deletions(-) create mode 100644 doc/source/examples/extended_examples/sfem/sfem.ipynb create mode 100644 doc/source/examples/extended_examples/sfem/sfem.py diff --git a/doc/source/conf.py b/doc/source/conf.py index 13506bc8e48..d6b87ea0180 100755 --- a/doc/source/conf.py +++ b/doc/source/conf.py @@ -103,7 +103,6 @@ "sphinxemoji.sphinxemoji", "sphinx.ext.graphviz", "ansys_sphinx_theme.extension.linkcode", - "sphinx.ext.mathjax", ] # Intersphinx mapping diff --git a/doc/source/examples/extended_examples/sfem/sfem.ipynb b/doc/source/examples/extended_examples/sfem/sfem.ipynb new file mode 100644 index 00000000000..e69de29bb2d diff --git a/doc/source/examples/extended_examples/sfem/sfem.py b/doc/source/examples/extended_examples/sfem/sfem.py new file mode 100644 index 00000000000..e69de29bb2d diff --git a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst index ce994b43eec..306a83db42d 100644 --- a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst +++ b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst @@ -215,4 +215,8 @@ We are to do the following: Carlo simulation to the probability density function of the response :math:`u`, at the bottom right corner of the cantilever. -2. If :math:`u` must not exceed :math:`0.2 m`, how confident can we be of this requirement? \ No newline at end of file +2. If :math:`u` must not exceed :math:`0.2 \thickspace m`, how confident can we be of this requirement? + +Evaluating +~~~~~~~~~~~~~~~~~~~~~~~~~~~ +Firstly, we implement code that allows us to represent the zero-mean field :math:`f`. From db2acecb3c4274672669cec29941c559d6dfbb24 Mon Sep 17 00:00:00 2001 From: moe-ad Date: Thu, 16 Jan 2025 17:52:06 +0100 Subject: [PATCH 10/26] feat: a lot of content --- doc/source/conf.py | 1 + .../examples/extended_examples/sfem/mean.png | Bin 0 -> 59257 bytes .../extended_examples/sfem/sfem.ipynb | 488 ++++++++++++++++++ .../examples/extended_examples/sfem/sfem.py | 376 ++++++++++++++ .../extended_examples/sfem/stochastic_fem.rst | 146 +++++- .../extended_examples/sfem/variance.png | Bin 0 -> 45468 bytes .../sfem/young_modulus_realizations.png | Bin 0 -> 248243 bytes 7 files changed, 1000 insertions(+), 11 deletions(-) create mode 100644 doc/source/examples/extended_examples/sfem/mean.png create mode 100644 doc/source/examples/extended_examples/sfem/variance.png create mode 100644 doc/source/examples/extended_examples/sfem/young_modulus_realizations.png diff --git a/doc/source/conf.py b/doc/source/conf.py index d6b87ea0180..7fe4a5a4e3d 100755 --- a/doc/source/conf.py +++ b/doc/source/conf.py @@ -103,6 +103,7 @@ "sphinxemoji.sphinxemoji", "sphinx.ext.graphviz", "ansys_sphinx_theme.extension.linkcode", + "sphinx.ext.mathjax" ] # Intersphinx mapping diff --git a/doc/source/examples/extended_examples/sfem/mean.png b/doc/source/examples/extended_examples/sfem/mean.png new file mode 100644 index 0000000000000000000000000000000000000000..83b75c764229111f27fb65f1e9c830fac4bd8e34 GIT binary patch literal 59257 zcmeFZby!sE+ct~=1`4_r5hS(>C?KFnNUI1qAYIZbjdYE~0Lpe_0XmdOcQbUCq9QHb zB^^W0fDG|nOK^X`{k-q<9pC%k`^Uop2NNsqb>CN<*Lj_5y;M?=IewJ>C>a^qan#*A zDr98j{bXbZ{yakWbzLkZ7ppaEzKYO>1=H8U~Xf5 zo%`BV?yFb+G;?&cbr9y^vHE8VZX0`3onmYnIU1`Qw2Ffm+d5dU%bJqb=2xa2IH4?DPs>=@{?F$BGc*5V z1pnh6WdAaPMO*YCFUl_#`7>j+0Y{G=3;g)N7QGiVhS>zd1RbV^H4OAPn@MBV!G1 zG~v=OyD$0ov3E&HNu{L+qE9y|M^F6NJZK?+ypWZZRZ&w56yw>i`@D+LNm`jMw5sYR zIXQW8u^^c&Z&>5<%8IIz(h1KOWc(*4FDp6NdFiX@M+8qrUSrOUO 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zf1t*OEG$E{1Yx_ObHlw2wT(Rp1{?L?dMR0LI!u1v?D0+zHaH z8s}7R@S2q?`B0(^My(5UI9B1oq*`o;8^E%Wq*4k|og;=2Cr-`SkLOZ_0Juc>4aUIe z^NSnAtibFf5b7SAZivK(3k;!(#4zmI2JI@kH)mTy8~YX#lQ{Syv8Y0B2ZtKHxxla6fk6$r|8GGfG*W2nc*HB3RIXkIblz3p7c>g?bb)xeR(GX0s^pO zyt#A7zc&yq0ZFcY_9v4GP+ANoDL|Jvv%Aq#97HSYk|lbMB(DHxQWbPX!$?0MxuOKU z>RjoU$?m9)KdBDaIu0cRLqPOPek+)@NEfb^7{UCe8K3@u%U1$ float:\n", + " \"\"\"Find the solution of g(x) = 0 within solution range where g(x) is non-linear.\n", + "\n", + " Parameters\n", + " ----------\n", + " func : Callable[float, float]\n", + " The function definition\n", + " derivative_func : Callable[float, float]\n", + " The derivative of the above function\n", + " acceptable_solution_error : float\n", + " Error at which the solution is acceptable\n", + " solution_range : Tuple[float, float]\n", + " The range within which the solution will be searched\n", + "\n", + " Returns\n", + " -------\n", + " float\n", + " Solution to g(x) = 0\n", + " \"\"\"\n", + "\n", + " current_guess = random.uniform(*solution_range)\n", + " iteration_counter = 1\n", + "\n", + " while True:\n", + " if iteration_counter > 100:\n", + " iteration_counter = 1\n", + " current_guess = random.uniform(*solution_range)\n", + " continue\n", + "\n", + " updated_guess = current_guess - func(current_guess) / derivative_func(current_guess)\n", + " error = abs(updated_guess - current_guess)\n", + "\n", + " if error < acceptable_solution_error and not (\n", + " solution_range[0] < updated_guess < solution_range[1]\n", + " ):\n", + " current_guess = random.uniform(*solution_range)\n", + " continue\n", + " elif error < acceptable_solution_error and (\n", + " solution_range[0] < updated_guess < solution_range[1]\n", + " ):\n", + " return updated_guess\n", + "\n", + " current_guess = updated_guess\n", + " iteration_counter += 1\n", + "\n", + "\n", + "def evaluate_KL_cosine_terms(\n", + " domain: Tuple[float, float], correl_length_param: float, min_eigen_value: float\n", + ") -> Tuple[np.ndarray, np.ndarray, np.ndarray]:\n", + " \"\"\"Build array of eigenvalues and constants of the cosine terms in the KL expansion of a gaussian stochastic process.\n", + "\n", + " Parameters\n", + " ----------\n", + " domain : Tuple[float, float]\n", + " Domain over which the KL representation of the stochastic process should be found\n", + " correl_length_param : float\n", + " Correlation length parameter of the autocorrelation function of the process\n", + " min_eigen_value : float\n", + " Minimum eigenvalue to achieve require accuracy\n", + "\n", + " Returns\n", + " -------\n", + " Tuple[np.ndarray, np.ndarray, np.ndarray]\n", + " Arrays of frequencies, eigenvalues, and constants of retained cosine terms (P in total) in the KL expansion\n", + " \"\"\"\n", + "\n", + " A = (domain[1] - domain[0]) / 2 # Symmetric domain parameter -> [-A, A]\n", + "\n", + " frequency_array = []\n", + " cosine_eigen_values_array = []\n", + " cosine_constants_array = []\n", + "\n", + " # Define the functions related to the sine terms\n", + " def func(w_n):\n", + " return 1 / correl_length_param - w_n * math.tan(w_n * A)\n", + "\n", + " def deriv_func(w_n):\n", + " return -w_n * A / math.cos(w_n * correl_length_param) ** 2 - math.tan(w_n * A)\n", + "\n", + " def eigen_value(w_n):\n", + " return (2 * correl_length_param) / (1 + (correl_length_param * w_n) ** 2)\n", + "\n", + " def cosine_constant(w_n):\n", + " return 1 / (A + (math.sin(2 * w_n * A) / (2 * w_n))) ** 0.5\n", + "\n", + " # Build the array of eigenvalues and constant terms for the accuracy required\n", + " for n in range(1, 100):\n", + " # start solving here\n", + " acceptable_solution_error = 1e-10\n", + " solution_range = [(n - 1) * math.pi / A, (n - 0.5) * math.pi / A]\n", + " solution = find_solution(func, deriv_func, acceptable_solution_error, solution_range)\n", + "\n", + " frequency_array.append(solution)\n", + " cosine_eigen_values_array.append(eigen_value(solution))\n", + " cosine_constants_array.append(cosine_constant(solution))\n", + " if eigen_value(solution) < min_eigen_value:\n", + " break\n", + "\n", + " return (\n", + " np.array(frequency_array),\n", + " np.array(cosine_eigen_values_array),\n", + " np.array(cosine_constants_array),\n", + " )\n", + "\n", + "\n", + "def evaluate_KL_sine_terms(\n", + " domain: Tuple[float, float], correl_length_param: float, min_eigen_value: float\n", + ") -> Tuple[np.ndarray, np.ndarray, np.ndarray]:\n", + " \"\"\"Build array of eigenvalues and constants of the sine terms in the KL expansion of a gaussian stochastic process.\n", + "\n", + " Parameters\n", + " ----------\n", + " domain : Tuple[float, float]\n", + " Domain over which the KL representation of the stochastic process should be found\n", + " correl_length_param : float\n", + " Correlation length parameter of the autocorrelation function of the process\n", + " min_eigen_value : float\n", + " Minimum eigenvalue to achieve require accuracy\n", + "\n", + " Returns\n", + " -------\n", + " Tuple[np.ndarray, np.ndarray, np.ndarray]\n", + " Arrays of frequencies, eigenvalues, and constants of retained sine terms (Q in total) in the KL expansion\n", + " \"\"\"\n", + "\n", + " A = (domain[1] - domain[0]) / 2 # Symmetric domain parameter -> [-A, A]\n", + "\n", + " frequency_array = []\n", + " sine_eigen_values_array = []\n", + " sine_constants_array = []\n", + "\n", + " # Define functions related to the sine terms\n", + " def func(w_n):\n", + " return (1 / correl_length_param) * math.tan(w_n * A) + w_n\n", + "\n", + " def deriv_func(w_n):\n", + " return A / (correl_length_param * math.cos(w_n * A) ** 2) + 1\n", + "\n", + " def eigen_value(w_n):\n", + " return (2 * correl_length_param) / (1 + (correl_length_param * w_n) ** 2)\n", + "\n", + " def sine_constant(w_n):\n", + " return 1 / (A - (math.sin(2 * w_n * A) / (2 * w_n))) ** 0.5\n", + "\n", + " # Build the array of eigenvalues and constant terms for the accuracy required\n", + " for n in range(1, 100):\n", + " # start solving here\n", + " acceptable_solution_error = 1e-10\n", + " solution_range = [(n - 0.5) * math.pi / A, n * math.pi / A]\n", + " solution = find_solution(func, deriv_func, acceptable_solution_error, solution_range)\n", + "\n", + " frequency_array.append(solution)\n", + " sine_eigen_values_array.append(eigen_value(solution))\n", + " sine_constants_array.append(sine_constant(solution))\n", + " if eigen_value(solution) < min_eigen_value:\n", + " break\n", + "\n", + " return (\n", + " np.array(frequency_array),\n", + " np.array(sine_eigen_values_array),\n", + " np.array(sine_constants_array),\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def stochastic_field_realization(\n", + " cosine_frequency_array: np.ndarray,\n", + " cosine_eigen_values: np.ndarray,\n", + " cosine_constants: np.ndarray,\n", + " cosine_random_variables_set: np.ndarray,\n", + " sine_frequency_array: np.ndarray,\n", + " sine_eigen_values: np.ndarray,\n", + " sine_constants: np.ndarray,\n", + " sine_random_variables_set: np.ndarray,\n", + " domain: Tuple[float, float],\n", + " evaluation_point: float,\n", + ") -> float:\n", + " \"\"\"The realization of the gaussian field f(x)\n", + "\n", + " Parameters\n", + " ----------\n", + " cosine_frequency_array : np.ndarray\n", + " Array of length P, containining frequencies associated with retained cosine terms\n", + " cosine_eigen_values : np.ndarray\n", + " Array of length P, containing eigenvalues associated with retained cosine terms\n", + " cosine_constants : np.ndarray\n", + " Array of length P, containing constants associated with retained cosine terms\n", + " cosine_random_variables_set : np.ndarray\n", + " Array of length P, containing random variable drawn from N(0,1) for the cosine terms\n", + " sine_frequency_array : np.ndarray\n", + " Array of length Q, containining frequencies associated with retained sine terms\n", + " sine_eigen_values : np.ndarray\n", + " Array of length Q, containing eigenvalues associated with retained sine terms\n", + " sine_constants : np.ndarray\n", + " Array of length Q, containing constants associated with retained sine terms\n", + " sine_random_variables_set : np.ndarray\n", + " Array of length P, containing random variable drawn from N(0,1) for the sine terms\n", + " domain : Tuple[float, float]\n", + " Domain over which the KL representation of the stochastic process should be found\n", + " evaluation_point : float\n", + " Point within the domain at which the value of a realization is required\n", + "\n", + " Returns\n", + " -------\n", + " float\n", + " The value of the realization at a given point within the domain\n", + " \"\"\"\n", + " # Shift parameter -> Because we had solved for terms in a symmetric domain [-A, A]\n", + " T = (domain[0] + domain[1]) / 2\n", + "\n", + " # Making use of array operation provided by the numpy package is much simpler for expressing the stochastic process\n", + " cosine_function_terms = (\n", + " np.sqrt(cosine_eigen_values)\n", + " * cosine_constants\n", + " * np.cos((evaluation_point - T) * cosine_frequency_array)\n", + " * cosine_random_variables_set\n", + " )\n", + "\n", + " sine_function_terms = (\n", + " np.sqrt(sine_eigen_values)\n", + " * sine_constants\n", + " * np.sin((evaluation_point - T) * sine_frequency_array)\n", + " * sine_random_variables_set\n", + " )\n", + "\n", + " return np.sum(cosine_function_terms) + np.sum(sine_function_terms)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "def young_modulus_realization(\n", + " cosine_frequency_list,\n", + " cosine_eigen_values,\n", + " cosine_constants,\n", + " cosine_random_variables_set,\n", + " sine_frequency_list,\n", + " sine_eigen_values,\n", + " sine_constants,\n", + " sine_random_variables_set,\n", + " domain,\n", + " evaluation_point,\n", + "):\n", + " return 1e5 * (\n", + " 1\n", + " + 0.1\n", + " * stochastic_field_realization(\n", + " cosine_frequency_list,\n", + " cosine_eigen_values,\n", + " cosine_constants,\n", + " cosine_random_variables_set,\n", + " sine_frequency_list,\n", + " sine_eigen_values,\n", + " sine_constants,\n", + " sine_random_variables_set,\n", + " domain,\n", + " evaluation_point,\n", + " )\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# Generation of K-L expansion parameters\n", + "import matplotlib.pyplot as plt\n", + "\n", + "domain = (0, 4)\n", + "correl_length_param = 3\n", + "min_eigen_value = 0.001\n", + "\n", + "cosine_frequency_array, cosine_eigen_values, cosine_constants = evaluate_KL_cosine_terms(\n", + " domain, correl_length_param, min_eigen_value\n", + ")\n", + "sine_frequency_array, sine_eigen_values, sine_constants = evaluate_KL_sine_terms(\n", + " domain, correl_length_param, min_eigen_value\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "

" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Now let's see how some realizations looks like\n", + "no_of_realizations = 10\n", + "x = np.linspace(domain[0], domain[1], 101)\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel(r\"$x \\: (m)$\")\n", + "ax.set_ylabel(r\"Realizations of $E$\")\n", + "ax.grid(True)\n", + "fig.set_size_inches(15, 8)\n", + "ax.set_xlim(domain[0], domain[1])\n", + "\n", + "for i in range(no_of_realizations):\n", + " cosine_random_variables_set = np.random.normal(0, 1, size=len(cosine_frequency_array))\n", + " sine_random_variables_set = np.random.normal(0, 1, size=len(sine_frequency_array))\n", + " \n", + " realization = np.array(\n", + " [\n", + " young_modulus_realization(\n", + " cosine_frequency_array,\n", + " cosine_eigen_values,\n", + " cosine_constants,\n", + " cosine_random_variables_set,\n", + " sine_frequency_array,\n", + " sine_eigen_values,\n", + " sine_constants,\n", + " sine_random_variables_set,\n", + " domain,\n", + " evaluation_point,\n", + " )\n", + " for evaluation_point in x\n", + " ]\n", + " )\n", + " ax.plot(x, realization)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "# Verification that the above implementation indeed represents the young's modulus\n", + "no_of_realizations = 5000\n", + "x = np.linspace(domain[0], domain[1], 101)\n", + "realization_collection = np.zeros((no_of_realizations, len(x)))\n", + "\n", + "for i in range(no_of_realizations):\n", + " cosine_random_variables_set = np.random.normal(0, 1, size=len(cosine_frequency_array))\n", + " sine_random_variables_set = np.random.normal(0, 1, size=len(sine_frequency_array))\n", + "\n", + " realization = np.array(\n", + " [\n", + " young_modulus_realization(\n", + " cosine_frequency_array,\n", + " cosine_eigen_values,\n", + " cosine_constants,\n", + " cosine_random_variables_set,\n", + " sine_frequency_array,\n", + " sine_eigen_values,\n", + " sine_constants,\n", + " sine_random_variables_set,\n", + " domain,\n", + " evaluation_point,\n", + " )\n", + " for evaluation_point in x\n", + " ]\n", + " )\n", + "\n", + " realization_collection[i:] = realization\n", + "\n", + "ensemble_mean_with_realization = np.zeros(realization_collection.shape[0])\n", + "ensemble_var_with_realization = np.zeros(realization_collection.shape[0])\n", + "for i in range(realization_collection.shape[0]):\n", + " ensemble_mean_with_realization[i] = np.mean(realization_collection[:i+1, :])\n", + " ensemble_var_with_realization[i] = np.var(realization_collection[:i+1, :])" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plot of ensemble mean\n", + "fig, ax = plt.subplots()\n", + "fig.set_size_inches(15, 8)\n", + "ax.plot(ensemble_mean_with_realization, label='Computed mean')\n", + "ax.axhline(y=1e5, color='r', linestyle='dashed', label='Actual mean')\n", + "plt.xlabel(\"No of realizations\")\n", + "plt.ylabel(r\"Ensemble mean of $E$\")\n", + "ax.grid(True)\n", + "ax.set_xlim(0, no_of_realizations)\n", + "ax.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plot of ensemble variance\n", + "fig, ax = plt.subplots()\n", + "fig.set_size_inches(15, 8)\n", + "ax.plot(ensemble_var_with_realization, label='Actual variance')\n", + "ax.axhline(y=1e8, color='r', linestyle='dashed', label='Computed variance')\n", + "plt.xlabel(\"No of realizations\")\n", + "plt.ylabel(r\"Ensemble varianc of $E$\")\n", + "ax.grid(True)\n", + "ax.set_xlim(0, no_of_realizations)\n", + "ax.legend()\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.7" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/doc/source/examples/extended_examples/sfem/sfem.py b/doc/source/examples/extended_examples/sfem/sfem.py index e69de29bb2d..7246d321174 100644 --- a/doc/source/examples/extended_examples/sfem/sfem.py +++ b/doc/source/examples/extended_examples/sfem/sfem.py @@ -0,0 +1,376 @@ +import math +import random +import numpy as np +from typing import Tuple, Callable + + +def find_solution( + func: Callable[[float], float], + derivative_func: Callable[[float], float], + acceptable_solution_error: float, + solution_range: Tuple[float, float], +) -> float: + """Find the solution of g(x) = 0 within solution range where g(x) is non-linear. + + Parameters + ---------- + func : Callable[float, float] + The function definition + derivative_func : Callable[float, float] + The derivative of the above function + acceptable_solution_error : float + Error at which the solution is acceptable + solution_range : Tuple[float, float] + The range within which the solution will be searched + + Returns + ------- + float + Solution to g(x) = 0 + """ + + current_guess = random.uniform(*solution_range) + iteration_counter = 1 + + while True: + if iteration_counter > 100: + iteration_counter = 1 + current_guess = random.uniform(*solution_range) + continue + + updated_guess = current_guess - func(current_guess) / derivative_func(current_guess) + error = abs(updated_guess - current_guess) + + if error < acceptable_solution_error and not ( + solution_range[0] < updated_guess < solution_range[1] + ): + current_guess = random.uniform(*solution_range) + continue + elif error < acceptable_solution_error and ( + solution_range[0] < updated_guess < solution_range[1] + ): + return updated_guess + + current_guess = updated_guess + iteration_counter += 1 + + +def evaluate_KL_cosine_terms( + domain: Tuple[float, float], correl_length_param: float, min_eigen_value: float +) -> Tuple[np.ndarray, np.ndarray, np.ndarray]: + """Build array of eigenvalues and constants of the cosine terms in the KL expansion of a gaussian stochastic process. + + Parameters + ---------- + domain : Tuple[float, float] + Domain over which the KL representation of the stochastic process should be found + correl_length_param : float + Correlation length parameter of the autocorrelation function of the process + min_eigen_value : float + Minimum eigenvalue to achieve require accuracy + + Returns + ------- + Tuple[np.ndarray, np.ndarray, np.ndarray] + Arrays of frequencies, eigenvalues, and constants of retained cosine terms (P in total) in the KL expansion + """ + + A = (domain[1] - domain[0]) / 2 # Symmetric domain parameter -> [-A, A] + + frequency_array = [] + cosine_eigen_values_array = [] + cosine_constants_array = [] + + # Define the functions related to the sine terms + def func(w_n): + return 1 / correl_length_param - w_n * math.tan(w_n * A) + + def deriv_func(w_n): + return -w_n * A / math.cos(w_n * correl_length_param) ** 2 - math.tan(w_n * A) + + def eigen_value(w_n): + return (2 * correl_length_param) / (1 + (correl_length_param * w_n) ** 2) + + def cosine_constant(w_n): + return 1 / (A + (math.sin(2 * w_n * A) / (2 * w_n))) ** 0.5 + + # Build the array of eigenvalues and constant terms for the accuracy required + for n in range(1, 100): + # start solving here + acceptable_solution_error = 1e-10 + solution_range = [(n - 1) * math.pi / A, (n - 0.5) * math.pi / A] + solution = find_solution(func, deriv_func, acceptable_solution_error, solution_range) + + frequency_array.append(solution) + cosine_eigen_values_array.append(eigen_value(solution)) + cosine_constants_array.append(cosine_constant(solution)) + if eigen_value(solution) < min_eigen_value: + break + + return ( + np.array(frequency_array), + np.array(cosine_eigen_values_array), + np.array(cosine_constants_array), + ) + + +def evaluate_KL_sine_terms( + domain: Tuple[float, float], correl_length_param: float, min_eigen_value: float +) -> Tuple[np.ndarray, np.ndarray, np.ndarray]: + """Build array of eigenvalues and constants of the sine terms in the KL expansion of a gaussian stochastic process. + + Parameters + ---------- + domain : Tuple[float, float] + Domain over which the KL representation of the stochastic process should be found + correl_length_param : float + Correlation length parameter of the autocorrelation function of the process + min_eigen_value : float + Minimum eigenvalue to achieve require accuracy + + Returns + ------- + Tuple[np.ndarray, np.ndarray, np.ndarray] + Arrays of frequencies, eigenvalues, and constants of retained sine terms (Q in total) in the KL expansion + """ + + A = (domain[1] - domain[0]) / 2 # Symmetric domain parameter -> [-A, A] + + frequency_array = [] + sine_eigen_values_array = [] + sine_constants_array = [] + + # Define functions related to the sine terms + def func(w_n): + return (1 / correl_length_param) * math.tan(w_n * A) + w_n + + def deriv_func(w_n): + return A / (correl_length_param * math.cos(w_n * A) ** 2) + 1 + + def eigen_value(w_n): + return (2 * correl_length_param) / (1 + (correl_length_param * w_n) ** 2) + + def sine_constant(w_n): + return 1 / (A - (math.sin(2 * w_n * A) / (2 * w_n))) ** 0.5 + + # Build the array of eigenvalues and constant terms for the accuracy required + for n in range(1, 100): + # start solving here + acceptable_solution_error = 1e-10 + solution_range = [(n - 0.5) * math.pi / A, n * math.pi / A] + solution = find_solution(func, deriv_func, acceptable_solution_error, solution_range) + + frequency_array.append(solution) + sine_eigen_values_array.append(eigen_value(solution)) + sine_constants_array.append(sine_constant(solution)) + if eigen_value(solution) < min_eigen_value: + break + + return ( + np.array(frequency_array), + np.array(sine_eigen_values_array), + np.array(sine_constants_array), + ) + + +def stochastic_field_realization( + cosine_frequency_array: np.ndarray, + cosine_eigen_values: np.ndarray, + cosine_constants: np.ndarray, + cosine_random_variables_set: np.ndarray, + sine_frequency_array: np.ndarray, + sine_eigen_values: np.ndarray, + sine_constants: np.ndarray, + sine_random_variables_set: np.ndarray, + domain: Tuple[float, float], + evaluation_point: float, +) -> float: + """The realization of the gaussian field f(x) + + Parameters + ---------- + cosine_frequency_array : np.ndarray + Array of length P, containining frequencies associated with retained cosine terms + cosine_eigen_values : np.ndarray + Array of length P, containing eigenvalues associated with retained cosine terms + cosine_constants : np.ndarray + Array of length P, containing constants associated with retained cosine terms + cosine_random_variables_set : np.ndarray + Array of length P, containing random variable drawn from N(0,1) for the cosine terms + sine_frequency_array : np.ndarray + Array of length Q, containining frequencies associated with retained sine terms + sine_eigen_values : np.ndarray + Array of length Q, containing eigenvalues associated with retained sine terms + sine_constants : np.ndarray + Array of length Q, containing constants associated with retained sine terms + sine_random_variables_set : np.ndarray + Array of length P, containing random variable drawn from N(0,1) for the sine terms + domain : Tuple[float, float] + Domain over which the KL representation of the stochastic process should be found + evaluation_point : float + Point within the domain at which the value of a realization is required + + Returns + ------- + float + The value of the realization at a given point within the domain + """ + # Shift parameter -> Because we had solved for terms in a symmetric domain [-A, A] + T = (domain[0] + domain[1]) / 2 + + # Making use of array operation provided by the numpy package is much simpler for expressing the stochastic process + cosine_function_terms = ( + np.sqrt(cosine_eigen_values) + * cosine_constants + * np.cos((evaluation_point - T) * cosine_frequency_array) + * cosine_random_variables_set + ) + + sine_function_terms = ( + np.sqrt(sine_eigen_values) + * sine_constants + * np.sin((evaluation_point - T) * sine_frequency_array) + * sine_random_variables_set + ) + + return np.sum(cosine_function_terms) + np.sum(sine_function_terms) + + +def young_modulus_realization( + cosine_frequency_list, + cosine_eigen_values, + cosine_constants, + cosine_random_variables_set, + sine_frequency_list, + sine_eigen_values, + sine_constants, + sine_random_variables_set, + domain, + evaluation_point, +): + return 1e5 * ( + 1 + + 0.1 + * stochastic_field_realization( + cosine_frequency_list, + cosine_eigen_values, + cosine_constants, + cosine_random_variables_set, + sine_frequency_list, + sine_eigen_values, + sine_constants, + sine_random_variables_set, + domain, + evaluation_point, + ) + ) + + +# Generation of K-L expansion parameters +import matplotlib.pyplot as plt + +domain = (0, 4) +correl_length_param = 3 +min_eigen_value = 0.001 + +cosine_frequency_array, cosine_eigen_values, cosine_constants = evaluate_KL_cosine_terms( + domain, correl_length_param, min_eigen_value +) +sine_frequency_array, sine_eigen_values, sine_constants = evaluate_KL_sine_terms( + domain, correl_length_param, min_eigen_value +) + +# Now let's see how some realizations looks like +no_of_realizations = 10 +x = np.linspace(domain[0], domain[1], 101) + +fig, ax = plt.subplots() +ax.set_xlabel(r"$x \: (m)$") +ax.set_ylabel(r"Realizations of $E$") +ax.grid(True) +fig.set_size_inches(15, 8) +ax.set_xlim(domain[0], domain[1]) + +for i in range(no_of_realizations): + cosine_random_variables_set = np.random.normal(0, 1, size=len(cosine_frequency_array)) + sine_random_variables_set = np.random.normal(0, 1, size=len(sine_frequency_array)) + + realization = np.array( + [ + young_modulus_realization( + cosine_frequency_array, + cosine_eigen_values, + cosine_constants, + cosine_random_variables_set, + sine_frequency_array, + sine_eigen_values, + sine_constants, + sine_random_variables_set, + domain, + evaluation_point, + ) + for evaluation_point in x + ] + ) + ax.plot(x, realization) + +plt.show() + +# Verification that the above implementation indeed represents the young's modulus +no_of_realizations = 5000 +x = np.linspace(domain[0], domain[1], 101) +realization_collection = np.zeros((no_of_realizations, len(x))) + +for i in range(no_of_realizations): + cosine_random_variables_set = np.random.normal(0, 1, size=len(cosine_frequency_array)) + sine_random_variables_set = np.random.normal(0, 1, size=len(sine_frequency_array)) + + realization = np.array( + [ + young_modulus_realization( + cosine_frequency_array, + cosine_eigen_values, + cosine_constants, + cosine_random_variables_set, + sine_frequency_array, + sine_eigen_values, + sine_constants, + sine_random_variables_set, + domain, + evaluation_point, + ) + for evaluation_point in x + ] + ) + + realization_collection[i:] = realization + +ensemble_mean_with_realization = np.zeros(realization_collection.shape[0]) +ensemble_var_with_realization = np.zeros(realization_collection.shape[0]) +for i in range(realization_collection.shape[0]): + ensemble_mean_with_realization[i] = np.mean(realization_collection[:i+1, :]) + ensemble_var_with_realization[i] = np.var(realization_collection[:i+1, :]) + +# Plot of ensemble mean +fig, ax = plt.subplots() +fig.set_size_inches(15, 8) +ax.plot(ensemble_mean_with_realization, label='Computed mean') +ax.axhline(y=1e5, color='r', linestyle='dashed', label='Actual mean') +plt.xlabel("No of realizations") +plt.ylabel(r"Ensemble mean of $E$") +ax.grid(True) +ax.set_xlim(0, no_of_realizations) +ax.legend() +plt.show() + +# Plot of ensemble variance +fig, ax = plt.subplots() +fig.set_size_inches(15, 8) +ax.plot(ensemble_var_with_realization, label='Actual variance') +ax.axhline(y=1e8, color='r', linestyle='dashed', label='Computed variance') +plt.xlabel("No of realizations") +plt.ylabel(r"Ensemble varianc of $E$") +ax.grid(True) +ax.set_xlim(0, no_of_realizations) +ax.legend() +plt.show() \ No newline at end of file diff --git a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst index 306a83db42d..1eb6a30ef67 100644 --- a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst +++ b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst @@ -99,7 +99,7 @@ realization/sample function assigned to each outcome of an experiment. .. figure:: realizations.png - A random field as a collection of random variables or realizations + A random field :math:`E(x)` viewed as a collection of random variables or as realizations .. note:: The concepts above generalize to more dimensions, for example, a random vector instead of a random @@ -124,24 +124,37 @@ For a zero-mean stationary Gaussian process, :math:`X(t)`, with covariance funct the K-L series expansion is given by: .. math:: X(t) = \sum_{n=1}^\infty \sqrt{\lambda_{c,n}}\cdot\varphi_{c,n}(t)\cdot\xi_{c,n} + \sum_{n=1}^\infty \sqrt{\lambda_{s,n}}\cdot\varphi_{s,n}(t)\cdot\xi_{s,n},\quad t\in\mathbb{D} + :label: K-L expansion where, -.. math:: \lambda_{c,n} = \frac{2b}{1+\omega_{c,n}^2\cdot b^2},\quad \varphi_{c,n}(t) = k_{c,n}\cos(\omega_{c,n}\cdot t) -.. math:: k_{c,n} = \frac{1}{\sqrt{a+\frac{\sin(2\omega_{c,n}\cdot a)}{2\omega_{c,n}}}} +.. math:: + :label: cosine terms + + \lambda_{c,n} = \frac{2b}{1+\omega_{c,n}^2\cdot b^2},\quad \varphi_{c,n}(t) = k_{c,n}\cos(\omega_{c,n}\cdot t) + + k_{c,n} = \frac{1}{\sqrt{a+\frac{\sin(2\omega_{c,n}\cdot a)}{2\omega_{c,n}}}} where :math:`\omega_{c,n}` is obtained as the solution of .. math:: \frac{1}{b} - \omega_{c,n}\cdot\tan(\omega_{c,n}\cdot a) = 0 \quad \text{in the range} \quad \biggl[(n-1)\frac{\pi}{a}, (n-\frac{1}{2})\frac{\pi}{a}\biggr] + :label: cosine equation and, -.. math:: \lambda_{s,n} = \frac{2b}{1+\omega_{s,n}^2\cdot b^2},\quad \varphi_{s,n}(t) = k_{s,n}\sin(\omega_{s,n}\cdot t) -.. math:: k_{s,n} = \frac{1}{\sqrt{a-\frac{\sin(2\omega_{s,n}\cdot a)}{2\omega_{s,n}}}} +.. math:: + :label: sine terms + + \lambda_{s,n} = \frac{2b}{1+\omega_{s,n}^2\cdot b^2},\quad \varphi_{s,n}(t) = k_{s,n}\sin(\omega_{s,n}\cdot t) + + k_{s,n} = \frac{1}{\sqrt{a-\frac{\sin(2\omega_{s,n}\cdot a)}{2\omega_{s,n}}}} where :math:`\omega_{s,n}` is obtained as the solution of .. math:: \frac{1}{b}\cdot\tan(\omega_{s,n}\cdot a) + \omega_{s,n} = 0 \quad \text{in the range} \quad \biggl[(n-\frac{1}{2})\frac{\pi}{a}, n\frac{\pi}{a}\biggr] + :label: sine equation + +It is worth mentioning that :math:`\lambda` and :math:`\omega` in the series expansion are referred to as eigenvalue and frequency respectively. .. note:: In the case of an asymmetric domain e.g. :math:`\mathbb{D}=[-t_{min},t_{max}]`, a shift parameter :math:`T = (t_{min}+t_{max})/2` is required and the corresponding @@ -159,18 +172,22 @@ that :math:`\lambda_{c,n}` and :math:`\lambda_{s,n}` converge to zero fast (in t this means that the infinite series of the K-L expansion above is truncated after a finite number of terms, giving the approximation: .. math:: X(t) \approx \hat{X}(t) = \sum_{n=1}^P \sqrt{\lambda_{c,n}}\cdot\varphi_{c,n}(t)\cdot\xi_{c,n} + \sum_{n=1}^Q \sqrt{\lambda_{s,n}}\cdot\varphi_{s,n}(t)\cdot\xi_{s,n} + :label: approximation -The equation above is computationally feasible to handle. Let's summarize how it can be used to generate realizations of :math:`X(t)`. +Equation :math:numref:`approximation` is computationally feasible to handle. Let's summarize how it can be used to generate realizations of :math:`X(t)`: 1. To generate the j-th realization, we draw a random value for each :math:`\xi_{c,n}, n=1,\dots ,P, \quad \xi_{s,n}, n=1,\dots ,Q` from the standard normal distribution :math:`\mathcal{N}(0,1)` and obtain :math:`\xi_{c,1}^j,\dots ,\xi_{c,P}^j, \quad \xi_{s,1}^j,\dots ,\xi_{s,P}^j` -2. We insert these values into the equation in other to obtain the j-th realization: +2. We insert these values into equation :math:numref:`approximation` in other to obtain the j-th realization: .. math:: \hat{X}^j(t) = \sum_{n=1}^P \sqrt{\lambda_{c,n}}\cdot\varphi_{c,n}(t)\cdot\xi_{c,n}^j + \sum_{n=1}^Q \sqrt{\lambda_{s,n}}\cdot\varphi_{s,n}(t)\cdot\xi_{s,n}^j 3. To generate additional realizations, we simply draw new random values for :math:`\xi_{c,n}, n=1,\dots ,P, \quad \xi_{s,n}, n=1,\dots ,Q` each from :math:`\mathcal{N}(0,1)` +.. note:: + In this case of a field, the same discussion above applies as the only difference is a change in notation (e.g. :math:`t` to :math:`x`). + The Monte Carlo simulation -------------------------- For linear static problems in the context of FEM, the system equations which must be solved change from @@ -215,8 +232,115 @@ We are to do the following: Carlo simulation to the probability density function of the response :math:`u`, at the bottom right corner of the cantilever. -2. If :math:`u` must not exceed :math:`0.2 \thickspace m`, how confident can we be of this requirement? +2. If :math:`u` must not exceed :math:`0.2 \: m`, how confident can we be of this requirement? + +.. note:: + This example really emphasizes how PyMAPDL can help to supercharge workflows. At a very high level, what will be done + in subsequent sections involves using python libraries to handle computations related to the stochasticity of the problem, and + using MAPDL to run the necessary simulations, all within the comfort of a python environment. + +Evaluating the young modulus +~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +Firstly, we implement code that allows us to represent the zero-mean Gaussian field :math:`f`. This simply means solving +:math:numref:`cosine equation` and :math:numref:`sine equation`, then substituting calculated values into +:math:numref:`cosine terms` and :math:numref:`sine terms` to obtain the constant terms in those equations. The +number of retained terms :math:`P` and :math:`Q` in :math:numref:`approximation` can be automatically determined +by structuring our code to stop computing values when :math:`\lambda_{c,n}, \lambda_{s,n}` become lower than +our desired accuracy level. The implementation is as follows: + +.. literalinclude:: sfem.py + :language: python + :lines: 1-173 + +The next step is to put this all together in a function that expresses :math:`f` using equation :math:numref:`approximation` +as follows: + +.. literalinclude:: sfem.py + :language: python + :lines: 176-236 + +And then the function for evaluating the young modulus itself is straight forward: + +.. literalinclude:: sfem.py + :language: python + :lines: 239-266 + +Realizations of the young modulus ++++++++++++++++++++++++++++++++++++++++++++++ +We can now generate sample realizations of the young's modulus to see how they look like: + +.. literalinclude:: sfem.py + :language: python + :lines: 269-317 + +.. figure:: young_modulus_realizations.png + + 10 realizations of the young's modulus depicting randomness from one realization to another + +Verification of the implementation +++++++++++++++++++++++++++++++++++ +Let us compute the theoretical mean and variance of the young modulus and then show that our implementation of the +young's modulus is correct. + +For the mean: + +.. math:: + :label: theoretical mean + + \mathbb{E}(E) = \mathbb{E}(10^5(1+0.10f)) + + \mathbb{E}(E) = 10^5(1 + 0.1\mathbb{E}(f)) + + \mathbb{E}(E) = 10^5(1 + 0.1(0)) = 10^5 \: kN/m^2 + + +For the variance: + +.. math:: + :label: theoretical variance + + Var(E) = \mathbb{E}(E^2) - [\mathbb{E}(E)]^2 + + Var(E) = \mathbb{E}[10^{10}(1 + 0.2f + 0.01f^2)] - 10^{10} + + Var(E) = 10^{10}[1 + 0.2\mathbb{E}(f) + 0.01\mathbb{E}(f^2)] - 10^{10} + + Var(E) = 10^{10}[0.2(0) + 0.01(1)] + + Var(E) = 10^8 \: {kN}^2/m^4 + +We should then expect that as the number of realizations increase indefinitely, the ensemble mean and +variance will converge towards theoretical values calculated in :math:numref:`theoretical mean` and :math:numref:`theoretical variance`: + +First we generate a lot of realizations, 5000 is enough i.e. the same as the number of simulations we are required to run later on. We then +perform some statistical processing on these realizations + +.. literalinclude:: sfem.py + :language: python + :lines: 319-352 + +We can then generate a plot of the mean vs the number of realizations + +.. literalinclude:: sfem.py + :language: python + :lines: 354-364 + +.. figure:: mean.png + + Convergence of the mean to the true value as the number of realizations is increased + +And also a plot of the variance vs the number of realizations + +.. literalinclude:: sfem.py + :language: python + :lines: 366-376 + +.. figure:: variance.png + + Convergence of the variance to the true value as the number of realizations is increased + +The plots above confirms that our implementation is indeed correct. If one desires more accuracy, the minimum eigenvalue +can be further decreased but the value already chosen is sufficient. -Evaluating -~~~~~~~~~~~~~~~~~~~~~~~~~~~ -Firstly, we implement code that allows us to represent the zero-mean field :math:`f`. +Running the simulations +~~~~~~~~~~~~~~~~~~~~~~~ \ No newline at end of file diff --git a/doc/source/examples/extended_examples/sfem/variance.png b/doc/source/examples/extended_examples/sfem/variance.png new file mode 100644 index 0000000000000000000000000000000000000000..498fb2333771516140a7490a5b81e985115270cd GIT binary patch literal 45468 zcmeGDbzIZkA3uzvUSa~50VoI9*A@!H5jR=C8Z`?~Hz!w5C;P{jy{+9n>|I?%1aI9G zyvcvr&ePM)LrO@<`F}?Uy1Ls6#kw21gR`7)duZfAL&IPJeI3e^&$XwaDLoETxU1`v zvWQ3c>rwVvR;ch{zjyx}KH+!m8Ncb>p$)qlf;!UOsdf@!ui-|L5@kGcy0D2>!oY z9)Y&4(OgM#0qE$M80(uC*0<);IjB+%dmAPZ7jE5~oSY1ciW;&`fam=9p_)!*{IhQF z?A)E8$LeTleYhJ!ONcWtll;(PYh^Y6F!rX}2?L#!Y_|6R|#oGoQ0!JG)Lq^+hF!Ox_^Cv)yEm=s5xAvbD~(F=mbhNbsB z<~j#vJCeP=F&fyd{%Rem_p9c#|Ni!hFiS*|m}C4U`cP$M<#jS<$zkg2>*u6D=LqJo zd@j8^(sOOJysWIh($T=$+L}jFa=6b09K<5-^ghjJ>IAHJ>RY(iOq@YMM#dfb(EHbv zBKwETgNpO=^7MU}{@%>UVa1vw6sO^`2jB=$JxcKKL?%?iB(D#e@EI*RGL_ae#W4}J% z6H%34RJ5)dZ=5Tbf{;qht&95ahOaBPH7>;_BsfktM~u`w$>ij@cI`f^gp01eemrtx zG5?~7&HPJNm+sv3z=Ah#P8XZi8;jU>_8XW7aKVzqos$NOj51r;{ZuiCrNM2=g4bGy zM4?K8Ad8HT8=suW->VeAhUrWqm;{WoR;F7d3tKfWCYU3QgegxculepPFG54xAKk3*{!2&Q%BF$|ZEbC_ zDJlG!?{2j&vmHikM%)jj=i%bYuEhM|uVC@V2m5=({(K!r#1Y$n4+XqIm!cjPQJ?5H!Fx;+Jz?T9$msP$9nX;t{%IXfKmqVUrvO?!L$w7TQV zjL?M{85vnb?cTc7&M?7|gzOe4tX1pT)S&$>eXjLSMRWXl{;AhUrfJ)YldEkC#yx@kUpJ$ z&8@{=!n*CeTB30FH8b(x}7E%sbrORexS^se>n~knWOMd(+n5 z4y`V6oXhNwMC5vp5-Y!XjoXKN_wK3dQE5`1Z>`N$do$CBh6J3q!~B$gS``6a`0?`b znP5)czJC$SVPU28p#y+sk&^Zf0UonIdPvpdB?tRdY|`x~kIS7|Strw?qdzV#I(=(y zPE)NuwE4cnrf+v^&1-*aP6v0^F64isKJrD5=yuzx8uvivxyb9LM{kFn;#;j8%GB=O zeHtAdt*fp5*)(XGN3kXo|6UqV;({TG2Y@?nIgR7uxp`Cb>C>ll@h1H7;yZVbEhGLn zw9tz|CaP9Kdv;37B}QiEYHx#Jo$I{3%CBF)j!=IyGPnUtkvu-yBUpE^zk{BMHxWgU zP1Taciz_ilpi;hr(PysW=H$G=$(hx2=d2wHJTw@9xP%057=Sg08TO|1e`}^I_=JRp z(q#Q)szro_AyoeM^=lpgM&xqSF|Xx`yY*|G($S;VRxWibiuIdQ;Vg3gHSX^2oUo>* zCIBx^adW@d%^klPx7#un(p&~la!%6I$8!QK;kk0uBhJ|oq1jjaD2G7`tg zr~lnb*nXtKzGd%cf4^@1^5;_xOS*i@FqoFNchxp^X?z5JXqWx}_X&w{e;w>T1yu=F z8k>}7UL~flph&+^^?Jueq#x|g(J8mxzC@2lE)*-PsOY%4eL_-* z+05qtJ&v*xc+VKYhRw&aYd=IlacMg_6+x5OYE$kz(%;`dPsJY81Nu3C;X)o6k6GxD z7+)Vf0LW+G7Rz(;)F~ZsdCxt{5TCp}_8aPi+x4q|UBR-4V1i1VzF*<4N3Chgzz~D{ zt|qu;eUw?fC*Es_P+UE>YTN?&C0j+XRzW9Mec&Y>YsI6c!*s0Ts?qC&-1GwQCUUW~ zB{ns+cyV!&$+fzuNL6CYCo^6UUJ%D;P@ojWo+RZ}05IKneUq=G=HAhxM~wlN*cw?_ zd;sbo7m(UR_jJ|w;2>4U*PL-xYC-#J>68}veJzf_%?}2c7pIsVmd5I#ON<5XICrGU;uijCrjr=WppFNb z3)QbjSGkUt1nn)DgMo?R1S{Y1^YascB0mk5zzcoXW_cte3=GVCt;5Y2CRD$9UH?

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associated documentation files (the "Software"), to deal +# in the Software without restriction, including without limitation the rights +# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +# copies of the Software, and to permit persons to whom the Software is +# furnished to do so, subject to the following conditions: +# +# The above copyright notice and this permission notice shall be included in all +# copies or substantial portions of the Software. +# +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +# SOFTWARE. + import math import random import numpy as np From 254bf2431a01fdd29bc075832c4db423919e91cd Mon Sep 17 00:00:00 2001 From: moe-ad Date: Fri, 17 Jan 2025 21:40:39 +0100 Subject: [PATCH 12/26] feat: more content --- .../examples/extended_examples/sfem/pdf.png | Bin 0 -> 36901 bytes .../extended_examples/sfem/sfem.ipynb | 1076 ++++++++++++++++- .../examples/extended_examples/sfem/sfem.py | 331 ++++- .../extended_examples/sfem/stochastic_fem.rst | 91 +- 4 files changed, 1443 insertions(+), 55 deletions(-) create mode 100644 doc/source/examples/extended_examples/sfem/pdf.png diff --git a/doc/source/examples/extended_examples/sfem/pdf.png b/doc/source/examples/extended_examples/sfem/pdf.png new file mode 100644 index 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "# Plot of ensemble mean\n", "fig, ax = plt.subplots()\n", @@ -435,20 +413,9 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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46VEoXvoTituiRYtSvV7BA7nmzZtH3bp1Y8GCBTW2L1iwICoqKjZ47PXXXx8jRoyIp59+Ojp16rTecaWlpVFaWrrW9rp16/qHEIpY/fr19SgUKf0JxU2PQvHSn1Cc0u7Lgr/UoaSkJLp06VLjhQxfv6ChR48e6z3u2muvjauuuirGjRsXXbt2TaNUAAAAAPjeCj5DLiJi8ODBMWDAgOjatWt069Ytfv/738fy5cvjtNNOi4iIU089NXbZZZcYPnx4RERcc801MXTo0HjggQeiTZs2MX/+V8+Ba9SoUTRq1Gijr5vLbf57AQAAAIANKYpArl+/fvHxxx/H0KFDY/78+bHffvvFuHHj8i96mDt3btSp8/+T+UaNGhWrV6+On//85zXOM2zYsLj88svTLB0AAAAANklRBHIREYMGDYpBgwatc19lZWWN73PmzNks18yZIgcAAABAygr+DDkAAAAAyBKBHAAAAACkKNOBnBWrAAAAAKRNIAcAAAAAKcp2IBcSOQAAAADSle1ATh4HAAAAQMoyHcgBAAAAQNoyHciZIAcAAABA2rIdyEnkAAAAAEhZpgM5AAAAAEhbpgM5M+QAAAAASFumAzkAAAAASFumAzkT5AAAAABIW7YDOWtWAQAAAEhZtgO5QhcAAAAAQOZkO5CTyAEAAACQskwHcgAAAACQtkwHcibIAQAAAJC2TAdy1qwCAAAAkLZMB3LiOAAAAADSlu1ATiIHAAAAQMoyHcgBAAAAQNoyHcjlLFoFAAAAIGXZDuTkcQAAAACkLNOBHAAAAACkLdOBnBlyAAAAAKQt04EcAAAAAKQt44GcKXIAAAAApCvTgZwlqwAAAACkLduBXKELAAAAACBzMh3IAQAAAEDaMh3ImSEHAAAAQNoyHsiJ5AAAAABIV7YDOXkcAAAAACnLdiBX6AIAAAAAyJxMB3IAAAAAkLZsB3LWrAIAAACQskwHcuI4AAAAANKW7UBOIgcAAABAyrIdyBW6AAAAAAAyJ9OBHAAAAACkLdOBXM6aVQAAAABSlu1ArtAFAAAAAJA52Q7kJHIAAAAApCzTgRwAAAAApE0gBwAAAAApynQg56UOAAAAAKQt24FcoQsAAAAAIHMyHciVb1+/0CUAAAAAkDGZDuS6tG5a6BIAAAAAyJhMB3IAAAAAkDaBHAAAAACkSCAHAAAAACkSyAEAAABAigRyAAAAAJAigRwAAAAApEggBwAAAAApEsgBAAAAQIoEcgAAAACQIoEcAAAAAKRIIAcAAAAAKRLIAQAAAECKBHIAAAAAkCKBHAAAAACkSCAHAAAAACkSyAEAAABAigRyAAAAAJAigRwAAAAApEggBwAAAAApEsgBAAAAQIoEcgAAAACQIoEcAAAAAKRIIAcAAAAAKRLIAQAAAECKBHIAAAAAkKJ6hS6gEJIkiYiIpUuXRv369QtcDfBtVVVVsWLFiliyZIkehSKjP6G46VEoXvoTitvSpUsj4v8zoy0tk4HcokWLIiJit912K3AlAAAAABSLRYsWRZMmTbb4dTIZyDVr1iwiIubOnZvKjwxsmiVLlkSrVq3iww8/jLKyskKXA3yD/oTipkeheOlPKG6ff/55tG7dOp8ZbWmZDOTq1Pnq0XlNmjTxDyEUsbKyMj0KRUp/QnHTo1C89CcUt68zoy1+nVSuAgAAAABEhEAOAAAAAFKVyUCutLQ0hg0bFqWlpYUuBVgHPQrFS39CcdOjULz0JxS3tHs0l6T1PlcAAAAAIJsz5AAAAACgUARyAAAAAJAigRwAAAAApEggBwAAAAApymQgd8stt0SbNm2iQYMG0b1793jppZcKXRJsc5599tk49thjY+edd45cLhePPvpojf1JksTQoUNjp512iu222y569+4ds2bNqjHm008/jf79+0dZWVmUl5fH6aefHsuWLasx5vXXX4+ePXtGgwYNolWrVnHttddu6VuDrd7w4cPjhz/8YTRu3DhatGgRxx13XMycObPGmJUrV8Z5550XO+ywQzRq1Ch+9rOfxYIFC2qMmTt3bhx99NHRsGHDaNGiRVxyySXx5Zdf1hhTWVkZBxxwQJSWlsaee+4ZY8aM2dK3B1u1UaNGRadOnaKsrCzKysqiR48e8de//jW/X29C8RgxYkTkcrm48MIL89v0KBTO5ZdfHrlcrsanffv2+f3F1p+ZC+QefPDBGDx4cAwbNiymT58enTt3jj59+sTChQsLXRpsU5YvXx6dO3eOW265ZZ37r7322rjxxhvj1ltvjalTp8b2228fffr0iZUrV+bH9O/fP/72t7/F+PHj4/HHH49nn302zjrrrPz+JUuWxOGHHx677rprTJs2La677rq4/PLL4/bbb9/i9wdbs0mTJsV5550XL774YowfPz6qqqri8MMPj+XLl+fH/Ou//mv85S9/iYceeigmTZoU//jHP+KEE07I71+zZk0cffTRsXr16njhhRfinnvuiTFjxsTQoUPzY2bPnh1HH310HHrooTFjxoy48MIL44wzzognn3wy1fuFrckPfvCDGDFiREybNi1eeeWV+MlPfhJ9+/aNv/3tbxGhN6FYvPzyy3HbbbdFp06damzXo1BY++yzT8ybNy//mTx5cn5f0fVnkjHdunVLzjvvvPz3NWvWJDvvvHMyfPjwAlYF27aISB555JH89+rq6qSioiK57rrr8tsWL16clJaWJn/4wx+SJEmSt956K4mI5OWXX86P+etf/5rkcrnko48+SpIkSf7rv/4radq0abJq1ar8mN/85jdJu3bttvAdwbZl4cKFSUQkkyZNSpLkq36sX79+8tBDD+XHvP3220lEJFOmTEmSJEmeeOKJpE6dOsn8+fPzY0aNGpWUlZXle/Lf/u3fkn322afGtfr165f06dNnS98SbFOaNm2a3HnnnXoTisTSpUuTtm3bJuPHj08OOeSQ5IILLkiSxN9PKLRhw4YlnTt3Xue+YuzPTM2QW716dUybNi169+6d31anTp3o3bt3TJkypYCVQbbMnj075s+fX6MXmzRpEt27d8/34pQpU6K8vDy6du2aH9O7d++oU6dOTJ06NT/m4IMPjpKSkvyYPn36xMyZM+Ozzz5L6W5g6/f5559HRESzZs0iImLatGlRVVVVo0fbt28frVu3rtGj++67b7Rs2TI/pk+fPrFkyZL8TJ4pU6bUOMfXY/zNhY2zZs2aGDt2bCxfvjx69OihN6FInHfeeXH00Uev1Ud6FApv1qxZsfPOO8fuu+8e/fv3j7lz50ZEcfZnpgK5Tz75JNasWVPjx42IaNmyZcyfP79AVUH2fN1vG+rF+fPnR4sWLWrsr1evXjRr1qzGmHWd45vXADasuro6LrzwwjjooIOiY8eOEfFV/5SUlER5eXmNsd/u0e/qv/WNWbJkSXzxxRdb4nZgm/DGG29Eo0aNorS0NM4555x45JFHokOHDnoTisDYsWNj+vTpMXz48LX26VEorO7du8eYMWNi3LhxMWrUqJg9e3b07Nkzli5dWpT9WW+TRgMA25Tzzjsv3nzzzRrP1wAKq127djFjxoz4/PPP409/+lMMGDAgJk2aVOiyIPM+/PDDuOCCC2L8+PHRoEGDQpcDfMuRRx6Z/+9OnTpF9+7dY9ddd40//vGPsd122xWwsnXL1Ay55s2bR926ddd6i8aCBQuioqKiQFVB9nzdbxvqxYqKirVetvLll1/Gp59+WmPMus7xzWsA6zdo0KB4/PHHY+LEifGDH/wgv72ioiJWr14dixcvrjH+2z36Xf23vjFlZWVF+X+KoFiUlJTEnnvuGV26dInhw4dH586d44YbbtCbUGDTpk2LhQsXxgEHHBD16tWLevXqxaRJk+LGG2+MevXqRcuWLfUoFJHy8vLYa6+94r333ivKv6GZCuRKSkqiS5cuMWHChPy26urqmDBhQvTo0aOAlUG27LbbblFRUVGjF5csWRJTp07N92KPHj1i8eLFMW3atPyYZ555Jqqrq6N79+75Mc8++2xUVVXlx4wfPz7atWsXTZs2TeluYOuTJEkMGjQoHnnkkXjmmWdit912q7G/S5cuUb9+/Ro9OnPmzJg7d26NHn3jjTdqBOfjx4+PsrKy6NChQ37MN8/x9Rh/c2HTVFdXx6pVq/QmFFivXr3ijTfeiBkzZuQ/Xbt2jf79++f/W49C8Vi2bFm8//77sdNOOxXn39BNfg3EVm7s2LFJaWlpMmbMmOStt95KzjrrrKS8vLzGWzSA72/p0qXJq6++mrz66qtJRCQjR45MXn311eSDDz5IkiRJRowYkZSXlyf/8z//k7z++utJ3759k9122y354osv8uc44ogjkv333z+ZOnVqMnny5KRt27bJSSedlN+/ePHipGXLlskpp5ySvPnmm8nYsWOThg0bJrfddlvq9wtbk1//+tdJkyZNksrKymTevHn5z4oVK/JjzjnnnKR169bJM888k7zyyitJjx49kh49euT3f/nll0nHjh2Tww8/PJkxY0Yybty4ZMcdd0yGDBmSH/P3v/89adiwYXLJJZckb7/9dnLLLbckdevWTcaNG5fq/cLW5NJLL00mTZqUzJ49O3n99deTSy+9NMnlcslTTz2VJInehGLzzbesJokehUK66KKLksrKymT27NnJ888/n/Tu3Ttp3rx5snDhwiRJiq8/MxfIJUmS3HTTTUnr1q2TkpKSpFu3bsmLL75Y6JJgmzNx4sQkItb6DBgwIEmSJKmurk4uu+yypGXLlklpaWnSq1evZObMmTXOsWjRouSkk05KGjVqlJSVlSWnnXZasnTp0hpjXnvtteRHP/pRUlpamuyyyy7JiBEj0rpF2GqtqzcjIhk9enR+zBdffJGce+65SdOmTZOGDRsmxx9/fDJv3rwa55kzZ05y5JFHJtttt13SvHnz5KKLLkqqqqpqjJk4cWKy3377JSUlJcnuu+9e4xrA2n71q18lu+66a1JSUpLsuOOOSa9evfJhXJLoTSg23w7k9CgUTr9+/ZKddtopKSkpSXbZZZekX79+yXvvvZffX2z9mUuSJNn0eXUAAAAAQG1k6hlyAAAAAFBoAjkAAAAASJFADgAAAABSJJADAAAAgBQJ5AAAAAAgRQI5AAAAAEiRQA4AAAAAUiSQAwAoMvPnz4/DDjsstt9++ygvL0/9+rlcLh599NGIiJgzZ07kcrmYMWPGFr3mj3/847jwwgu36DUAAIqFQA4A4FsGDhwYuVwuRowYUWP7o48+Grlcbotf/z//8z9j3rx5MWPGjHj33Xe3+PU2pFWrVjFv3rzo2LHjZjlfZWVl5HK5WLx4cY3tf/7zn+Oqq67aLNcAACh2AjkAgHVo0KBBXHPNNfHZZ5+lfu33338/unTpEm3bto0WLVps1DGrV6/eIrXUrVs3Kioqol69elvk/F9r1qxZNG7ceIteAwCgWAjkAADWoXfv3lFRURHDhw/f4LiHH3449tlnnygtLY02bdrE7373u+8896hRo2KPPfaIkpKSaNeuXdx33335fW3atImHH3447r333sjlcjFw4MB1nmPgwIFx3HHHxX/8x3/EzjvvHO3atYuIiA8//DBOPPHEKC8vj2bNmkXfvn1jzpw5+eNefvnlOOyww6J58+bRpEmTOOSQQ2L69OnrrfXbS1a/nj347U9lZWVERNx3333RtWvXaNy4cVRUVMQvf/nLWLhwYf5chx56aERENG3atMb9fXvJ6meffRannnpqNG3aNBo2bBhHHnlkzJo1K79/zJgxUV5eHk8++WTsvffe0ahRozjiiCNi3rx5+TGVlZXRrVu3/NLfgw46KD744IMN/m8DAJAGgRwAwDrUrVs3rr766rjpppvif//3f9c5Ztq0aXHiiSfGP//zP8cbb7wRl19+eVx22WUxZsyY9Z73kUceiQsuuCAuuuiiePPNN+Pss8+O0047LSZOnBgRXwVmRxxxRJx44okxb968uOGGG9Z7rgkTJsTMmTNj/Pjx8fjjj0dVVVX06dMnGjduHM8991w8//zz+aDq6xl0S5cujQEDBsTkyZPjxRdfjLZt28ZRRx0VS5cu3ajf5YYbboh58+blPxdccEG0aNEi2rdvHxERVVVVcdVVV8Vrr70Wjz76aMyZMycfurVq1SoefvjhiIiYOXPmBu9v4MCB8corr8Rjjz0WU6ZMiSRJ4qijjoqqqqr8mBUrVsT1118f9913Xzz77LMxd+7cuPjiiyMi4ssvv4zjjjsuDjnkkHj99ddjypQpcdZZZ6Wy5BgA4Lts2bUHAABbseOPPz7222+/GDZsWNx1111r7R85cmT06tUrLrvssoiI2GuvveKtt96K6667br0z266//voYOHBgnHvuuRERMXjw4HjxxRfj+uuvj0MPPTR23HHHKC0tje222y4qKio2WN/2228fd955Z5SUlERExH//939HdXV13HnnnfngafTo0VFeXh6VlZVx+OGHx09+8pMa57j99tujvLw8Jk2aFMccc8x3/iZNmjSJJk2aRMRXz3277bbb4umnn87X+qtf/So/dvfdd48bb7wxfvjDH8ayZcuiUaNG0axZs4iIaNGixXpfWDFr1qx47LHH4vnnn48DDzwwIiLuv//+aNWqVTz66KPxi1/8IiK+Cv9uvfXW2GOPPSIiYtCgQXHllVdGRMSSJUvi888/j2OOOSa/f++99/7O+wMASIMZcgAAG3DNNdfEPffcE2+//fZa+95+++046KCDamw76KCDYtasWbFmzZp1nm99x6zr/N9l3333zYdxERGvvfZavPfee9G4ceNo1KhRPgBbuXJlvP/++xERsWDBgjjzzDOjbdu20aRJkygrK4tly5bF3LlzN+nar776apxyyilx880317ifadOmxbHHHhutW7eOxo0bxyGHHBIRsUnnf/vtt6NevXrRvXv3/LYddtgh2rVrV+N3atiwYT5si4jYaaed8stjmzVrFgMHDow+ffrEsccem5/ZBwBQDARyAAAbcPDBB0efPn1iyJAhhS5lLdtvv32N78uWLYsuXbrEjBkzanzefffd+OUvfxkREQMGDIgZM2bEDTfcEC+88ELMmDEjdthhh016KcT8+fPjpz/9aZxxxhlx+umn57cvX748+vTpE2VlZXH//ffHyy+/HI888khEbJmXTtSvX7/G91wuF0mS5L+PHj06pkyZEgceeGA8+OCDsddee8WLL7642esAANhUAjkAgO8wYsSI+Mtf/hJTpkypsX3vvfeO559/vsa2559/Pvbaa6+oW7fuOs+1vmM6dOjwves84IADYtasWdGiRYvYc889a3y+Xmb6/PPPx/nnnx9HHXVU/mUUn3zyyUZfY+XKldG3b99o3759jBw5ssa+d955JxYtWhQjRoyInj17Rvv27fMz1r729Yy+9c0gjPjqN/ryyy9j6tSp+W2LFi2KmTNnbvLvtP/++8eQIUPihRdeiI4dO8YDDzywSccDAGwJAjkAgO+w7777Rv/+/ePGG2+ssf2iiy6KCRMmxFVXXRXvvvtu3HPPPXHzzTfnXyywLpdcckmMGTMmRo0aFbNmzYqRI0fGn//85w0es7H69+8fzZs3j759+8Zzzz0Xs2fPjsrKyjj//PPzL6Zo27Zt3HffffH222/H1KlTo3///rHddttt9DXOPvvs+PDDD+PGG2+Mjz/+OObPnx/z58+P1atXR+vWraOkpCRuuumm+Pvf/x6PPfZYXHXVVTWO33XXXSOXy8Xjjz8eH3/8cSxbtmyta7Rt2zb69u0bZ555ZkyePDlee+21OPnkk2OXXXaJvn37blSds2fPjiFDhsSUKVPigw8+iKeeeipmzZrlOXIAQFEQyAEAbIQrr7wyqqura2w74IAD4o9//GOMHTs2OnbsGEOHDo0rr7xyvS90iIg47rjj4oYbbojrr78+9tlnn7jtttti9OjR8eMf//h719iwYcN49tlno3Xr1nHCCSfE3nvvHaeffnqsXLkyysrKIiLirrvuis8++ywOOOCAOOWUU+L888+PFi1abPQ1Jk2aFPPmzYsOHTrETjvtlP+88MILseOOO8aYMWPioYceig4dOsSIESPi+uuvr3H8LrvsEldccUVceuml0bJlyxg0aNA6rzN69Ojo0qVLHHPMMdGjR49IkiSeeOKJtZapbui3eOedd+JnP/tZ7LXXXnHWWWfFeeedF2efffZG3ysAwJaSS775oA0AAAAAYIsyQw4AAAAAUiSQAwAAAIAUCeQAAAAAIEUCOQAAAABIkUAOAAAAAFIkkAMAAACAFAnkAAAAACBFAjkAAAAASJFADgAAAABSJJADAAAAgBQJ5AAAAAAgRQI5AAAAAEjR/wGHdaz7S/WASgAAAABJRU5ErkJggg==", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "# Plot of ensemble variance\n", "fig, ax = plt.subplots()\n", @@ -462,6 +429,1035 @@ "ax.legend()\n", "plt.show()" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Function for running the simulations\n", + "def run_simulations(\n", + " length: float, height: float, thickness: float, mesh_size: float, no_of_simulations: int\n", + ") -> np.ndarray:\n", + " \"\"\"Run desired number of simulations to obtain response data.\n", + "\n", + " Parameters\n", + " ----------\n", + " length : float\n", + " The length of the cantilever structure\n", + " height : float\n", + " The height of the cantilever structure\n", + " thickness : float\n", + " The thickness of the cantilever structure\n", + " mesh_size : float\n", + " The desired mesh size\n", + " no_of_simulations : int\n", + " The number of simulations to run\n", + "\n", + " Returns\n", + " -------\n", + " np.ndarray\n", + " Array containing simulation results.\n", + " \"\"\"\n", + "\n", + " from pathlib import Path\n", + " from ansys.mapdl.core import launch_mapdl\n", + "\n", + " path = Path.cwd()\n", + " mapdl = launch_mapdl(run_location=path)\n", + "\n", + " domain = [0, length]\n", + " correl_length_param = 3\n", + " min_eigen_value = 0.001\n", + " poisson_ratio = 0.3\n", + "\n", + " mapdl.prep7() # Enter preprocessor\n", + "\n", + " mapdl.r(r1=thickness)\n", + " mapdl.et(1, \"PLANE182\", kop3=3, kop6=0)\n", + " mapdl.rectng(0, length, 0, height)\n", + " mapdl.mshkey(1)\n", + " mapdl.mshape(0, \"2D\")\n", + " mapdl.esize(mesh_size)\n", + " mapdl.amesh(\"ALL\")\n", + "\n", + " # Fixed edge\n", + " mapdl.nsel(\"S\", \"LOC\", \"X\", 0)\n", + " mapdl.cm(\"FIXED_END\", \"NODE\")\n", + "\n", + " # Load application node\n", + " mapdl.nsel(\"S\", \"LOC\", \"X\", length)\n", + " mapdl.nsel(\"R\", \"LOC\", \"Y\", height)\n", + " mapdl.cm(\"LOAD_APPLICATION_POINT\", \"NODE\")\n", + "\n", + " mapdl.finish() # Exit preprocessor\n", + "\n", + " mapdl.slashsolu() # Enter solution processor\n", + "\n", + " element_ids = mapdl.esel(\n", + " \"S\", \"CENT\", \"Y\", 0, mesh_size\n", + " ) # Select bottom row elements and store the ids\n", + "\n", + " # Generate quantities required to define the young's modulus stochastic process\n", + " cosine_frequency_list, cosine_eigen_values, cosine_constants = evaluate_KL_cosine_terms(\n", + " domain, correl_length_param, min_eigen_value\n", + " )\n", + " sine_frequency_list, sine_eigen_values, sine_constants = evaluate_KL_sine_terms(\n", + " domain, correl_length_param, min_eigen_value\n", + " )\n", + "\n", + " simulation_results = np.zeros(no_of_simulations)\n", + "\n", + " for simulation in range(no_of_simulations):\n", + " # Generate random variables and load needed for one realization of the process\n", + " cosine_random_variables_set = np.random.normal(0, 1, size=len(cosine_frequency_list))\n", + " sine_random_variables_set = np.random.normal(0, 1, size=len(sine_frequency_list))\n", + " load = -np.random.normal(10, 2**0.5) # Generate a random load\n", + "\n", + " material_property = 0 # Initialize material property ID\n", + " for element_id in element_ids:\n", + " material_property += 1\n", + " mapdl.get(\"ELEMENT_ID\", \"ELEM\", element_id, \"CENT\", \"X\")\n", + " element_centroid_x_coord = mapdl.parameters[\"ELEMENT_ID\"]\n", + " mapdl.esel(\n", + " \"S\", \"CENT\", \"X\", element_centroid_x_coord\n", + " ) # Select all elements having this coordinate as centroid\n", + "\n", + " # Evaluate young's modulus at this material point\n", + " young_modulus_value = young_modulus_realization(\n", + " cosine_frequency_list,\n", + " cosine_eigen_values,\n", + " cosine_constants,\n", + " cosine_random_variables_set,\n", + " sine_frequency_list,\n", + " sine_eigen_values,\n", + " sine_constants,\n", + " sine_random_variables_set,\n", + " domain,\n", + " element_centroid_x_coord,\n", + " )\n", + "\n", + " mapdl.mp(\n", + " \"EX\", f\"{material_property}\", young_modulus_value\n", + " ) # Define property ID, assign young's modulus\n", + " mapdl.mp(\"NUXY\", f\"{material_property}\", poisson_ratio) # Assign poisson ratio\n", + " mapdl.mpchg(material_property, \"ALL\") # Assign property to selected elements\n", + "\n", + " mapdl.allsel()\n", + "\n", + " mapdl.d(\"FIXED_END\", lab=\"UX\", value=0, lab2=\"UY\") # Apply fixed end BC\n", + " mapdl.f(\"LOAD_APPLICATION_POINT\", lab=\"FY\", value=load) # Apply load BC\n", + " mapdl.solve()\n", + "\n", + " # Displacement probe point - where Uy results will be extracted\n", + " mapdl.nsel(\"S\", \"LOC\", \"X\", 4)\n", + " displacement_probe_point = mapdl.nsel(\"R\", \"LOC\", \"Y\", 0)\n", + " displacement = mapdl.get(\n", + " \"DISP_AT_PROBE_POINT\", \"NODE\", int(displacement_probe_point[0]), \"U\", \"Y\"\n", + " )\n", + "\n", + " simulation_results[simulation] = displacement\n", + "\n", + " mapdl.mpdele(\"ALL\", \"ALL\")\n", + " if int((simulation + 1) % 10) == 0:\n", + " print(f\"Completed {simulation + 1} simulations ...\")\n", + "\n", + " mapdl.exit()\n", + " print()\n", + " print(\"All simulations completed!\")\n", + "\n", + " return simulation_results" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "simulation_results = run_simulations(4, 1, 0.2, 0.1, 5000)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Perform statistical post processing and plot the pdf\n", + "import scipy.stats as stats\n", + "\n", + "kde = stats.gaussian_kde(simulation_results) # Kernel density estimate\n", + "\n", + "fig, ax = plt.subplots()\n", + "fig.set_size_inches(15, 8)\n", + "x_eval = np.linspace(min(simulation_results), max(simulation_results), num=200)\n", + "ax.plot(x_eval, kde.evaluate(x_eval), 'r-')\n", + "plt.xlabel(\"Displacement in (m)\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# We can then proceed to evaluate the probability that response u is less than 0.2 m\n", + "probability = kde.integrate_box_1d(-0.2, x_eval[-1])\n", + "print(f\"The probability that u is less than 0.2 m is {probability:.0%}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# Multi-threaded approach\n", + "# Note, no of instances should not be more than the number of available CPU cores on your PC\n", + "def run_simulations_threaded(\n", + " mapdl, length, height, thickness, mesh_size, no_of_simulations, instance_identifier\n", + "):\n", + " domain = [0, length]\n", + " correl_length_param = 3\n", + " min_eigen_value = 0.001\n", + " poisson_ratio = 0.3\n", + "\n", + " mapdl.prep7() # Enter preprocessor\n", + "\n", + " mapdl.r(r1=thickness)\n", + " mapdl.et(1, \"PLANE182\", kop3=3, kop6=0)\n", + " mapdl.rectng(0, length, 0, height)\n", + " mapdl.mshkey(1)\n", + " mapdl.mshape(0, \"2D\")\n", + " mapdl.esize(mesh_size)\n", + " mapdl.amesh(\"ALL\")\n", + "\n", + " # Fixed edge\n", + " mapdl.nsel(\"S\", \"LOC\", \"X\", 0)\n", + " mapdl.cm(\"FIXED_END\", \"NODE\")\n", + "\n", + " # Load application node\n", + " mapdl.nsel(\"S\", \"LOC\", \"X\", length)\n", + " mapdl.nsel(\"R\", \"LOC\", \"Y\", height)\n", + " mapdl.cm(\"LOAD_APPLICATION_POINT\", \"NODE\")\n", + "\n", + " mapdl.finish() # Exit preprocessor\n", + "\n", + " mapdl.slashsolu() # Enter solution processor\n", + "\n", + " element_ids = mapdl.esel(\n", + " \"S\", \"CENT\", \"Y\", 0, mesh_size\n", + " ) # Select bottom row elements and store the ids\n", + "\n", + " # Generate quantities required to define the young's modulus stochastic process\n", + " cosine_frequency_list, cosine_eigen_values, cosine_constants = evaluate_KL_cosine_terms(\n", + " domain, correl_length_param, min_eigen_value\n", + " )\n", + " sine_frequency_list, sine_eigen_values, sine_constants = evaluate_KL_sine_terms(\n", + " domain, correl_length_param, min_eigen_value\n", + " )\n", + "\n", + " simulation_results = np.zeros(no_of_simulations)\n", + "\n", + " for simulation in range(no_of_simulations):\n", + " # Generate random variables and load needed for one realization of the process\n", + " cosine_random_variables_set = np.random.normal(0, 1, size=len(cosine_frequency_list))\n", + " sine_random_variables_set = np.random.normal(0, 1, size=len(sine_frequency_list))\n", + " load = -np.random.normal(10, 2**0.5) # Generate a random load\n", + "\n", + " material_property = 0 # Initialize material property ID\n", + " for element_id in element_ids:\n", + " material_property += 1\n", + " mapdl.get(\"ELEMENT_ID\", \"ELEM\", element_id, \"CENT\", \"X\")\n", + " element_centroid_x_coord = mapdl.parameters[\"ELEMENT_ID\"]\n", + " mapdl.esel(\n", + " \"S\", \"CENT\", \"X\", element_centroid_x_coord\n", + " ) # Select all elements having this coordinate as centroid\n", + "\n", + " # Evaluate young's modulus at this material point\n", + " young_modulus_value = young_modulus_realization(\n", + " cosine_frequency_list,\n", + " cosine_eigen_values,\n", + " cosine_constants,\n", + " cosine_random_variables_set,\n", + " sine_frequency_list,\n", + " sine_eigen_values,\n", + " sine_constants,\n", + " sine_random_variables_set,\n", + " domain,\n", + " element_centroid_x_coord,\n", + " )\n", + "\n", + " mapdl.mp(\n", + " \"EX\", f\"{material_property}\", young_modulus_value\n", + " ) # Define property ID, assign young's modulus\n", + " mapdl.mp(\"NUXY\", f\"{material_property}\", poisson_ratio) # Assign poisson ratio\n", + " mapdl.mpchg(material_property, \"ALL\") # Assign property to selected elements\n", + "\n", + " mapdl.allsel()\n", + "\n", + " mapdl.d(\"FIXED_END\", lab=\"UX\", value=0, lab2=\"UY\") # Apply fixed end BC\n", + " mapdl.f(\"LOAD_APPLICATION_POINT\", lab=\"FY\", value=load) # Apply load BC\n", + " mapdl.solve()\n", + "\n", + " # Displacement probe point - where Uy results will be extracted\n", + " mapdl.nsel(\"S\", \"LOC\", \"X\", 4)\n", + " displacement_probe_point = mapdl.nsel(\"R\", \"LOC\", \"Y\", 0)\n", + " displacement = mapdl.get(\n", + " \"DISP_AT_PROBE_POINT\", \"NODE\", int(displacement_probe_point[0]), \"U\", \"Y\"\n", + " )\n", + "\n", + " simulation_results[simulation] = displacement\n", + "\n", + " mapdl.mpdele(\"ALL\", \"ALL\")\n", + " if int((simulation + 1) % 10) == 0:\n", + " print(f\"Completed {simulation + 1} simulations in instance {instance_identifier} ...\")\n", + "\n", + " mapdl.exit()\n", + " print()\n", + " print(f\"All simulations completed in instance {instance_identifier}!\")\n", + "\n", + " return instance_identifier, no_of_simulations, simulation_results\n", + "\n", + "\n", + "def run_simulations_over_multple_instances(\n", + " length, height, thickness, mesh_size, no_of_simulations, no_of_instances\n", + "):\n", + " from pathlib import Path\n", + " from ansys.mapdl.core import MapdlPool\n", + "\n", + " # First determine the number of simulations to run per instance\n", + " if no_of_simulations % no_of_instances == 0:\n", + " # Simlations can be split equally across instances\n", + " simulations_per_instance = no_of_simulations // no_of_instances\n", + " simulations_per_instance_list = [simulations_per_instance for i in range(no_of_instances)]\n", + " else:\n", + " # Simulations can not be split equally across instances\n", + " simulations_per_instance = no_of_simulations // no_of_instances\n", + " simulations_per_instance_list = [\n", + " simulations_per_instance for i in range(no_of_instances - 1)\n", + " ]\n", + " remaining_simulations = no_of_simulations - sum(simulations_per_instance_list)\n", + " simulations_per_instance_list.append(remaining_simulations)\n", + "\n", + " path = Path.cwd()\n", + " pool = MapdlPool(no_of_instances, nproc=1, run_location=path, start_timeout=120)\n", + "\n", + " inputs = [\n", + " (length, height, thickness, mesh_size, simulations, id + 1)\n", + " for id, simulations in enumerate(simulations_per_instance_list)\n", + " ]\n", + "\n", + " overall_simulation_results = pool.map(run_simulations_threaded, inputs)\n", + " pool.exit()\n", + "\n", + " return overall_simulation_results" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Creating Pool: 100%|███████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:25<00:00, 2.56s/it]\n", + "MAPDL Running: 0%| | 0/10 [00:00 np.ndarray: + """Run desired number of simulations to obtain response data. + + Parameters + ---------- + length : float + The length of the cantilever structure + height : float + The height of the cantilever structure + thickness : float + The thickness of the cantilever structure + mesh_size : float + The desired mesh size + no_of_simulations : int + The number of simulations to run + + Returns + ------- + np.ndarray + Array containing simulation results. + """ + + from pathlib import Path + from ansys.mapdl.core import launch_mapdl + + path = Path.cwd() + mapdl = launch_mapdl(run_location=path) + + domain = [0, length] + correl_length_param = 3 + min_eigen_value = 0.001 + poisson_ratio = 0.3 + + mapdl.prep7() # Enter preprocessor + + mapdl.r(r1=thickness) + mapdl.et(1, "PLANE182", kop3=3, kop6=0) + mapdl.rectng(0, length, 0, height) + mapdl.mshkey(1) + mapdl.mshape(0, "2D") + mapdl.esize(mesh_size) + mapdl.amesh("ALL") + + # Fixed edge + mapdl.nsel("S", "LOC", "X", 0) + mapdl.cm("FIXED_END", "NODE") + + # Load application node + mapdl.nsel("S", "LOC", "X", length) + mapdl.nsel("R", "LOC", "Y", height) + mapdl.cm("LOAD_APPLICATION_POINT", "NODE") + + mapdl.finish() # Exit preprocessor + + mapdl.slashsolu() # Enter solution processor + + element_ids = mapdl.esel( + "S", "CENT", "Y", 0, mesh_size + ) # Select bottom row elements and store the ids + + # Generate quantities required to define the young's modulus stochastic process + cosine_frequency_list, cosine_eigen_values, cosine_constants = evaluate_KL_cosine_terms( + domain, correl_length_param, min_eigen_value + ) + sine_frequency_list, sine_eigen_values, sine_constants = evaluate_KL_sine_terms( + domain, correl_length_param, min_eigen_value + ) + + simulation_results = np.zeros(no_of_simulations) + + for simulation in range(no_of_simulations): + # Generate random variables and load needed for one realization of the process + cosine_random_variables_set = np.random.normal(0, 1, size=len(cosine_frequency_list)) + sine_random_variables_set = np.random.normal(0, 1, size=len(sine_frequency_list)) + load = -np.random.normal(10, 2**0.5) # Generate a random load + + material_property = 0 # Initialize material property ID + for element_id in element_ids: + material_property += 1 + mapdl.get("ELEMENT_ID", "ELEM", element_id, "CENT", "X") + element_centroid_x_coord = mapdl.parameters["ELEMENT_ID"] + mapdl.esel( + "S", "CENT", "X", element_centroid_x_coord + ) # Select all elements having this coordinate as centroid + + # Evaluate young's modulus at this material point + young_modulus_value = young_modulus_realization( + cosine_frequency_list, + cosine_eigen_values, + cosine_constants, + cosine_random_variables_set, + sine_frequency_list, + sine_eigen_values, + sine_constants, + sine_random_variables_set, + domain, + element_centroid_x_coord, + ) + + mapdl.mp( + "EX", f"{material_property}", young_modulus_value + ) # Define property ID, assign young's modulus + mapdl.mp("NUXY", f"{material_property}", poisson_ratio) # Assign poisson ratio + mapdl.mpchg(material_property, "ALL") # Assign property to selected elements + + mapdl.allsel() + + mapdl.d("FIXED_END", lab="UX", value=0, lab2="UY") # Apply fixed end BC + mapdl.f("LOAD_APPLICATION_POINT", lab="FY", value=load) # Apply load BC + mapdl.solve() + + # Displacement probe point - where Uy results will be extracted + mapdl.nsel("S", "LOC", "X", 4) + displacement_probe_point = mapdl.nsel("R", "LOC", "Y", 0) + displacement = mapdl.get( + "DISP_AT_PROBE_POINT", "NODE", int(displacement_probe_point[0]), "U", "Y" + ) + + simulation_results[simulation] = displacement + + mapdl.mpdele("ALL", "ALL") + if int((simulation + 1) % 10) == 0: + print(f"Completed {simulation + 1} simulations ...") + + mapdl.exit() + print() + print("All simulations completed!") + + return simulation_results + + +# Run the simulations +simulation_results = run_simulations(4, 1, 0.2, 0.1, 5000) + +# Perform statistical post processing and plot the pdf +import scipy.stats as stats + +kde = stats.gaussian_kde(simulation_results) # Kernel density estimate + +fig, ax = plt.subplots() +fig.set_size_inches(15, 8) +x_eval = np.linspace(min(simulation_results), max(simulation_results), num=200) +ax.plot(x_eval, kde.pdf(x_eval), "r-", label="PDF of response $u$") +plt.xlabel("Displacement in (m)") +ax.legend() +plt.show() + +# We can then proceed to evaluate the probability that response u is less than 0.2 m +probability = kde.integrate_box_1d(-0.2, x_eval[-1]) +print(f"The probability that u is less than 0.2 m is {probability:.0%}") + + +# Multi-threaded approach +# Note, no of instances should not be more than the number of available CPU cores on your PC +def run_simulations_threaded( + mapdl, length, height, thickness, mesh_size, no_of_simulations, instance_identifier +): + domain = [0, length] + correl_length_param = 3 + min_eigen_value = 0.001 + poisson_ratio = 0.3 + + mapdl.prep7() # Enter preprocessor + + mapdl.r(r1=thickness) + mapdl.et(1, "PLANE182", kop3=3, kop6=0) + mapdl.rectng(0, length, 0, height) + mapdl.mshkey(1) + mapdl.mshape(0, "2D") + mapdl.esize(mesh_size) + mapdl.amesh("ALL") + + # Fixed edge + mapdl.nsel("S", "LOC", "X", 0) + mapdl.cm("FIXED_END", "NODE") + + # Load application node + mapdl.nsel("S", "LOC", "X", length) + mapdl.nsel("R", "LOC", "Y", height) + mapdl.cm("LOAD_APPLICATION_POINT", "NODE") + + mapdl.finish() # Exit preprocessor + + mapdl.slashsolu() # Enter solution processor + + element_ids = mapdl.esel( + "S", "CENT", "Y", 0, mesh_size + ) # Select bottom row elements and store the ids + + # Generate quantities required to define the young's modulus stochastic process + cosine_frequency_list, cosine_eigen_values, cosine_constants = evaluate_KL_cosine_terms( + domain, correl_length_param, min_eigen_value + ) + sine_frequency_list, sine_eigen_values, sine_constants = evaluate_KL_sine_terms( + domain, correl_length_param, min_eigen_value + ) + + simulation_results = np.zeros(no_of_simulations) + + for simulation in range(no_of_simulations): + # Generate random variables and load needed for one realization of the process + cosine_random_variables_set = np.random.normal(0, 1, size=len(cosine_frequency_list)) + sine_random_variables_set = np.random.normal(0, 1, size=len(sine_frequency_list)) + load = -np.random.normal(10, 2**0.5) # Generate a random load + + material_property = 0 # Initialize material property ID + for element_id in element_ids: + material_property += 1 + mapdl.get("ELEMENT_ID", "ELEM", element_id, "CENT", "X") + element_centroid_x_coord = mapdl.parameters["ELEMENT_ID"] + mapdl.esel( + "S", "CENT", "X", element_centroid_x_coord + ) # Select all elements having this coordinate as centroid + + # Evaluate young's modulus at this material point + young_modulus_value = young_modulus_realization( + cosine_frequency_list, + cosine_eigen_values, + cosine_constants, + cosine_random_variables_set, + sine_frequency_list, + sine_eigen_values, + sine_constants, + sine_random_variables_set, + domain, + element_centroid_x_coord, + ) + + mapdl.mp( + "EX", f"{material_property}", young_modulus_value + ) # Define property ID, assign young's modulus + mapdl.mp("NUXY", f"{material_property}", poisson_ratio) # Assign poisson ratio + mapdl.mpchg(material_property, "ALL") # Assign property to selected elements + + mapdl.allsel() + + mapdl.d("FIXED_END", lab="UX", value=0, lab2="UY") # Apply fixed end BC + mapdl.f("LOAD_APPLICATION_POINT", lab="FY", value=load) # Apply load BC + mapdl.solve() + + # Displacement probe point - where Uy results will be extracted + mapdl.nsel("S", "LOC", "X", 4) + displacement_probe_point = mapdl.nsel("R", "LOC", "Y", 0) + displacement = mapdl.get( + "DISP_AT_PROBE_POINT", "NODE", int(displacement_probe_point[0]), "U", "Y" + ) + + simulation_results[simulation] = displacement + + mapdl.mpdele("ALL", "ALL") + if int((simulation + 1) % 10) == 0: + print(f"Completed {simulation + 1} simulations in instance {instance_identifier} ...") + + mapdl.exit() + print() + print(f"All simulations completed in instance {instance_identifier}!") + + return instance_identifier, no_of_simulations, simulation_results + + +def run_simulations_over_multple_instances( + length, height, thickness, mesh_size, no_of_simulations, no_of_instances +): + from pathlib import Path + from ansys.mapdl.core import MapdlPool + + # First determine the number of simulations to run per instance + if no_of_simulations % no_of_instances == 0: + # Simlations can be split equally across instances + simulations_per_instance = no_of_simulations // no_of_instances + simulations_per_instance_list = [simulations_per_instance for i in range(no_of_instances)] + else: + # Simulations can not be split equally across instances + simulations_per_instance = no_of_simulations // no_of_instances + simulations_per_instance_list = [ + simulations_per_instance for i in range(no_of_instances - 1) + ] + remaining_simulations = no_of_simulations - sum(simulations_per_instance_list) + simulations_per_instance_list.append(remaining_simulations) + + path = Path.cwd() + pool = MapdlPool(no_of_instances, nproc=1, run_location=path, start_timeout=120) + + inputs = [ + (length, height, thickness, mesh_size, simulations, id + 1) + for id, simulations in enumerate(simulations_per_instance_list) + ] + + overall_simulation_results = pool.map(run_simulations_threaded, inputs) + pool.exit() + + return overall_simulation_results + + +# Run the simulations over several instances +simulation_results = run_simulations_over_multple_instances(10, 1, 0.2, 0.1, 5000, 10) + +# Collect the results from each instance +combined_results = [result[2] for result in simulation_results] +combined_results = np.concatenate(combined_results) + +# Calculate the probability +kde = stats.gaussian_kde(combined_results) # Kernel density estimate +probability = kde.integrate_box_1d(-0.2, max(combined_results)) +print(f"The probability that u is less than 0.2 m is {probability:.0%}") diff --git a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst index 1eb6a30ef67..bfda8772b7c 100644 --- a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst +++ b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst @@ -200,7 +200,7 @@ to where :math:`\pmb{\xi}` collects a sources of system randomness. The Monte Carlo simulation for solving the equation above consists of generating a large number of :math:`N_{sim}` of samples :math:`\pmb{\xi}, i=1,\dots ,N_{sim}` from their probability -distribution and for each of these samples, solve the deterministic problem +distribution and for each of these samples, solving the deterministic problem .. math:: \pmb{K}(\pmb{\xi}_{(i)})\pmb{U}(\pmb{\xi}_{(i)}) = \pmb{F}(\pmb{\xi}_{(i)}) @@ -229,10 +229,11 @@ with :math:`f(x)` being a zero mean stationary Gaussian field with unit variance We are to do the following: 1. Using the K-L series expansion, generate 5000 realizations for :math:`E(x)` and perform Monte - Carlo simulation to the probability density function of the response :math:`u`, at the bottom right corner + Carlo simulation to determine the probability density function of the response :math:`u`, at the bottom right corner of the cantilever. -2. If :math:`u` must not exceed :math:`0.2 \: m`, how confident can we be of this requirement? +2. If some design code stipulates that the displacement :math:`u` must not exceed :math:`0.2 \: m`, how confident can + we be that the above structure meets this requirement? .. note:: This example really emphasizes how PyMAPDL can help to supercharge workflows. At a very high level, what will be done @@ -245,8 +246,8 @@ Firstly, we implement code that allows us to represent the zero-mean Gaussian fi :math:numref:`cosine equation` and :math:numref:`sine equation`, then substituting calculated values into :math:numref:`cosine terms` and :math:numref:`sine terms` to obtain the constant terms in those equations. The number of retained terms :math:`P` and :math:`Q` in :math:numref:`approximation` can be automatically determined -by structuring our code to stop computing values when :math:`\lambda_{c,n}, \lambda_{s,n}` become lower than -our desired accuracy level. The implementation is as follows: +by structuring our code to stop computing values when :math:`\lambda_{c,n}, \lambda_{s,n}` become lower than a +desired accuracy level. The implementation is as follows: .. literalinclude:: sfem.py :language: python @@ -343,4 +344,82 @@ The plots above confirms that our implementation is indeed correct. If one desir can be further decreased but the value already chosen is sufficient. Running the simulations -~~~~~~~~~~~~~~~~~~~~~~~ \ No newline at end of file +~~~~~~~~~~~~~~~~~~~~~~~ +Now we focus on the PyMAPDL part of this example. Remember that the problem requires running 5000 simulations. Therefore, we need +to write a workflow that does the following: + +1. Create the geometry of the cantilever model + +2. Mesh the model. For this, 4-node PLANE182 elements will be used + +3. Generate one realization of :math:`E` and one sample of :math:`P` for each simulation + +4. For each simulation, loop through the elements and for each element, use the realization + above to assign the value of the young's modulus. Also assign the load for each simulation. + +5. Solve the model and store :math:`u` for each simulation. + +.. note:: + One realization continuously varies with :math:`x` but a plane stress element like PLANE182 can only have a constant + young modulus assigned. Therefore, for an element whose :math:`x`-coordinates are between :math:`x_1` and :math:`x_2`, one can simply + assign the average value of :math:`E` between these two values or assign the value of :math:`E` at the centroid. The later is + chosen for this implementation. The method chosen becomes insignificant with a finer mesh as both methods should produce similar + results. + +A function implementing the steps above follows: + +.. literalinclude:: sfem.py + :language: python + :lines: 381-513 + +Required arguments can be passed to the above function to run the simulations: + +.. literalinclude:: sfem.py + :language: python + :lines: 516-517 + +Answering problem questions +~~~~~~~~~~~~~~~~~~~~~~~~~~~ +To finish answering the first question (simulations have already been run), we proceed to perform a statistical +post-processing of simulation results to determine the pdf of the response :math:`u`: + +.. literalinclude:: sfem.py + :language: python + :lines: 519-529 + +.. figure:: pdf.png + + The probability density function of response :math:`u` + +To answer the second question, we simply evaluate the probability that the response :math:`u` is less than +:math:`0.2 \: m`: + +.. literalinclude:: sfem.py + :language: python + :lines: 532-534 + +The computed probability is aprroximately 99%, which is a measure of how well the structure satisfies the design +requirement. + +.. note:: + The implementation above was split into several functiomns so users can modify practically any aspect of the problem + statement with minimal edits to the code for testing out other scenarios. For example, different structural geometry, + different mesh size, different loading condition etc. + +Improving simulation speed via multi-threading +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +One of the main drawbacks of MCS is the number of simulations required. In the example above, 5000 simulations can take quite +some time to run on a single MAPDL instance. To speed things up, the :class:`~ansys.mapdl.core.pool.MapdlPool` class can be +run simulations across multiple MAPDL instances. The implementation is as follows: + +.. literalinclude:: sfem.py + :language: python + :lines: 537-676 + +To run simulations over 10 MAPDL instances, the function above is simply called with appropriate arguments: + +.. literalinclude:: sfem.py + :language: python + :lines: 679-689 + +Now the simulations will be completed much faster. From 2d4ac645f70dc259bf0ec4877d8c997df3ae97ff Mon Sep 17 00:00:00 2001 From: "pre-commit-ci[bot]" <66853113+pre-commit-ci[bot]@users.noreply.github.com> Date: Fri, 17 Jan 2025 20:44:03 +0000 Subject: [PATCH 13/26] ci: auto fixes from pre-commit.com hooks. for more information, see https://pre-commit.ci --- doc/source/examples/extended_examples/sfem/sfem.py | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/doc/source/examples/extended_examples/sfem/sfem.py b/doc/source/examples/extended_examples/sfem/sfem.py index 243125fb9d8..02125bb55b7 100644 --- a/doc/source/examples/extended_examples/sfem/sfem.py +++ b/doc/source/examples/extended_examples/sfem/sfem.py @@ -22,8 +22,9 @@ import math import random +from typing import Callable, Tuple + import numpy as np -from typing import Tuple, Callable def find_solution( @@ -427,6 +428,7 @@ def run_simulations( """ from pathlib import Path + from ansys.mapdl.core import launch_mapdl path = Path.cwd() @@ -668,6 +670,7 @@ def run_simulations_over_multple_instances( length, height, thickness, mesh_size, no_of_simulations, no_of_instances ): from pathlib import Path + from ansys.mapdl.core import MapdlPool # First determine the number of simulations to run per instance From 6ef84ee5de8367ba2fc74a12348a60bd4ca0ffc0 Mon Sep 17 00:00:00 2001 From: moe-ad Date: Mon, 20 Jan 2025 08:39:59 +0100 Subject: [PATCH 14/26] feat: minor corrections --- .../examples/extended_examples/sfem/stochastic_fem.rst | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst index bfda8772b7c..40f2d38e3e8 100644 --- a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst +++ b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst @@ -402,15 +402,15 @@ The computed probability is aprroximately 99%, which is a measure of how well th requirement. .. note:: - The implementation above was split into several functiomns so users can modify practically any aspect of the problem + The implementation above was split into several functions so users can modify practically any aspect of the problem statement with minimal edits to the code for testing out other scenarios. For example, different structural geometry, different mesh size, different loading condition etc. Improving simulation speed via multi-threading ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ One of the main drawbacks of MCS is the number of simulations required. In the example above, 5000 simulations can take quite -some time to run on a single MAPDL instance. To speed things up, the :class:`~ansys.mapdl.core.pool.MapdlPool` class can be -run simulations across multiple MAPDL instances. The implementation is as follows: +some time to run on a single MAPDL instance. To speed things up, the :class:`~ansys.mapdl.core.pool.MapdlPool` class can be utilized +to run simulations across multiple MAPDL instances. The implementation is as follows: .. literalinclude:: sfem.py :language: python From 699cbf8f500c018f96a80ec4dd22c2df2d8eeee0 Mon Sep 17 00:00:00 2001 From: "pre-commit-ci[bot]" <66853113+pre-commit-ci[bot]@users.noreply.github.com> Date: Mon, 20 Jan 2025 07:41:21 +0000 Subject: [PATCH 15/26] ci: auto fixes from pre-commit.com hooks. for more information, see https://pre-commit.ci --- doc/source/conf.py | 2 +- .../examples/extended_examples/sfem/sfem.py | 78 +++++++++++++------ 2 files changed, 57 insertions(+), 23 deletions(-) diff --git a/doc/source/conf.py b/doc/source/conf.py index 7fe4a5a4e3d..13506bc8e48 100755 --- a/doc/source/conf.py +++ b/doc/source/conf.py @@ -103,7 +103,7 @@ "sphinxemoji.sphinxemoji", "sphinx.ext.graphviz", "ansys_sphinx_theme.extension.linkcode", - "sphinx.ext.mathjax" + "sphinx.ext.mathjax", ] # Intersphinx mapping diff --git a/doc/source/examples/extended_examples/sfem/sfem.py b/doc/source/examples/extended_examples/sfem/sfem.py index 02125bb55b7..d5d9cfb586a 100644 --- a/doc/source/examples/extended_examples/sfem/sfem.py +++ b/doc/source/examples/extended_examples/sfem/sfem.py @@ -61,7 +61,9 @@ def find_solution( current_guess = random.uniform(*solution_range) continue - updated_guess = current_guess - func(current_guess) / derivative_func(current_guess) + updated_guess = current_guess - func(current_guess) / derivative_func( + current_guess + ) error = abs(updated_guess - current_guess) if error < acceptable_solution_error and not ( @@ -122,7 +124,9 @@ def cosine_constant(w_n): # start solving here acceptable_solution_error = 1e-10 solution_range = [(n - 1) * math.pi / A, (n - 0.5) * math.pi / A] - solution = find_solution(func, deriv_func, acceptable_solution_error, solution_range) + solution = find_solution( + func, deriv_func, acceptable_solution_error, solution_range + ) frequency_array.append(solution) cosine_eigen_values_array.append(eigen_value(solution)) @@ -181,7 +185,9 @@ def sine_constant(w_n): # start solving here acceptable_solution_error = 1e-10 solution_range = [(n - 0.5) * math.pi / A, n * math.pi / A] - solution = find_solution(func, deriv_func, acceptable_solution_error, solution_range) + solution = find_solution( + func, deriv_func, acceptable_solution_error, solution_range + ) frequency_array.append(solution) sine_eigen_values_array.append(eigen_value(solution)) @@ -296,8 +302,8 @@ def young_modulus_realization( correl_length_param = 3 min_eigen_value = 0.001 -cosine_frequency_array, cosine_eigen_values, cosine_constants = evaluate_KL_cosine_terms( - domain, correl_length_param, min_eigen_value +cosine_frequency_array, cosine_eigen_values, cosine_constants = ( + evaluate_KL_cosine_terms(domain, correl_length_param, min_eigen_value) ) sine_frequency_array, sine_eigen_values, sine_constants = evaluate_KL_sine_terms( domain, correl_length_param, min_eigen_value @@ -315,7 +321,9 @@ def young_modulus_realization( ax.set_xlim(domain[0], domain[1]) for i in range(no_of_realizations): - cosine_random_variables_set = np.random.normal(0, 1, size=len(cosine_frequency_array)) + cosine_random_variables_set = np.random.normal( + 0, 1, size=len(cosine_frequency_array) + ) sine_random_variables_set = np.random.normal(0, 1, size=len(sine_frequency_array)) realization = np.array( @@ -345,7 +353,9 @@ def young_modulus_realization( realization_collection = np.zeros((no_of_realizations, len(x))) for i in range(no_of_realizations): - cosine_random_variables_set = np.random.normal(0, 1, size=len(cosine_frequency_array)) + cosine_random_variables_set = np.random.normal( + 0, 1, size=len(cosine_frequency_array) + ) sine_random_variables_set = np.random.normal(0, 1, size=len(sine_frequency_array)) realization = np.array( @@ -404,7 +414,11 @@ def young_modulus_realization( # Single-threaded approach # Function for running the simulations def run_simulations( - length: float, height: float, thickness: float, mesh_size: float, no_of_simulations: int + length: float, + height: float, + thickness: float, + mesh_size: float, + no_of_simulations: int, ) -> np.ndarray: """Run desired number of simulations to obtain response data. @@ -467,8 +481,8 @@ def run_simulations( ) # Select bottom row elements and store the ids # Generate quantities required to define the young's modulus stochastic process - cosine_frequency_list, cosine_eigen_values, cosine_constants = evaluate_KL_cosine_terms( - domain, correl_length_param, min_eigen_value + cosine_frequency_list, cosine_eigen_values, cosine_constants = ( + evaluate_KL_cosine_terms(domain, correl_length_param, min_eigen_value) ) sine_frequency_list, sine_eigen_values, sine_constants = evaluate_KL_sine_terms( domain, correl_length_param, min_eigen_value @@ -478,8 +492,12 @@ def run_simulations( for simulation in range(no_of_simulations): # Generate random variables and load needed for one realization of the process - cosine_random_variables_set = np.random.normal(0, 1, size=len(cosine_frequency_list)) - sine_random_variables_set = np.random.normal(0, 1, size=len(sine_frequency_list)) + cosine_random_variables_set = np.random.normal( + 0, 1, size=len(cosine_frequency_list) + ) + sine_random_variables_set = np.random.normal( + 0, 1, size=len(sine_frequency_list) + ) load = -np.random.normal(10, 2**0.5) # Generate a random load material_property = 0 # Initialize material property ID @@ -508,8 +526,12 @@ def run_simulations( mapdl.mp( "EX", f"{material_property}", young_modulus_value ) # Define property ID, assign young's modulus - mapdl.mp("NUXY", f"{material_property}", poisson_ratio) # Assign poisson ratio - mapdl.mpchg(material_property, "ALL") # Assign property to selected elements + mapdl.mp( + "NUXY", f"{material_property}", poisson_ratio + ) # Assign poisson ratio + mapdl.mpchg( + material_property, "ALL" + ) # Assign property to selected elements mapdl.allsel() @@ -596,8 +618,8 @@ def run_simulations_threaded( ) # Select bottom row elements and store the ids # Generate quantities required to define the young's modulus stochastic process - cosine_frequency_list, cosine_eigen_values, cosine_constants = evaluate_KL_cosine_terms( - domain, correl_length_param, min_eigen_value + cosine_frequency_list, cosine_eigen_values, cosine_constants = ( + evaluate_KL_cosine_terms(domain, correl_length_param, min_eigen_value) ) sine_frequency_list, sine_eigen_values, sine_constants = evaluate_KL_sine_terms( domain, correl_length_param, min_eigen_value @@ -607,8 +629,12 @@ def run_simulations_threaded( for simulation in range(no_of_simulations): # Generate random variables and load needed for one realization of the process - cosine_random_variables_set = np.random.normal(0, 1, size=len(cosine_frequency_list)) - sine_random_variables_set = np.random.normal(0, 1, size=len(sine_frequency_list)) + cosine_random_variables_set = np.random.normal( + 0, 1, size=len(cosine_frequency_list) + ) + sine_random_variables_set = np.random.normal( + 0, 1, size=len(sine_frequency_list) + ) load = -np.random.normal(10, 2**0.5) # Generate a random load material_property = 0 # Initialize material property ID @@ -637,8 +663,12 @@ def run_simulations_threaded( mapdl.mp( "EX", f"{material_property}", young_modulus_value ) # Define property ID, assign young's modulus - mapdl.mp("NUXY", f"{material_property}", poisson_ratio) # Assign poisson ratio - mapdl.mpchg(material_property, "ALL") # Assign property to selected elements + mapdl.mp( + "NUXY", f"{material_property}", poisson_ratio + ) # Assign poisson ratio + mapdl.mpchg( + material_property, "ALL" + ) # Assign property to selected elements mapdl.allsel() @@ -657,7 +687,9 @@ def run_simulations_threaded( mapdl.mpdele("ALL", "ALL") if int((simulation + 1) % 10) == 0: - print(f"Completed {simulation + 1} simulations in instance {instance_identifier} ...") + print( + f"Completed {simulation + 1} simulations in instance {instance_identifier} ..." + ) mapdl.exit() print() @@ -677,7 +709,9 @@ def run_simulations_over_multple_instances( if no_of_simulations % no_of_instances == 0: # Simlations can be split equally across instances simulations_per_instance = no_of_simulations // no_of_instances - simulations_per_instance_list = [simulations_per_instance for i in range(no_of_instances)] + simulations_per_instance_list = [ + simulations_per_instance for i in range(no_of_instances) + ] else: # Simulations can not be split equally across instances simulations_per_instance = no_of_simulations // no_of_instances From 03cc3f4ab5f4975829825ea62904a0a77fd98334 Mon Sep 17 00:00:00 2001 From: moe-ad Date: Tue, 21 Jan 2025 12:33:00 +0100 Subject: [PATCH 16/26] fix: implemented review suggestions --- .../extended_examples/sfem/realizations.png | Bin 131959 -> 134412 bytes .../extended_examples/sfem/sfem.ipynb | 1484 ----------------- .../examples/extended_examples/sfem/sfem.py | 42 +- .../extended_examples/sfem/stochastic_fem.rst | 46 +- .../sfem/young_modulus_realizations.png | Bin 248243 -> 206677 bytes 5 files changed, 56 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zvji=SlJ?fop+l^de)a{FbOQN6iGwmmJ}B?VG%gO#u2>1&FKYQ|d_3@6`sJDj`)zv( zVK2_4^vyVeOw6G=GASiRU+OL>`@L*zo@bA{k_9`C1vrR&GH8`w>{Wu`oZCE6UjP@^ zWB)SfN`l*6ur4jiVZUtu<4BaTxw-id7@Tl=FIb+-Zvyt90yU7MTwPlCpHLOygOY`W k{PX{<0LXX#FE?H13?t67JBaGLP{5D6ijHy?_Trs?0h`V=a{vGU diff --git a/doc/source/examples/extended_examples/sfem/sfem.ipynb b/doc/source/examples/extended_examples/sfem/sfem.ipynb deleted file mode 100644 index 90a9b403a0b..00000000000 --- a/doc/source/examples/extended_examples/sfem/sfem.ipynb +++ /dev/null @@ -1,1484 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import math\n", - "import random\n", - "import numpy as np\n", - "from typing import Tuple, Callable\n", - "\n", - "\n", - "def find_solution(\n", - " func: Callable[[float], float],\n", - " derivative_func: Callable[[float], float],\n", - " acceptable_solution_error: float,\n", - " solution_range: Tuple[float, float],\n", - ") -> float:\n", - " \"\"\"Find the solution of g(x) = 0 within solution range where g(x) is non-linear.\n", - "\n", - " Parameters\n", - " ----------\n", - " func : Callable[float, float]\n", - " The function definition\n", - " derivative_func : Callable[float, float]\n", - " The derivative of the above function\n", - " acceptable_solution_error : float\n", - " Error at which the solution is acceptable\n", - " solution_range : Tuple[float, float]\n", - " The range within which the solution will be searched\n", - "\n", - " Returns\n", - " -------\n", - " float\n", - " Solution to g(x) = 0\n", - " \"\"\"\n", - "\n", - " current_guess = random.uniform(*solution_range)\n", - " iteration_counter = 1\n", - "\n", - " while True:\n", - " if iteration_counter > 100:\n", - " iteration_counter = 1\n", - " current_guess = random.uniform(*solution_range)\n", - " continue\n", - "\n", - " updated_guess = current_guess - func(current_guess) / derivative_func(current_guess)\n", - " error = abs(updated_guess - current_guess)\n", - "\n", - " if error < acceptable_solution_error and not (\n", - " solution_range[0] < updated_guess < solution_range[1]\n", - " ):\n", - " current_guess = random.uniform(*solution_range)\n", - " continue\n", - " elif error < acceptable_solution_error and (\n", - " solution_range[0] < updated_guess < solution_range[1]\n", - " ):\n", - " return updated_guess\n", - "\n", - " current_guess = updated_guess\n", - " iteration_counter += 1\n", - "\n", - "\n", - "def evaluate_KL_cosine_terms(\n", - " domain: Tuple[float, float], correl_length_param: float, min_eigen_value: float\n", - ") -> Tuple[np.ndarray, np.ndarray, np.ndarray]:\n", - " \"\"\"Build array of eigenvalues and constants of the cosine terms in the KL expansion of a gaussian stochastic process.\n", - "\n", - " Parameters\n", - " ----------\n", - " domain : Tuple[float, float]\n", - " Domain over which the KL representation of the stochastic process should be found\n", - " correl_length_param : float\n", - " Correlation length parameter of the autocorrelation function of the process\n", - " min_eigen_value : float\n", - " Minimum eigenvalue to achieve require accuracy\n", - "\n", - " Returns\n", - " -------\n", - " Tuple[np.ndarray, np.ndarray, np.ndarray]\n", - " Arrays of frequencies, eigenvalues, and constants of retained cosine terms (P in total) in the KL expansion\n", - " \"\"\"\n", - "\n", - " A = (domain[1] - domain[0]) / 2 # Symmetric domain parameter -> [-A, A]\n", - "\n", - " frequency_array = []\n", - " cosine_eigen_values_array = []\n", - " cosine_constants_array = []\n", - "\n", - " # Define the functions related to the sine terms\n", - " def func(w_n):\n", - " return 1 / correl_length_param - w_n * math.tan(w_n * A)\n", - "\n", - " def deriv_func(w_n):\n", - " return -w_n * A / math.cos(w_n * correl_length_param) ** 2 - math.tan(w_n * A)\n", - "\n", - " def eigen_value(w_n):\n", - " return (2 * correl_length_param) / (1 + (correl_length_param * w_n) ** 2)\n", - "\n", - " def cosine_constant(w_n):\n", - " return 1 / (A + (math.sin(2 * w_n * A) / (2 * w_n))) ** 0.5\n", - "\n", - " # Build the array of eigenvalues and constant terms for the accuracy required\n", - " for n in range(1, 100):\n", - " # start solving here\n", - " acceptable_solution_error = 1e-10\n", - " solution_range = [(n - 1) * math.pi / A, (n - 0.5) * math.pi / A]\n", - " solution = find_solution(func, deriv_func, acceptable_solution_error, solution_range)\n", - "\n", - " frequency_array.append(solution)\n", - " cosine_eigen_values_array.append(eigen_value(solution))\n", - " cosine_constants_array.append(cosine_constant(solution))\n", - " if eigen_value(solution) < min_eigen_value:\n", - " break\n", - "\n", - " return (\n", - " np.array(frequency_array),\n", - " np.array(cosine_eigen_values_array),\n", - " np.array(cosine_constants_array),\n", - " )\n", - "\n", - "\n", - "def evaluate_KL_sine_terms(\n", - " domain: Tuple[float, float], correl_length_param: float, min_eigen_value: float\n", - ") -> Tuple[np.ndarray, np.ndarray, np.ndarray]:\n", - " \"\"\"Build array of eigenvalues and constants of the sine terms in the KL expansion of a gaussian stochastic process.\n", - "\n", - " Parameters\n", - " ----------\n", - " domain : Tuple[float, float]\n", - " Domain over which the KL representation of the stochastic process should be found\n", - " correl_length_param : float\n", - " Correlation length parameter of the autocorrelation function of the process\n", - " min_eigen_value : float\n", - " Minimum eigenvalue to achieve require accuracy\n", - "\n", - " Returns\n", - " -------\n", - " Tuple[np.ndarray, np.ndarray, np.ndarray]\n", - " Arrays of frequencies, eigenvalues, and constants of retained sine terms (Q in total) in the KL expansion\n", - " \"\"\"\n", - "\n", - " A = (domain[1] - domain[0]) / 2 # Symmetric domain parameter -> [-A, A]\n", - "\n", - " frequency_array = []\n", - " sine_eigen_values_array = []\n", - " sine_constants_array = []\n", - "\n", - " # Define functions related to the sine terms\n", - " def func(w_n):\n", - " return (1 / correl_length_param) * math.tan(w_n * A) + w_n\n", - "\n", - " def deriv_func(w_n):\n", - " return A / (correl_length_param * math.cos(w_n * A) ** 2) + 1\n", - "\n", - " def eigen_value(w_n):\n", - " return (2 * correl_length_param) / (1 + (correl_length_param * w_n) ** 2)\n", - "\n", - " def sine_constant(w_n):\n", - " return 1 / (A - (math.sin(2 * w_n * A) / (2 * w_n))) ** 0.5\n", - "\n", - " # Build the array of eigenvalues and constant terms for the accuracy required\n", - " for n in range(1, 100):\n", - " # start solving here\n", - " acceptable_solution_error = 1e-10\n", - " solution_range = [(n - 0.5) * math.pi / A, n * math.pi / A]\n", - " solution = find_solution(func, deriv_func, acceptable_solution_error, solution_range)\n", - "\n", - " frequency_array.append(solution)\n", - " sine_eigen_values_array.append(eigen_value(solution))\n", - " sine_constants_array.append(sine_constant(solution))\n", - " if eigen_value(solution) < min_eigen_value:\n", - " break\n", - "\n", - " return (\n", - " np.array(frequency_array),\n", - " np.array(sine_eigen_values_array),\n", - " np.array(sine_constants_array),\n", - " )" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "def stochastic_field_realization(\n", - " cosine_frequency_array: np.ndarray,\n", - " cosine_eigen_values: np.ndarray,\n", - " cosine_constants: np.ndarray,\n", - " cosine_random_variables_set: np.ndarray,\n", - " sine_frequency_array: np.ndarray,\n", - " sine_eigen_values: np.ndarray,\n", - " sine_constants: np.ndarray,\n", - " sine_random_variables_set: np.ndarray,\n", - " domain: Tuple[float, float],\n", - " evaluation_point: float,\n", - ") -> float:\n", - " \"\"\"The realization of the gaussian field f(x)\n", - "\n", - " Parameters\n", - " ----------\n", - " cosine_frequency_array : np.ndarray\n", - " Array of length P, containining frequencies associated with retained cosine terms\n", - " cosine_eigen_values : np.ndarray\n", - " Array of length P, containing eigenvalues associated with retained cosine terms\n", - " cosine_constants : np.ndarray\n", - " Array of length P, containing constants associated with retained cosine terms\n", - " cosine_random_variables_set : np.ndarray\n", - " Array of length P, containing random variable drawn from N(0,1) for the cosine terms\n", - " sine_frequency_array : np.ndarray\n", - " Array of length Q, containining frequencies associated with retained sine terms\n", - " sine_eigen_values : np.ndarray\n", - " Array of length Q, containing eigenvalues associated with retained sine terms\n", - " sine_constants : np.ndarray\n", - " Array of length Q, containing constants associated with retained sine terms\n", - " sine_random_variables_set : np.ndarray\n", - " Array of length P, containing random variable drawn from N(0,1) for the sine terms\n", - " domain : Tuple[float, float]\n", - " Domain over which the KL representation of the stochastic process should be found\n", - " evaluation_point : float\n", - " Point within the domain at which the value of a realization is required\n", - "\n", - " Returns\n", - " -------\n", - " float\n", - " The value of the realization at a given point within the domain\n", - " \"\"\"\n", - " # Shift parameter -> Because we had solved for terms in a symmetric domain [-A, A]\n", - " T = (domain[0] + domain[1]) / 2\n", - "\n", - " # Making use of array operation provided by the numpy package is much simpler for expressing the stochastic process\n", - " cosine_function_terms = (\n", - " np.sqrt(cosine_eigen_values)\n", - " * cosine_constants\n", - " * np.cos((evaluation_point - T) * cosine_frequency_array)\n", - " * cosine_random_variables_set\n", - " )\n", - "\n", - " sine_function_terms = (\n", - " np.sqrt(sine_eigen_values)\n", - " * sine_constants\n", - " * np.sin((evaluation_point - T) * sine_frequency_array)\n", - " * sine_random_variables_set\n", - " )\n", - "\n", - " return np.sum(cosine_function_terms) + np.sum(sine_function_terms)" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "def young_modulus_realization(\n", - " cosine_frequency_list,\n", - " cosine_eigen_values,\n", - " cosine_constants,\n", - " cosine_random_variables_set,\n", - " sine_frequency_list,\n", - " sine_eigen_values,\n", - " sine_constants,\n", - " sine_random_variables_set,\n", - " domain,\n", - " evaluation_point,\n", - "):\n", - " return 1e5 * (\n", - " 1\n", - " + 0.1\n", - " * stochastic_field_realization(\n", - " cosine_frequency_list,\n", - " cosine_eigen_values,\n", - " cosine_constants,\n", - " cosine_random_variables_set,\n", - " sine_frequency_list,\n", - " sine_eigen_values,\n", - " sine_constants,\n", - " sine_random_variables_set,\n", - " domain,\n", - " evaluation_point,\n", - " )\n", - " )" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "# Generation of K-L expansion parameters\n", - "import matplotlib.pyplot as plt\n", - "\n", - "domain = (0, 4)\n", - "correl_length_param = 3\n", - "min_eigen_value = 0.001\n", - "\n", - "cosine_frequency_array, cosine_eigen_values, cosine_constants = evaluate_KL_cosine_terms(\n", - " domain, correl_length_param, min_eigen_value\n", - ")\n", - "sine_frequency_array, sine_eigen_values, sine_constants = evaluate_KL_sine_terms(\n", - " domain, correl_length_param, min_eigen_value\n", - ")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "# Now let's see how some realizations looks like\n", - "no_of_realizations = 10\n", - "x = np.linspace(domain[0], domain[1], 101)\n", - "\n", - "fig, ax = plt.subplots()\n", - "ax.set_xlabel(r\"$x \\: (m)$\")\n", - "ax.set_ylabel(r\"Realizations of $E$\")\n", - "ax.grid(True)\n", - "fig.set_size_inches(15, 8)\n", - "ax.set_xlim(domain[0], domain[1])\n", - "\n", - "for i in range(no_of_realizations):\n", - " cosine_random_variables_set = np.random.normal(0, 1, size=len(cosine_frequency_array))\n", - " sine_random_variables_set = np.random.normal(0, 1, size=len(sine_frequency_array))\n", - " \n", - " realization = np.array(\n", - " [\n", - " young_modulus_realization(\n", - " cosine_frequency_array,\n", - " cosine_eigen_values,\n", - " cosine_constants,\n", - " cosine_random_variables_set,\n", - " sine_frequency_array,\n", - " sine_eigen_values,\n", - " sine_constants,\n", - " sine_random_variables_set,\n", - " domain,\n", - " evaluation_point,\n", - " )\n", - " for evaluation_point in x\n", - " ]\n", - " )\n", - " ax.plot(x, realization)\n", - "\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "# Verification that the above implementation indeed represents the young's modulus\n", - "no_of_realizations = 5000\n", - "x = np.linspace(domain[0], domain[1], 101)\n", - "realization_collection = np.zeros((no_of_realizations, len(x)))\n", - "\n", - "for i in range(no_of_realizations):\n", - " cosine_random_variables_set = np.random.normal(0, 1, size=len(cosine_frequency_array))\n", - " sine_random_variables_set = np.random.normal(0, 1, size=len(sine_frequency_array))\n", - "\n", - " realization = np.array(\n", - " [\n", - " young_modulus_realization(\n", - " cosine_frequency_array,\n", - " cosine_eigen_values,\n", - " cosine_constants,\n", - " cosine_random_variables_set,\n", - " sine_frequency_array,\n", - " sine_eigen_values,\n", - " sine_constants,\n", - " sine_random_variables_set,\n", - " domain,\n", - " evaluation_point,\n", - " )\n", - " for evaluation_point in x\n", - " ]\n", - " )\n", - "\n", - " realization_collection[i:] = realization\n", - "\n", - "ensemble_mean_with_realization = np.zeros(realization_collection.shape[0])\n", - "ensemble_var_with_realization = np.zeros(realization_collection.shape[0])\n", - "for i in range(realization_collection.shape[0]):\n", - " ensemble_mean_with_realization[i] = np.mean(realization_collection[:i+1, :])\n", - " ensemble_var_with_realization[i] = np.var(realization_collection[:i+1, :])" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "# Plot of ensemble mean\n", - "fig, ax = plt.subplots()\n", - "fig.set_size_inches(15, 8)\n", - "ax.plot(ensemble_mean_with_realization, label='Computed mean')\n", - "ax.axhline(y=1e5, color='r', linestyle='dashed', label='Actual mean')\n", - "plt.xlabel(\"No of realizations\")\n", - "plt.ylabel(r\"Ensemble mean of $E$\")\n", - "ax.grid(True)\n", - "ax.set_xlim(0, no_of_realizations)\n", - "ax.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "# Plot of ensemble variance\n", - "fig, ax = plt.subplots()\n", - "fig.set_size_inches(15, 8)\n", - "ax.plot(ensemble_var_with_realization, label='Actual variance')\n", - "ax.axhline(y=1e8, color='r', linestyle='dashed', label='Computed variance')\n", - "plt.xlabel(\"No of realizations\")\n", - "plt.ylabel(r\"Ensemble varianc of $E$\")\n", - "ax.grid(True)\n", - "ax.set_xlim(0, no_of_realizations)\n", - "ax.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "# Function for running the simulations\n", - "def run_simulations(\n", - " length: float, height: float, thickness: float, mesh_size: float, no_of_simulations: int\n", - ") -> np.ndarray:\n", - " \"\"\"Run desired number of simulations to obtain response data.\n", - "\n", - " Parameters\n", - " ----------\n", - " length : float\n", - " The length of the cantilever structure\n", - " height : float\n", - " The height of the cantilever structure\n", - " thickness : float\n", - " The thickness of the cantilever structure\n", - " mesh_size : float\n", - " The desired mesh size\n", - " no_of_simulations : int\n", - " The number of simulations to run\n", - "\n", - " Returns\n", - " -------\n", - " np.ndarray\n", - " Array containing simulation results.\n", - " \"\"\"\n", - "\n", - " from pathlib import Path\n", - " from ansys.mapdl.core import launch_mapdl\n", - "\n", - " path = Path.cwd()\n", - " mapdl = launch_mapdl(run_location=path)\n", - "\n", - " domain = [0, length]\n", - " correl_length_param = 3\n", - " min_eigen_value = 0.001\n", - " poisson_ratio = 0.3\n", - "\n", - " mapdl.prep7() # Enter preprocessor\n", - "\n", - " mapdl.r(r1=thickness)\n", - " mapdl.et(1, \"PLANE182\", kop3=3, kop6=0)\n", - " mapdl.rectng(0, length, 0, height)\n", - " mapdl.mshkey(1)\n", - " mapdl.mshape(0, \"2D\")\n", - " mapdl.esize(mesh_size)\n", - " mapdl.amesh(\"ALL\")\n", - "\n", - " # Fixed edge\n", - " mapdl.nsel(\"S\", \"LOC\", \"X\", 0)\n", - " mapdl.cm(\"FIXED_END\", \"NODE\")\n", - "\n", - " # Load application node\n", - " mapdl.nsel(\"S\", \"LOC\", \"X\", length)\n", - " mapdl.nsel(\"R\", \"LOC\", \"Y\", height)\n", - " mapdl.cm(\"LOAD_APPLICATION_POINT\", \"NODE\")\n", - "\n", - " mapdl.finish() # Exit preprocessor\n", - "\n", - " mapdl.slashsolu() # Enter solution processor\n", - "\n", - " element_ids = mapdl.esel(\n", - " \"S\", \"CENT\", \"Y\", 0, mesh_size\n", - " ) # Select bottom row elements and store the ids\n", - "\n", - " # Generate quantities required to define the young's modulus stochastic process\n", - " cosine_frequency_list, cosine_eigen_values, cosine_constants = evaluate_KL_cosine_terms(\n", - " domain, correl_length_param, min_eigen_value\n", - " )\n", - " sine_frequency_list, sine_eigen_values, sine_constants = evaluate_KL_sine_terms(\n", - " domain, correl_length_param, min_eigen_value\n", - " )\n", - "\n", - " simulation_results = np.zeros(no_of_simulations)\n", - "\n", - " for simulation in range(no_of_simulations):\n", - " # Generate random variables and load needed for one realization of the process\n", - " cosine_random_variables_set = np.random.normal(0, 1, size=len(cosine_frequency_list))\n", - " sine_random_variables_set = np.random.normal(0, 1, size=len(sine_frequency_list))\n", - " load = -np.random.normal(10, 2**0.5) # Generate a random load\n", - "\n", - " material_property = 0 # Initialize material property ID\n", - " for element_id in element_ids:\n", - " material_property += 1\n", - " mapdl.get(\"ELEMENT_ID\", \"ELEM\", element_id, \"CENT\", \"X\")\n", - " element_centroid_x_coord = mapdl.parameters[\"ELEMENT_ID\"]\n", - " mapdl.esel(\n", - " \"S\", \"CENT\", \"X\", element_centroid_x_coord\n", - " ) # Select all elements having this coordinate as centroid\n", - "\n", - " # Evaluate young's modulus at this material point\n", - " young_modulus_value = young_modulus_realization(\n", - " cosine_frequency_list,\n", - " cosine_eigen_values,\n", - " cosine_constants,\n", - " cosine_random_variables_set,\n", - " sine_frequency_list,\n", - " sine_eigen_values,\n", - " sine_constants,\n", - " sine_random_variables_set,\n", - " domain,\n", - " element_centroid_x_coord,\n", - " )\n", - "\n", - " mapdl.mp(\n", - " \"EX\", f\"{material_property}\", young_modulus_value\n", - " ) # Define property ID, assign young's modulus\n", - " mapdl.mp(\"NUXY\", f\"{material_property}\", poisson_ratio) # Assign poisson ratio\n", - " mapdl.mpchg(material_property, \"ALL\") # Assign property to selected elements\n", - "\n", - " mapdl.allsel()\n", - "\n", - " mapdl.d(\"FIXED_END\", lab=\"UX\", value=0, lab2=\"UY\") # Apply fixed end BC\n", - " mapdl.f(\"LOAD_APPLICATION_POINT\", lab=\"FY\", value=load) # Apply load BC\n", - " mapdl.solve()\n", - "\n", - " # Displacement probe point - where Uy results will be extracted\n", - " mapdl.nsel(\"S\", \"LOC\", \"X\", 4)\n", - " displacement_probe_point = mapdl.nsel(\"R\", \"LOC\", \"Y\", 0)\n", - " displacement = mapdl.get(\n", - " \"DISP_AT_PROBE_POINT\", \"NODE\", int(displacement_probe_point[0]), \"U\", \"Y\"\n", - " )\n", - "\n", - " simulation_results[simulation] = displacement\n", - "\n", - " mapdl.mpdele(\"ALL\", \"ALL\")\n", - " if int((simulation + 1) % 10) == 0:\n", - " print(f\"Completed {simulation + 1} simulations ...\")\n", - "\n", - " mapdl.exit()\n", - " print()\n", - " print(\"All simulations completed!\")\n", - "\n", - " return simulation_results" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "simulation_results = run_simulations(4, 1, 0.2, 0.1, 5000)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "# Perform statistical post processing and plot the pdf\n", - "import scipy.stats as stats\n", - "\n", - "kde = stats.gaussian_kde(simulation_results) # Kernel density estimate\n", - "\n", - "fig, ax = plt.subplots()\n", - "fig.set_size_inches(15, 8)\n", - "x_eval = np.linspace(min(simulation_results), max(simulation_results), num=200)\n", - "ax.plot(x_eval, kde.evaluate(x_eval), 'r-')\n", - "plt.xlabel(\"Displacement in (m)\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "# We can then proceed to evaluate the probability that response u is less than 0.2 m\n", - "probability = kde.integrate_box_1d(-0.2, x_eval[-1])\n", - "print(f\"The probability that u is less than 0.2 m is {probability:.0%}\")" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [], - "source": [ - "# Multi-threaded approach\n", - "# Note, no of instances should not be more than the number of available CPU cores on your PC\n", - "def run_simulations_threaded(\n", - " mapdl, length, height, thickness, mesh_size, no_of_simulations, instance_identifier\n", - "):\n", - " domain = [0, length]\n", - " correl_length_param = 3\n", - " min_eigen_value = 0.001\n", - " poisson_ratio = 0.3\n", - "\n", - " mapdl.prep7() # Enter preprocessor\n", - "\n", - " mapdl.r(r1=thickness)\n", - " mapdl.et(1, \"PLANE182\", kop3=3, kop6=0)\n", - " mapdl.rectng(0, length, 0, height)\n", - " mapdl.mshkey(1)\n", - " mapdl.mshape(0, \"2D\")\n", - " mapdl.esize(mesh_size)\n", - " mapdl.amesh(\"ALL\")\n", - "\n", - " # Fixed edge\n", - " mapdl.nsel(\"S\", \"LOC\", \"X\", 0)\n", - " mapdl.cm(\"FIXED_END\", \"NODE\")\n", - "\n", - " # Load application node\n", - " mapdl.nsel(\"S\", \"LOC\", \"X\", length)\n", - " mapdl.nsel(\"R\", \"LOC\", \"Y\", height)\n", - " mapdl.cm(\"LOAD_APPLICATION_POINT\", \"NODE\")\n", - "\n", - " mapdl.finish() # Exit preprocessor\n", - "\n", - " mapdl.slashsolu() # Enter solution processor\n", - "\n", - " element_ids = mapdl.esel(\n", - " \"S\", \"CENT\", \"Y\", 0, mesh_size\n", - " ) # Select bottom row elements and store the ids\n", - "\n", - " # Generate quantities required to define the young's modulus stochastic process\n", - " cosine_frequency_list, cosine_eigen_values, cosine_constants = evaluate_KL_cosine_terms(\n", - " domain, correl_length_param, min_eigen_value\n", - " )\n", - " sine_frequency_list, sine_eigen_values, sine_constants = evaluate_KL_sine_terms(\n", - " domain, correl_length_param, min_eigen_value\n", - " )\n", - "\n", - " simulation_results = np.zeros(no_of_simulations)\n", - "\n", - " for simulation in range(no_of_simulations):\n", - " # Generate random variables and load needed for one realization of the process\n", - " cosine_random_variables_set = np.random.normal(0, 1, size=len(cosine_frequency_list))\n", - " sine_random_variables_set = np.random.normal(0, 1, size=len(sine_frequency_list))\n", - " load = -np.random.normal(10, 2**0.5) # Generate a random load\n", - "\n", - " material_property = 0 # Initialize material property ID\n", - " for element_id in element_ids:\n", - " material_property += 1\n", - " mapdl.get(\"ELEMENT_ID\", \"ELEM\", element_id, \"CENT\", \"X\")\n", - " element_centroid_x_coord = mapdl.parameters[\"ELEMENT_ID\"]\n", - " mapdl.esel(\n", - " \"S\", \"CENT\", \"X\", element_centroid_x_coord\n", - " ) # Select all elements having this coordinate as centroid\n", - "\n", - " # Evaluate young's modulus at this material point\n", - " young_modulus_value = young_modulus_realization(\n", - " cosine_frequency_list,\n", - " cosine_eigen_values,\n", - " cosine_constants,\n", - " cosine_random_variables_set,\n", - " sine_frequency_list,\n", - " sine_eigen_values,\n", - " sine_constants,\n", - " sine_random_variables_set,\n", - " domain,\n", - " element_centroid_x_coord,\n", - " )\n", - "\n", - " mapdl.mp(\n", - " \"EX\", f\"{material_property}\", young_modulus_value\n", - " ) # Define property ID, assign young's modulus\n", - " mapdl.mp(\"NUXY\", f\"{material_property}\", poisson_ratio) # Assign poisson ratio\n", - " mapdl.mpchg(material_property, \"ALL\") # Assign property to selected elements\n", - "\n", - " mapdl.allsel()\n", - "\n", - " mapdl.d(\"FIXED_END\", lab=\"UX\", value=0, lab2=\"UY\") # Apply fixed end BC\n", - " mapdl.f(\"LOAD_APPLICATION_POINT\", lab=\"FY\", value=load) # Apply load BC\n", - " mapdl.solve()\n", - "\n", - " # Displacement probe point - where Uy results will be extracted\n", - " mapdl.nsel(\"S\", \"LOC\", \"X\", 4)\n", - " displacement_probe_point = mapdl.nsel(\"R\", \"LOC\", \"Y\", 0)\n", - " displacement = mapdl.get(\n", - " \"DISP_AT_PROBE_POINT\", \"NODE\", int(displacement_probe_point[0]), \"U\", \"Y\"\n", - " )\n", - "\n", - " simulation_results[simulation] = displacement\n", - "\n", - " mapdl.mpdele(\"ALL\", \"ALL\")\n", - " if int((simulation + 1) % 10) == 0:\n", - " print(f\"Completed {simulation + 1} simulations in instance {instance_identifier} ...\")\n", - "\n", - " mapdl.exit()\n", - " print()\n", - " print(f\"All simulations completed in instance {instance_identifier}!\")\n", - "\n", - " return instance_identifier, no_of_simulations, simulation_results\n", - "\n", - "\n", - "def run_simulations_over_multple_instances(\n", - " length, height, thickness, mesh_size, no_of_simulations, no_of_instances\n", - "):\n", - " from pathlib import Path\n", - " from ansys.mapdl.core import MapdlPool\n", - "\n", - " # First determine the number of simulations to run per instance\n", - " if no_of_simulations % no_of_instances == 0:\n", - " # Simlations can be split equally across instances\n", - " simulations_per_instance = no_of_simulations // no_of_instances\n", - " simulations_per_instance_list = [simulations_per_instance for i in range(no_of_instances)]\n", - " else:\n", - " # Simulations can not be split equally across instances\n", - " simulations_per_instance = no_of_simulations // no_of_instances\n", - " simulations_per_instance_list = [\n", - " simulations_per_instance for i in range(no_of_instances - 1)\n", - " ]\n", - " remaining_simulations = no_of_simulations - sum(simulations_per_instance_list)\n", - " simulations_per_instance_list.append(remaining_simulations)\n", - "\n", - " path = Path.cwd()\n", - " pool = MapdlPool(no_of_instances, nproc=1, run_location=path, start_timeout=120)\n", - "\n", - " inputs = [\n", - " (length, height, thickness, mesh_size, simulations, id + 1)\n", - " for id, simulations in enumerate(simulations_per_instance_list)\n", - " ]\n", - "\n", - " overall_simulation_results = pool.map(run_simulations_threaded, inputs)\n", - " pool.exit()\n", - "\n", - " return overall_simulation_results" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Creating Pool: 100%|███████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:25<00:00, 2.56s/it]\n", - "MAPDL Running: 0%| | 0/10 [00:005x!Ty1TpY%kO_Y z=X|*L)BSq(7z_undG-_QnQN}O=4*tKf+Q9?2|64c9G0{cL2 zyMMof#lhKvHOX1i85rf6qm-5l92}0((-(Z9aDf#ZJRF=fMD)Gqm%VvZ-9(QE)FZ`< zK%^h~VEO~W9n1Z4H}}Kc%&Df``lf}27Qx3lpO#&>!+HJiKh`=$?mRmLy7csYVIox2 z{MT*%ZIZ>cf4(D~y!2ft6Z(nRwFZyya&hza*7xn0B_}%gKd+q^c83qVp#Qv{G1cS! 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z&s_ilZy*(5wT+I6X@T~}GjPr{z|hcphJ6r_0IUaC%87TKLF7Kc84GcYqUDRf zSC;P2%}GE$^gI5#BYLAPYE}avx7vo*d%Z@^94zY4(H$VM`A|lt zwUc%1RLuS{D-o$7Nv1_g(}Lt_b-@rO_X~|P0lH@XXKk@9z^b819`k!RqX?V>xe|5} z6B!4W&~&zg70giW87C+Rv;_gvB>#Kp@le_F@5S{25dQyOh>L{W^6%^aylVM< Date: Tue, 21 Jan 2025 12:55:42 +0100 Subject: [PATCH 17/26] fix: vale errors --- .../extended_examples/sfem/stochastic_fem.rst | 14 +++++++------- doc/styles/config/vocabularies/ANSYS/accept.txt | 8 ++++++++ 2 files changed, 15 insertions(+), 7 deletions(-) diff --git a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst index 69e1d556363..b472d78e49f 100644 --- a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst +++ b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst @@ -157,7 +157,7 @@ where :math:`\omega_{s,n}` is obtained as the solution of It is worth mentioning that :math:`\lambda` and :math:`\omega` in the series expansion are referred to as eigenvalue and frequency respectively. .. note:: - In the case of an asymmetric domain e.g. :math:`\mathbb{D}=[-t_{min},t_{max}]`, a shift parameter :math:`T = (t_{min}+t_{max})/2` is required and the corresponding + In the case of an asymmetric domain, for example, :math:`\mathbb{D}=[-t_{min},t_{max}]`, a shift parameter :math:`T = (t_{min}+t_{max})/2` is required and the corresponding symmetric domain becomes .. math:: D' = D - T = \biggl[\frac{t_{min}-t_{max}}{2}, \frac{t_{max}-t_{min}}{2} \biggr] @@ -166,7 +166,7 @@ It is worth mentioning that :math:`\lambda` and :math:`\omega` in the series exp .. math:: X(t) = \sum_{n=1}^\infty \sqrt{\lambda_{c,n}}\cdot\varphi_{c,n}(t-T)\cdot\xi_{c,n} + \sum_{n=1}^\infty \sqrt{\lambda_{s,n}}\cdot\varphi_{s,n}(t-T)\cdot\xi_{s,n},\quad t\in\mathbb{D} -The K-L expansion of a gaussian process has the property that :math:`\xi_{c,n}` and :math:`\xi_{s,n}` are independent +The K-L expansion of a Gaussian process has the property that :math:`\xi_{c,n}` and :math:`\xi_{s,n}` are independent standard normal variables, that is, they follow the :math:`\mathcal{N}(0,1)` distribution. The other great property is that :math:`\lambda_{c,n}` and :math:`\lambda_{s,n}` converge to zero fast (in the mean square sense). For practical implementation, this means that the infinite series of the K-L expansion above is truncated after a finite number of terms, giving the approximation: @@ -186,7 +186,7 @@ Equation :math:numref:`approximation` is computationally feasible to handle. Let 3. To generate additional realizations, we simply draw new random values for :math:`\xi_{c,n}, n=1,\dots ,P, \quad \xi_{s,n}, n=1,\dots ,Q` each from :math:`\mathcal{N}(0,1)` .. note:: - In this case of a field, the same discussion above applies as the only difference is a change in notation (e.g. :math:`t` to :math:`x`). + In this case of a field, the same discussion above applies as the only difference is a change in notation (for example :math:`t` to :math:`x`). The Monte Carlo simulation -------------------------- @@ -215,7 +215,7 @@ In the following plane stress problem .. figure:: problem.png - A two-dimensional cantilver structure under a point load + A two-dimensional cantilever structure under a point load :math:`P` is a random variable following the Gaussian distribution :math:`\mathcal{N}(0,1)` (kN) and the modulus of elasticity is a random field given by the expression: @@ -313,7 +313,7 @@ For the variance: We should then expect that as the number of realizations increase indefinitely, the ensemble mean and variance will converge towards theoretical values calculated in :math:numref:`theoretical mean` and :math:numref:`theoretical variance`: -First we generate a lot of realizations, 5000 is enough i.e. the same as the number of simulations we are required to run later on. We then +First we generate a lot of realizations, 5000 is enough, that is, the same as the number of simulations we are required to run later on. We then perform some statistical processing on these realizations .. literalinclude:: sfem.py @@ -381,7 +381,7 @@ Required arguments can be passed to the above function to run the simulations: Answering problem questions ~~~~~~~~~~~~~~~~~~~~~~~~~~~ To finish answering the first question (simulations have already been run), we proceed to perform a statistical -post-processing of simulation results to determine the pdf of the response :math:`u`: +post-processing of simulation results to determine the probability density function of the response :math:`u`: .. literalinclude:: sfem.py :language: python @@ -425,7 +425,7 @@ To run simulations over 10 MAPDL instances, the function above is simply called Now the simulations can be completed much faster. .. tip:: - In a local test, using the MapdlPool approach (with 10 MAPDL instances) took about 38 mins to run, while a single instance run + In a local test, using the MapdlPool approach (with 10 MAPDL instances) took about 38 minutes to run, while a single instance run lasted for about 3 hours. The simulation speed depends on a multitude of factors but this comparison provides an idea of the speed gain to expect when utilizing multiple instances. diff --git a/doc/styles/config/vocabularies/ANSYS/accept.txt b/doc/styles/config/vocabularies/ANSYS/accept.txt index 583fb27fac1..a2e04fc3db7 100644 --- a/doc/styles/config/vocabularies/ANSYS/accept.txt +++ b/doc/styles/config/vocabularies/ANSYS/accept.txt @@ -47,6 +47,7 @@ BCs Block Lanzos Boyce breakpoint +cantilever centerline CentOS CentOS7 @@ -58,6 +59,7 @@ datas delet Dependabot Dev +Dimitris devcontainer DevContainer dof @@ -76,6 +78,7 @@ FEMs filname Fortran FSW +Giovanis GitHub Gmsh GPa @@ -86,10 +89,12 @@ hexahedral hostname HTML Image[Mm]agick +Ioannis imagin importlib ist Julia +Kalogeris Krylov kwarg Lanzos @@ -118,6 +123,7 @@ NORML NumPy onefile optiSLang +Papadopoulos parm perf performant @@ -152,6 +158,7 @@ sord spotweld squeue srun +stationarity struc subselected substep @@ -173,6 +180,7 @@ UPF UPFs viscoplastic vise +Vissarion Visual Studio Code von VTK From f58d8b303c5ba1feff7c244717832b01de9cd6a2 Mon Sep 17 00:00:00 2001 From: moe-ad Date: Tue, 21 Jan 2025 13:46:04 +0100 Subject: [PATCH 18/26] fix: vale errors --- .../extended_examples/sfem/stochastic_fem.rst | 86 +++++++++---------- .../config/vocabularies/ANSYS/accept.txt | 1 - 2 files changed, 43 insertions(+), 44 deletions(-) diff --git a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst index b472d78e49f..36266e49926 100644 --- a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst +++ b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst @@ -102,16 +102,16 @@ realization/sample function assigned to each outcome of an experiment. A random field :math:`E(x)` viewed as a collection of random variables or as realizations .. note:: - The concepts above generalize to more dimensions, for example, a random vector instead of a random - variable, or an :math:`\mathbb{R}^d`-valued stochastic process. The presentation above is however + The concepts in the preceding sections generalize to more dimensions, for example, a random vector instead of a random + variable, or an :math:`\mathbb{R}^d`-valued stochastic process. The preceding presentation is however sufficient for this example. Series expansion of stochastic processes ---------------------------------------- Since a stochastic process involves an infinite number of random variables, most engineering applications -involving stochastic processes will be mathematically and computationally intractable if there isn't a way of -approximating them with a series of a finite number of random variables. A series expansion method which will -be used in this example is explained next. +involving stochastic processes are mathematically and computationally intractable if there isn't a way of +approximating them with a series of a finite number of random variables. A series expansion method used in +this example is explained next. The Karhunen-Loève (K-L) series expansion for a Gaussian process ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ @@ -169,24 +169,24 @@ It is worth mentioning that :math:`\lambda` and :math:`\omega` in the series exp The K-L expansion of a Gaussian process has the property that :math:`\xi_{c,n}` and :math:`\xi_{s,n}` are independent standard normal variables, that is, they follow the :math:`\mathcal{N}(0,1)` distribution. The other great property is that :math:`\lambda_{c,n}` and :math:`\lambda_{s,n}` converge to zero fast (in the mean square sense). For practical implementation, -this means that the infinite series of the K-L expansion above is truncated after a finite number of terms, giving the approximation: +this means that the infinite series of the K-L expansion is truncated after a finite number of terms, giving the approximation: .. math:: X(t) \approx \hat{X}(t) = \sum_{n=1}^P \sqrt{\lambda_{c,n}}\cdot\varphi_{c,n}(t)\cdot\xi_{c,n} + \sum_{n=1}^Q \sqrt{\lambda_{s,n}}\cdot\varphi_{s,n}(t)\cdot\xi_{s,n} :label: approximation -Equation :math:numref:`approximation` is computationally feasible to handle. Let's summarize how it can be used to generate realizations of :math:`X(t)`: +Equation :math:numref:`approximation` is computationally feasible to handle. A summary of how to use it to generate realizations of :math:`X(t)` follows: -1. To generate the j-th realization, we draw a random value for each :math:`\xi_{c,n}, n=1,\dots ,P, \quad \xi_{s,n}, n=1,\dots ,Q` from the standard +1. To generate the j-th realization, draw a random value for each :math:`\xi_{c,n}, n=1,\dots ,P, \quad \xi_{s,n}, n=1,\dots ,Q` from the standard normal distribution :math:`\mathcal{N}(0,1)` and obtain :math:`\xi_{c,1}^j,\dots ,\xi_{c,P}^j, \quad \xi_{s,1}^j,\dots ,\xi_{s,P}^j` -2. We insert these values into equation :math:numref:`approximation` in other to obtain the j-th realization: +2. Insert these values into equation :math:numref:`approximation` in other to obtain the j-th realization: .. math:: \hat{X}^j(t) = \sum_{n=1}^P \sqrt{\lambda_{c,n}}\cdot\varphi_{c,n}(t)\cdot\xi_{c,n}^j + \sum_{n=1}^Q \sqrt{\lambda_{s,n}}\cdot\varphi_{s,n}(t)\cdot\xi_{s,n}^j -3. To generate additional realizations, we simply draw new random values for :math:`\xi_{c,n}, n=1,\dots ,P, \quad \xi_{s,n}, n=1,\dots ,Q` each from :math:`\mathcal{N}(0,1)` +3. To generate additional realizations, simply draw new random values for :math:`\xi_{c,n}, n=1,\dots ,P, \quad \xi_{s,n}, n=1,\dots ,Q` each from :math:`\mathcal{N}(0,1)` .. note:: - In this case of a field, the same discussion above applies as the only difference is a change in notation (for example :math:`t` to :math:`x`). + In this case of a field, the preceding discussion applies as the only difference is a change in notation (for example :math:`t` to :math:`x`). The Monte Carlo simulation -------------------------- @@ -198,14 +198,14 @@ to .. math:: \pmb{K}(\pmb{\xi})\pmb{U}(\pmb{\xi}) = \pmb{F}(\pmb{\xi}) -where :math:`\pmb{\xi}` collects a sources of system randomness. The Monte Carlo simulation for solving the equation above +where :math:`\pmb{\xi}` collects a sources of system randomness. The Monte Carlo simulation for solving the preceding equation consists of generating a large number of :math:`N_{sim}` of samples :math:`\pmb{\xi}, i=1,\dots ,N_{sim}` from their probability distribution and for each of these samples, solving the deterministic problem .. math:: \pmb{K}(\pmb{\xi}_{(i)})\pmb{U}(\pmb{\xi}_{(i)}) = \pmb{F}(\pmb{\xi}_{(i)}) The next step is to collect the :math:`N_{sim}` response vectors :math:`\pmb{U} := \pmb{U}(\pmb{\xi}_{(i)})` and perform a statistical -post-processing in order to extract useful information such as mean value, variance, histogram, +post-processing to extract useful information such as mean value, variance, histogram, empirical pdf/cdf, etc. @@ -224,29 +224,29 @@ random field given by the expression: with :math:`f(x)` being a zero mean stationary Gaussian field with unit variance. The covariance function for :math:`f` is -.. math:: C_f(x_i,x_j)=e^{-\frac{\lvert x_i-x_j \rvert}{3}} +.. math:: C_f(x_r,x_s)=e^{-\frac{\lvert x_r-x_s \rvert}{3}} -We are to do the following: +The following are required: 1. Using the K-L series expansion, generate 5000 realizations for :math:`E(x)` and perform Monte Carlo simulation to determine the probability density function of the response :math:`u`, at the bottom right corner of the cantilever. 2. If some design code stipulates that the displacement :math:`u` must not exceed :math:`0.2 \: m`, how confident can - we be that the above structure meets this requirement? + one be that the structure meets this requirement? .. note:: - This example really emphasizes how PyMAPDL can help to supercharge workflows. At a very high level, what will be done - in subsequent sections involves using python libraries to handle computations related to the stochasticity of the problem, and - using MAPDL to run the necessary simulations, all within the comfort of a python environment. + This example really emphasizes how PyMAPDL can help to supercharge workflows. At a very high level, subsequent sections + involves using python libraries to handle computations related to the stochasticity of the problem, and using MAPDL to + run the necessary simulations, all within the comfort of a python environment. Evaluating the young modulus ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -Firstly, we implement code that allows us to represent the zero-mean Gaussian field :math:`f`. This simply means solving +Firstly, code that allows representation of the zero-mean Gaussian field :math:`f` is first implemented. This simply means solving :math:numref:`cosine equation` and :math:numref:`sine equation`, then substituting calculated values into :math:numref:`cosine terms` and :math:numref:`sine terms` to obtain the constant terms in those equations. The number of retained terms :math:`P` and :math:`Q` in :math:numref:`approximation` can be automatically determined -by structuring our code to stop computing values when :math:`\lambda_{c,n}, \lambda_{s,n}` become lower than a +by structuring the code to stop computing values when :math:`\lambda_{c,n}, \lambda_{s,n}` become lower than a desired accuracy level. The implementation is as follows: .. literalinclude:: sfem.py @@ -268,7 +268,7 @@ And then the function for evaluating the young modulus itself is straight forwar Realizations of the young modulus +++++++++++++++++++++++++++++++++++++++++++++ -We can now generate sample realizations of the young's modulus to see how they look like: +Sample realizations of the young's modulus can now be generated to see how they look like: .. literalinclude:: sfem.py :language: python @@ -280,8 +280,8 @@ We can now generate sample realizations of the young's modulus to see how they l Verification of the implementation ++++++++++++++++++++++++++++++++++ -Let us compute the theoretical mean and variance of the young modulus and then show that our implementation of the -young's modulus is correct. +The theoretical mean and variance of the young modulus can be computed and this can be used to verify the correctness +of the implemented code. For the mean: @@ -310,17 +310,17 @@ For the variance: Var(E) = 10^8 \: {kN}^2/m^4 -We should then expect that as the number of realizations increase indefinitely, the ensemble mean and -variance will converge towards theoretical values calculated in :math:numref:`theoretical mean` and :math:numref:`theoretical variance`: +It is expected that as the number of realizations increase indefinitely, the ensemble mean and +variance should converge towards theoretical values calculated in :math:numref:`theoretical mean` and :math:numref:`theoretical variance`. -First we generate a lot of realizations, 5000 is enough, that is, the same as the number of simulations we are required to run later on. We then -perform some statistical processing on these realizations +Firstly, several realizations are generated. 5000 is enough, which is the same as the number of simulations to be run later on. Statistical processing +is then performed on these realizations. .. literalinclude:: sfem.py :language: python :lines: 350-385 -We can then generate a plot of the mean vs the number of realizations +A plot of the mean vs the number of realizations can be generated: .. literalinclude:: sfem.py :language: python @@ -330,7 +330,7 @@ We can then generate a plot of the mean vs the number of realizations Convergence of the mean to the true value as the number of realizations is increased -And also a plot of the variance vs the number of realizations +And also a plot of the variance vs the number of realizations: .. literalinclude:: sfem.py :language: python @@ -340,22 +340,22 @@ And also a plot of the variance vs the number of realizations Convergence of the variance to the true value as the number of realizations is increased -The plots above confirms that our implementation is indeed correct. If one desires more accuracy, the minimum eigenvalue +The preceding plots confirms that the implementation is indeed correct. If one desires more accuracy, the minimum eigenvalue can be further decreased but the value already chosen is sufficient. Running the simulations ~~~~~~~~~~~~~~~~~~~~~~~ -Now we focus on the PyMAPDL part of this example. Remember that the problem requires running 5000 simulations. Therefore, we need +Now focus shifts to the PyMAPDL part of this example. Remember that the problem requires running 5000 simulations. Therefore, there is need to write a workflow that does the following: 1. Create the geometry of the cantilever model -2. Mesh the model. For this, 4-node PLANE182 elements will be used +2. Mesh the model. For this, 4-node PLANE182 elements is going to be used 3. Generate one realization of :math:`E` and one sample of :math:`P` for each simulation -4. For each simulation, loop through the elements and for each element, use the realization - above to assign the value of the young's modulus. Also assign the load for each simulation. +4. For each simulation, loop through the elements and for each element, use the generated + realization to assign the value of the young's modulus. Also assign the load for each simulation. 5. Solve the model and store :math:`u` for each simulation. @@ -366,13 +366,13 @@ to write a workflow that does the following: chosen for this implementation. The method chosen becomes insignificant with a finer mesh as both methods should produce similar results. -A function implementing the steps above follows: +A function implementing the preceding steps follows: .. literalinclude:: sfem.py :language: python :lines: 444-556 -Required arguments can be passed to the above function to run the simulations: +Required arguments can be passed to the defined function to run the simulations: .. literalinclude:: sfem.py :language: python @@ -380,8 +380,8 @@ Required arguments can be passed to the above function to run the simulations: Answering problem questions ~~~~~~~~~~~~~~~~~~~~~~~~~~~ -To finish answering the first question (simulations have already been run), we proceed to perform a statistical -post-processing of simulation results to determine the probability density function of the response :math:`u`: +To finish answering the first question (simulations have already been run), a statistical post-processing of +simulation results can performed to determine the probability density function of the response :math:`u`: .. literalinclude:: sfem.py :language: python @@ -391,7 +391,7 @@ post-processing of simulation results to determine the probability density funct The probability density function of response :math:`u` -To answer the second question, we simply evaluate the probability that the response :math:`u` is less than +To answer the second question, simply evaluate the probability that the response :math:`u` is less than :math:`0.2 \: m`: .. literalinclude:: sfem.py @@ -402,13 +402,13 @@ The computed probability is approximately 99%, which is a measure of how well th requirement. .. note:: - The implementation above was split into several functions so users can modify practically any aspect of the problem + The overall implementation of this example was split into several functions so users can modify practically any aspect of the problem statement with minimal edits to the code for testing out other scenarios. For example, different structural geometry, different mesh size, different loading condition etc. Improving simulation speed via multi-threading ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -One of the main drawbacks of MCS is the number of simulations required. In the example above, 5000 simulations can take quite +One of the main drawbacks of MCS is the number of simulations required. In this example, 5000 simulations can take quite some time to run on a single MAPDL instance. To speed things up, the :class:`~ansys.mapdl.core.pool.MapdlPool` class can be utilized to run simulations across multiple MAPDL instances. The implementation is as follows: @@ -416,7 +416,7 @@ to run simulations across multiple MAPDL instances. The implementation is as fol :language: python :lines: 589-738 -To run simulations over 10 MAPDL instances, the function above is simply called with appropriate arguments: +To run simulations over 10 MAPDL instances, the preceding function is simply called with appropriate arguments: .. literalinclude:: sfem.py :language: python diff --git a/doc/styles/config/vocabularies/ANSYS/accept.txt b/doc/styles/config/vocabularies/ANSYS/accept.txt index a2e04fc3db7..493aa3b9d97 100644 --- a/doc/styles/config/vocabularies/ANSYS/accept.txt +++ b/doc/styles/config/vocabularies/ANSYS/accept.txt @@ -47,7 +47,6 @@ BCs Block Lanzos Boyce breakpoint -cantilever centerline CentOS CentOS7 From b6ed31aae40a68fba14faf31ed72d070590642c6 Mon Sep 17 00:00:00 2001 From: moe-ad Date: Tue, 21 Jan 2025 17:01:52 +0100 Subject: [PATCH 19/26] fix: documentation review --- .../examples/extended_examples/sfem/sfem.py | 108 +++++++++--------- .../extended_examples/sfem/stochastic_fem.rst | 31 +++-- 2 files changed, 69 insertions(+), 70 deletions(-) diff --git a/doc/source/examples/extended_examples/sfem/sfem.py b/doc/source/examples/extended_examples/sfem/sfem.py index 4e81f12f277..b37f5fae594 100644 --- a/doc/source/examples/extended_examples/sfem/sfem.py +++ b/doc/source/examples/extended_examples/sfem/sfem.py @@ -33,23 +33,23 @@ def find_solution( acceptable_solution_error: float, solution_range: Tuple[float, float], ) -> float: - """Find the solution of g(x) = 0 within solution range where g(x) is non-linear. + """Find the solution of g(x) = 0 within a solution range where g(x) is non-linear. Parameters ---------- func : Callable[float, float] - The function definition + Definition of the function. derivative_func : Callable[float, float] - The derivative of the above function + Derivative of the preceding function. acceptable_solution_error : float - Error at which the solution is acceptable + Error the solution is acceptable at. solution_range : Tuple[float, float] - The range within which the solution will be searched + Range for searching for the solution. Returns ------- float - Solution to g(x) = 0 + Solution to g(x) = 0. """ current_guess = random.uniform(*solution_range) @@ -83,21 +83,21 @@ def find_solution( def evaluate_KL_cosine_terms( domain: Tuple[float, float], correl_length_param: float, min_eigen_value: float ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]: - """Build array of eigenvalues and constants of the cosine terms in the KL expansion of a gaussian stochastic process. + """Build array of eigenvalues and constants of the cosine terms in the KL expansion of a Gaussian stochastic process. Parameters ---------- domain : Tuple[float, float] - Domain over which the KL representation of the stochastic process should be found + Domain for finding the KL representation of the stochastic process. correl_length_param : float - Correlation length parameter of the autocorrelation function of the process + Correlation length parameter of the autocorrelation function of the process. min_eigen_value : float - Minimum eigenvalue to achieve require accuracy + Minimum eigenvalue to achieve require accuracy. Returns ------- Tuple[np.ndarray, np.ndarray, np.ndarray] - Arrays of frequencies, eigenvalues, and constants of retained cosine terms (P in total) in the KL expansion + Arrays of frequencies, eigenvalues, and constants of the retained cosine terms (P in total) in the KL expansion. """ A = (domain[1] - domain[0]) / 2 # Symmetric domain parameter -> [-A, A] @@ -144,21 +144,21 @@ def cosine_constant(w_n): def evaluate_KL_sine_terms( domain: Tuple[float, float], correl_length_param: float, min_eigen_value: float ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]: - """Build array of eigenvalues and constants of the sine terms in the KL expansion of a gaussian stochastic process. + """Build an array of eigenvalues and constants of the sine terms in the KL expansion of a gaussian stochastic process. Parameters ---------- domain : Tuple[float, float] - Domain over which the KL representation of the stochastic process should be found + Domain for finding the KL representation of the stochastic process. correl_length_param : float - Correlation length parameter of the autocorrelation function of the process + Correlation length parameter of the autocorrelation function of the process. min_eigen_value : float - Minimum eigenvalue to achieve require accuracy + Minimum eigenvalue to achieve require accuracy. Returns ------- Tuple[np.ndarray, np.ndarray, np.ndarray] - Arrays of frequencies, eigenvalues, and constants of retained sine terms (Q in total) in the KL expansion + Arrays of frequencies, eigenvalues, and constants of the retained sine terms (Q in total) in the KL expansion. """ A = (domain[1] - domain[0]) / 2 # Symmetric domain parameter -> [-A, A] @@ -214,40 +214,40 @@ def stochastic_field_realization( domain: Tuple[float, float], evaluation_point: float, ) -> float: - """The realization of the gaussian field f(x) + """Realization of the Gaussian field f(x). Parameters ---------- cosine_frequency_array : np.ndarray - Array of length P, containing frequencies associated with retained cosine terms + Array of length P, containing the frequencies associated with the retained cosine terms. cosine_eigen_values : np.ndarray - Array of length P, containing eigenvalues associated with retained cosine terms + Array of length P, containing the eigenvalues associated with the retained cosine terms. cosine_constants : np.ndarray - Array of length P, containing constants associated with retained cosine terms + Array of length P, containing constants associated with the retained cosine terms. cosine_random_variables_set : np.ndarray - Array of length P, containing random variable drawn from N(0,1) for the cosine terms + Array of length P, containing the random variables drawn from N(0,1) for the cosine terms. sine_frequency_array : np.ndarray - Array of length Q, containing frequencies associated with retained sine terms + Array of length Q, containing the frequencies associated with the retained sine terms. sine_eigen_values : np.ndarray - Array of length Q, containing eigenvalues associated with retained sine terms + Array of length Q, containing eigenvalues associated with retained sine terms. sine_constants : np.ndarray - Array of length Q, containing constants associated with retained sine terms + Array of length Q, containing the constants associated with the retained sine terms. sine_random_variables_set : np.ndarray - Array of length P, containing random variable drawn from N(0,1) for the sine terms + Array of length P, containing the random variable drawn from N(0,1) for the sine terms. domain : Tuple[float, float] - Domain over which the KL representation of the stochastic process should be found + Domain for finding the KL representation of the stochastic process. evaluation_point : float - Point within the domain at which the value of a realization is required + Point within the domain at which the value of a realization is required. Returns ------- float The value of the realization at a given point within the domain """ - # Shift parameter -> Because we had solved for terms in a symmetric domain [-A, A] + # Shift parameter -> Because terms are solved in a symmetric domain [-A, A] T = (domain[0] + domain[1]) / 2 - # Making use of array operation provided by the numpy package is much simpler for expressing the stochastic process + # Using the array operation provided by the numpy package is much simpler for expressing the stochastic process cosine_function_terms = ( np.sqrt(cosine_eigen_values) * cosine_constants @@ -309,7 +309,7 @@ def young_modulus_realization( domain, correl_length_param, min_eigen_value ) -# Now let's see how some realizations looks like +# See what the realizations looks like no_of_realizations = 10 x = np.linspace(domain[0], domain[1], 101) @@ -347,7 +347,7 @@ def young_modulus_realization( plt.show() -# Verification that the above implementation indeed represents the young's modulus +# Verify that the previous implementation represents the Young's modulus no_of_realizations = 5000 x = np.linspace(domain[0], domain[1], 101) realization_collection = np.zeros((no_of_realizations, len(x))) @@ -384,7 +384,7 @@ def young_modulus_realization( ensemble_mean_with_realization[i] = np.mean(realization_collection[: i + 1, :]) ensemble_var_with_realization[i] = np.var(realization_collection[: i + 1, :]) -# Plot of ensemble mean +# Plot the ensemble mean fig, ax = plt.subplots() fig.set_size_inches(15, 8) ax.plot(ensemble_mean_with_realization, label="Computed mean") @@ -425,15 +425,15 @@ def run_simulations( Parameters ---------- length : float - The length of the cantilever structure + Length of the cantilever structure. height : float - The height of the cantilever structure + Height of the cantilever structure. thickness : float - The thickness of the cantilever structure + Thickness of the cantilever structure. mesh_size : float - The desired mesh size + Desired mesh size. no_of_simulations : int - The number of simulations to run + Number of simulations to run. Returns ------- @@ -480,7 +480,7 @@ def run_simulations( "S", "CENT", "Y", 0, mesh_size ) # Select bottom row elements and store the ids - # Generate quantities required to define the young's modulus stochastic process + # Generate quantities required to define the Young's modulus stochastic process cosine_frequency_list, cosine_eigen_values, cosine_constants = ( evaluate_KL_cosine_terms(domain, correl_length_param, min_eigen_value) ) @@ -539,7 +539,7 @@ def run_simulations( mapdl.f("LOAD_APPLICATION_POINT", lab="FY", value=load) # Apply load BC mapdl.solve() - # Displacement probe point - where Uy results will be extracted + # Displacement probe point - where Uy results are to be extracted displacement_probe_point = mapdl.queries.node(length, 0, 0) displacement = mapdl.get_value("NODE", displacement_probe_point, "U", "Y") @@ -547,7 +547,7 @@ def run_simulations( mapdl.mpdele("ALL", "ALL") if (simulation + 1) % 10 == 0: - print(f"Completed {simulation + 1} simulations ...") + print(f"Completed {simulation + 1} simulations.") mapdl.exit() print() @@ -568,7 +568,7 @@ def run_simulations( ) ) -# Perform statistical post processing and plot the pdf +# Perform statistical postprocessing and plot the PDF import scipy.stats as stats kde = stats.gaussian_kde(simulation_results) # Kernel density estimate @@ -581,13 +581,13 @@ def run_simulations( ax.legend() plt.show() -# We can then proceed to evaluate the probability that response u is less than 0.2 m +# Proceed to evaluate the probability that the response u is less than 0.2 m probability = kde.integrate_box_1d(-0.2, x_eval[-1]) -print(f"The probability that u is less than 0.2 m is {probability:.0%}") +print(f"The probability that u is less than 0.2 m is {probability:.0%}.") # Multi-threaded approach -# Note, no of instances should not be more than the number of available CPU cores on your PC +# Note that the number of instances should not be more than the number of available CPU cores on your PC def run_simulations_threaded( mapdl, length, height, thickness, mesh_size, no_of_simulations, instance_identifier ): @@ -606,7 +606,7 @@ def run_simulations_threaded( mapdl.esize(mesh_size) mapdl.amesh("ALL") - # Fixed edge + # Defined fixed edge mapdl.nsel("S", "LOC", "X", 0) mapdl.cm("FIXED_END", "NODE") @@ -623,7 +623,7 @@ def run_simulations_threaded( "S", "CENT", "Y", 0, mesh_size ) # Select bottom row elements and store the ids - # Generate quantities required to define the young's modulus stochastic process + # Generate quantities required to define the Young's modulus stochastic process cosine_frequency_list, cosine_eigen_values, cosine_constants = ( evaluate_KL_cosine_terms(domain, correl_length_param, min_eigen_value) ) @@ -634,7 +634,7 @@ def run_simulations_threaded( simulation_results = np.zeros(no_of_simulations) for simulation in range(no_of_simulations): - # Generate random variables and load needed for one realization of the process + # Generate random variables and the load needed for one realization of the process cosine_random_variables_set = np.random.normal( 0, 1, size=len(cosine_frequency_list) ) @@ -652,7 +652,7 @@ def run_simulations_threaded( "S", "CENT", "X", element_centroid_x_coord ) # Select all elements having this coordinate as centroid - # Evaluate young's modulus at this material point + # Evaluate Young's modulus at this material point young_modulus_value = young_modulus_realization( cosine_frequency_list, cosine_eigen_values, @@ -668,10 +668,10 @@ def run_simulations_threaded( mapdl.mp( "EX", f"{material_property}", young_modulus_value - ) # Define property ID, assign young's modulus + ) # Define property ID and assign Young's modulus mapdl.mp( "NUXY", f"{material_property}", poisson_ratio - ) # Assign poisson ratio + ) # Assign Poisson ratio mapdl.mpchg( material_property, "ALL" ) # Assign property to selected elements @@ -682,7 +682,7 @@ def run_simulations_threaded( mapdl.f("LOAD_APPLICATION_POINT", lab="FY", value=load) # Apply load BC mapdl.solve() - # Displacement probe point - where Uy results will be extracted + # Displacement probe point - where Uy results are to be extracted displacement_probe_point = mapdl.queries.node(length, 0, 0) displacement = mapdl.get_value("NODE", displacement_probe_point, "U", "Y") @@ -691,12 +691,12 @@ def run_simulations_threaded( mapdl.mpdele("ALL", "ALL") if (simulation + 1) % 10 == 0: print( - f"Completed {simulation + 1} simulations in instance {instance_identifier} ..." + f"Completed {simulation + 1} simulations in instance {instance_identifier}." ) mapdl.exit() print() - print(f"All simulations completed in instance {instance_identifier}!") + print(f"All simulations completed in instance {instance_identifier}.") return instance_identifier, no_of_simulations, simulation_results @@ -716,7 +716,7 @@ def run_simulations_over_multple_instances( simulations_per_instance for i in range(no_of_instances) ] else: - # Simulations can not be split equally across instances + # Simulations cannot be split equally across instances simulations_per_instance = no_of_simulations // no_of_instances simulations_per_instance_list = [ simulations_per_instance for i in range(no_of_instances - 1) diff --git a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst index 36266e49926..7844e199321 100644 --- a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst +++ b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst @@ -3,33 +3,33 @@ Stochastic finite element method with PyMAPDL ============================================= -This example leverages PyMAPDL for stochastic finite element analysis via the Monte Carlo simulation. -Numerous advantages / workflow possibilities that PyMAPDL affords users is demonstrated through this -extended example. Important theoretical concepts are first explained before the example is presented. +This example leverages PyMAPDL for stochastic finite element analysis using the Monte Carlo simulation. +This extended example demonstrates numerous advantages and workflow possibilities that PyMAPDL +provides. It explains important theoretical concepts before presenting the example. Introduction ------------ -Often in a mechanical system, system parameters (geometry, materials, loads, etc.) and response parameters -(displacement, strain, stress, etc) are taken to be deterministic. This simplification, while sufficient for a -wide range of engineering applications, results in a crude approximation of actual system behaviour. +Often in a mechanical system, system parameters (such as geometry, materials, and loads) and response parameters +(such as displacement, strain, and stress) are taken to be deterministic. This simplification, while sufficient for a +wide range of engineering applications, results in a crude approximation of actual system behavior. To obtain a more accurate representation of a physical system, it is essential to consider the randomness in system parameters and loading conditions, along with the uncertainty in their estimation and their spatial variability. The finite element method is undoubtedly the most widely used tool for solving deterministic -physical problems today and to account for randomness and uncertainty in the modeling of engineering systems, +physical problems today. To account for randomness and uncertainty in the modeling of engineering systems, the stochastic finite element method (SFEM) was introduced. -The stochastic finite element method (SFEM) extends the classical deterministic finite element approach +SFEM extends the classical deterministic finite element approach to a stochastic framework, offering various techniques for calculating response variability. Among these, the Monte Carlo simulation (MCS) stands out as the most prominent method. Renowned for its versatility and ease of implementation, MCS can be applied to virtually any type of problem in stochastic analysis. -Random variables vs stochastic processes ----------------------------------------- -A distinction between random variables and stochastic processes is attempted in this section. Explaining these -concepts is important since they are used for modelling the system randomness. Random variables are easier to -understand from elementary probability theory, the same cannot be said for stochastic processes. Readers are -advised to consult books on SFEM if the explanation here seems too brief. [1]_ and [2]_ are recommended resources. +Random variables versus stochastic processes +-------------------------------------------------- +This section attempts to explain how random variables and stochastic processes differ. Because these +concepts are used for modeling the system randomness, explaining them is important. Random variables are easier to +understand from elementary probability theory, which isn't the case for stochastic processes. If the following +explanations are too brief, consult books on SFEM. Both [1]_and [2]_are recommended resources. Random variables ~~~~~~~~~~~~~~~~ @@ -40,8 +40,7 @@ random variable is written as :math:`X`. Practical example +++++++++++++++++ Imagine a beam with a concentrated load :math:`P` applied at a specific point. The value of :math:`P` -is uncertain—it could vary due to manufacturing tolerances, loading conditions, or measurement errors. Mathematically, -:math:`P` is a random variable: +is uncertain. It could vary due to manufacturing tolerances, loading conditions, or measurement errors. Mathematically, .. math:: P : \Theta \longrightarrow \mathbb{R} From 53c37bae5ebabc612acd3f531092dbb19dc963b2 Mon Sep 17 00:00:00 2001 From: Muhammed Adedigba <68085496+moe-ad@users.noreply.github.com> Date: Tue, 21 Jan 2025 21:26:56 +0100 Subject: [PATCH 20/26] fix: suggestions from code review Co-authored-by: Kathy Pippert <84872299+PipKat@users.noreply.github.com> --- .../extended_examples/sfem/stochastic_fem.rst | 140 +++++++++--------- 1 file changed, 70 insertions(+), 70 deletions(-) diff --git a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst index 7844e199321..902f643aa1f 100644 --- a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst +++ b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst @@ -44,32 +44,33 @@ is uncertain. It could vary due to manufacturing tolerances, loading conditions, .. math:: P : \Theta \longrightarrow \mathbb{R} -where :math:`\Theta` is the sample space of all possible loading scenarios, and :math:`\mathbb{R}` represents the set of +In the preceding equation, :math:`\Theta` is the sample space of all possible loading scenarios, and :math:`\mathbb{R}` represents the set of possible load magnitudes. For example, :math:`P` could be modeled as a random variable with a probability density function (PDF) such as: .. math:: f_P(p) = \frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{(p-\mu)^2}{2\sigma^2}}, -where :math:`\mu` is the mean load, and :math:`\sigma^2` is its variance. +Here :math:`\mu` is the mean load, and :math:`\sigma^2` is its variance. Stochastic processes ~~~~~~~~~~~~~~~~~~~~ **Definition:** -recall that a random variable is defined as a rule that assigns a number :math:`X` to every outcome :math:`\theta` +Recall that a random variable is defined as a rule that assigns a number :math:`X` to every outcome :math:`\theta` of an experiment. However, in some applications, the experiment evolves with respect to a deterministic parameter :math:`t`, which belongs to an interval :math:`I`. For example, this occurs in an engineering system subjected to random dynamic loads over a time interval :math:`I \subseteq \mathbb{R}^+`. In such cases, the system's response at a specific material point is described not by a single random variable but by a collection of random variables :math:`\{X(t)\}` indexed by :math:`t \in I`. + This 'infinite' collection of random variables over the interval :math:`I` is called a stochastic process and is denoted as -:math:`\{X(t), t \in I\}` or simply :math:`X`. In this way, a stochastic process generalizes the concept of a random variable, +:math:`\{X(t), t \in I\}` or simply :math:`X`. In this way, a stochastic process generalizes the concept of a random variable as it assigns to each outcome :math:`\theta` of the experiment a function :math:`X(t, \theta)`, known as a realization or sample function. Lastly, if :math:`X` is indexed by some spatial coordinate :math:`s \in D \subseteq \mathbb{R}^n` rather than time :math:`t`, then :math:`\{X(s), s \in D\}` is called a random field. Practical example +++++++++++++++++ -Now, consider the material property of the beam, such as Young's modulus :math:`E(x)`, which may vary randomly along -the length of the beam :math:`x`. Instead of being a single random value, :math:`E(x)` is a random field—its value +Consider the material property of the beam, such as Young's modulus :math:`E(x)`, which may vary randomly along +the length of the beam :math:`x`. Instead of being a single random value, :math:`E(x)` is a random field. Its value is uncertain at each point along the domain, and it changes continuously across the beam. Mathematically, :math:`E(x)` is a random field: @@ -86,19 +87,20 @@ property, making its statistics completely defined by its mean (:math:`\mu_E`), (:math:`\sigma_E`) and covariance function :math:`C_E(x_i,x_j)`. This 'stationarity' simply means that the mean and standard deviation of every random variable :math:`E(x)` is constant and equal to :math:`\mu_E` and :math:`\sigma_E` respectively. :math:`C_E(x_i,x_j)` describes how random variables -:math:`E(x_i)` and :math:`E(x_j)` are related. For a zero-mean Gaussian random field, the covariance function is given by: +:math:`E(x_i)` and :math:`E(x_j)` are related. For a zero-mean Gaussian random field, the covariance function is given by +this equation: .. math:: C_E(x_i,x_j) = \sigma_E^2e^{-\frac{\lvert x_i-x_j \rvert}{\ell}} -where :math:`\sigma_E^2` is the variance, and :math:`\ell` is the correlation length parameter. +Here :math:`\sigma_E^2` is the variance, and :math:`\ell` is the correlation length parameter. -To aid understanding, the figure below is a diagram depicting two equivalent ways of visualizing a -stochastic process / random field, that is, as an infinite collection of random variables or as a +To aid understanding, the following diagram depicts two equivalent ways of visualizing a +stochastic process/random field, that is as an infinite collection of random variables or as a realization/sample function assigned to each outcome of an experiment. .. figure:: realizations.png - A random field :math:`E(x)` viewed as a collection of random variables or as realizations + A random field :math:`E(x)` viewed as a collection of random variables or as realizations. .. note:: The concepts in the preceding sections generalize to more dimensions, for example, a random vector instead of a random @@ -109,18 +111,18 @@ Series expansion of stochastic processes ---------------------------------------- Since a stochastic process involves an infinite number of random variables, most engineering applications involving stochastic processes are mathematically and computationally intractable if there isn't a way of -approximating them with a series of a finite number of random variables. A series expansion method used in -this example is explained next. +approximating them with a series of a finite number of random variables. The next section explains +the series expansion method used in this example. -The Karhunen-Loève (K-L) series expansion for a Gaussian process -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -More generally, the K-L expansion of any process is based on a spectral decomposition of its covariance function. Analytical +Karhunen-Loève (K-L) series expansion for a Gaussian process +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +The K-L expansion of any process is based on a spectral decomposition of its covariance function. Analytical solutions are possible in a few cases, and such is the case of a Gaussian process. For a zero-mean stationary Gaussian process, :math:`X(t)`, with covariance function :math:`C_X(t_i,t_j)=\sigma_X^2e^{-\frac{\lvert t_i-t_j \rvert}{b}}` defined on a symmetric domain :math:`\mathbb{D}=[-a,a]`, -the K-L series expansion is given by: +the K-L series expansion is given by this equation: .. math:: X(t) = \sum_{n=1}^\infty \sqrt{\lambda_{c,n}}\cdot\varphi_{c,n}(t)\cdot\xi_{c,n} + \sum_{n=1}^\infty \sqrt{\lambda_{s,n}}\cdot\varphi_{s,n}(t)\cdot\xi_{s,n},\quad t\in\mathbb{D} :label: K-L expansion @@ -156,17 +158,17 @@ where :math:`\omega_{s,n}` is obtained as the solution of It is worth mentioning that :math:`\lambda` and :math:`\omega` in the series expansion are referred to as eigenvalue and frequency respectively. .. note:: - In the case of an asymmetric domain, for example, :math:`\mathbb{D}=[-t_{min},t_{max}]`, a shift parameter :math:`T = (t_{min}+t_{max})/2` is required and the corresponding - symmetric domain becomes + In the case of an asymmetric domain, such as :math:`\mathbb{D}=[-t_{min},t_{max}]`, a shift parameter :math:`T = (t_{min}+t_{max})/2` is required and the corresponding + symmetric domain becomes defined by this equation: .. math:: D' = D - T = \biggl[\frac{t_{min}-t_{max}}{2}, \frac{t_{max}-t_{min}}{2} \biggr] - And the series expansion becomes + The series expansion is then defined by this equation: .. math:: X(t) = \sum_{n=1}^\infty \sqrt{\lambda_{c,n}}\cdot\varphi_{c,n}(t-T)\cdot\xi_{c,n} + \sum_{n=1}^\infty \sqrt{\lambda_{s,n}}\cdot\varphi_{s,n}(t-T)\cdot\xi_{s,n},\quad t\in\mathbb{D} The K-L expansion of a Gaussian process has the property that :math:`\xi_{c,n}` and :math:`\xi_{s,n}` are independent -standard normal variables, that is, they follow the :math:`\mathcal{N}(0,1)` distribution. The other great property is +standard normal variables, that is they follow the :math:`\mathcal{N}(0,1)` distribution. The other great property is that :math:`\lambda_{c,n}` and :math:`\lambda_{s,n}` converge to zero fast (in the mean square sense). For practical implementation, this means that the infinite series of the K-L expansion is truncated after a finite number of terms, giving the approximation: @@ -182,14 +184,14 @@ Equation :math:numref:`approximation` is computationally feasible to handle. A s .. math:: \hat{X}^j(t) = \sum_{n=1}^P \sqrt{\lambda_{c,n}}\cdot\varphi_{c,n}(t)\cdot\xi_{c,n}^j + \sum_{n=1}^Q \sqrt{\lambda_{s,n}}\cdot\varphi_{s,n}(t)\cdot\xi_{s,n}^j -3. To generate additional realizations, simply draw new random values for :math:`\xi_{c,n}, n=1,\dots ,P, \quad \xi_{s,n}, n=1,\dots ,Q` each from :math:`\mathcal{N}(0,1)` +3. To generate additional realizations, simply draw new random values for :math:`\xi_{c,n}, n=1,\dots ,P, \quad \xi_{s,n}, n=1,\dots ,Q` each from :math:`\mathcal{N}(0,1)`. .. note:: In this case of a field, the preceding discussion applies as the only difference is a change in notation (for example :math:`t` to :math:`x`). -The Monte Carlo simulation --------------------------- -For linear static problems in the context of FEM, the system equations which must be solved change from +Monte Carlo simulation +---------------------- +For linear static problems in the context of FEM, the system equations that must be solved change. .. math:: \pmb{K}\pmb{U} = \pmb{F} @@ -197,9 +199,9 @@ to .. math:: \pmb{K}(\pmb{\xi})\pmb{U}(\pmb{\xi}) = \pmb{F}(\pmb{\xi}) -where :math:`\pmb{\xi}` collects a sources of system randomness. The Monte Carlo simulation for solving the preceding equation +Here :math:`\pmb{\xi}` collects sources of system randomness. The Monte Carlo simulation for solving the preceding equation consists of generating a large number of :math:`N_{sim}` of samples :math:`\pmb{\xi}, i=1,\dots ,N_{sim}` from their probability -distribution and for each of these samples, solving the deterministic problem +distribution and for each of these samples solving the deterministic problem: .. math:: \pmb{K}(\pmb{\xi}_{(i)})\pmb{U}(\pmb{\xi}_{(i)}) = \pmb{F}(\pmb{\xi}_{(i)}) @@ -210,18 +212,18 @@ empirical pdf/cdf, etc. Problem description ------------------- -In the following plane stress problem +The following plane stress problem shows a two-dimensional cantilever structure under a point load. .. figure:: problem.png - A two-dimensional cantilever structure under a point load + A two-dimensional cantilever structure under a point load. -:math:`P` is a random variable following the Gaussian distribution :math:`\mathcal{N}(0,1)` (kN) and the modulus of elasticity is a -random field given by the expression: +:math:`P` is a random variable following the Gaussian distribution :math:`\mathcal{N}(0,1)` (kN), and the modulus of elasticity is a +random field given by this expression: .. math:: E(x) = 10^5(1+0.10f(x)) (kN/m^2) -with :math:`f(x)` being a zero mean stationary Gaussian field with unit variance. The covariance function for :math:`f` is +Here :math:`f(x)` is a zero mean stationary Gaussian field with unit variance. The covariance function for :math:`f` follows: .. math:: C_f(x_r,x_s)=e^{-\frac{\lvert x_r-x_s \rvert}{3}} @@ -235,31 +237,30 @@ The following are required: one be that the structure meets this requirement? .. note:: - This example really emphasizes how PyMAPDL can help to supercharge workflows. At a very high level, subsequent sections - involves using python libraries to handle computations related to the stochasticity of the problem, and using MAPDL to - run the necessary simulations, all within the comfort of a python environment. - -Evaluating the young modulus -~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -Firstly, code that allows representation of the zero-mean Gaussian field :math:`f` is first implemented. This simply means solving -:math:numref:`cosine equation` and :math:numref:`sine equation`, then substituting calculated values into + This example strongly emphasizes how PyMAPDL can help to supercharge workflows. At a very high level, subsequent sections + use Python libraries to handle computations related to the stochasticity of the problem and use MAPDL to + run the necessary simulations all within the comfort of a Python environment. + +Evaluating the Young's modulus +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +Code that allows representation of the zero-mean Gaussian field :math:`f` is implemented. This simply means solving +the :math:numref:`cosine equation` and :math:numref:`sine equation` and then substituting calculated values into :math:numref:`cosine terms` and :math:numref:`sine terms` to obtain the constant terms in those equations. The number of retained terms :math:`P` and :math:`Q` in :math:numref:`approximation` can be automatically determined by structuring the code to stop computing values when :math:`\lambda_{c,n}, \lambda_{s,n}` become lower than a -desired accuracy level. The implementation is as follows: +desired accuracy level. The implementation follows: .. literalinclude:: sfem.py :language: python :lines: 23-202 -The next step is to put this all together in a function that expresses :math:`f` using equation :math:numref:`approximation` -as follows: +The next step is to put this all together in a function that expresses the :math:`f` using the :math:numref:`approximation` equation: .. literalinclude:: sfem.py :language: python :lines: 205-265 -And then the function for evaluating the young modulus itself is straight forward: +The function for evaluating the Young's modulus itself is straight forward: .. literalinclude:: sfem.py :language: python @@ -267,7 +268,7 @@ And then the function for evaluating the young modulus itself is straight forwar Realizations of the young modulus +++++++++++++++++++++++++++++++++++++++++++++ -Sample realizations of the young's modulus can now be generated to see how they look like: +You can now generate sample realizations of the Young's modulus to see what they look like: .. literalinclude:: sfem.py :language: python @@ -275,12 +276,12 @@ Sample realizations of the young's modulus can now be generated to see how they .. figure:: young_modulus_realizations.png - 10 realizations of the young's modulus depicting randomness from one realization to another + 10 realizations of the Young's modulus depict randomness from one realization to another. Verification of the implementation ++++++++++++++++++++++++++++++++++ -The theoretical mean and variance of the young modulus can be computed and this can be used to verify the correctness -of the implemented code. +You can compute the theoretical mean and variance of the Young's modulus and then use +them to verify the correctness of the implemented code. For the mean: @@ -319,7 +320,7 @@ is then performed on these realizations. :language: python :lines: 350-385 -A plot of the mean vs the number of realizations can be generated: +You can generate a plot of the mean versus the number of realizations: .. literalinclude:: sfem.py :language: python @@ -327,9 +328,9 @@ A plot of the mean vs the number of realizations can be generated: .. figure:: mean.png - Convergence of the mean to the true value as the number of realizations is increased + The mean converges to the true value as the number of realizations is increased. -And also a plot of the variance vs the number of realizations: +You can also generate a plot of the variance versus the number of realizations: .. literalinclude:: sfem.py :language: python @@ -337,10 +338,9 @@ And also a plot of the variance vs the number of realizations: .. figure:: variance.png - Convergence of the variance to the true value as the number of realizations is increased + The variance converges to the true value as the number of realizations is increased. -The preceding plots confirms that the implementation is indeed correct. If one desires more accuracy, the minimum eigenvalue -can be further decreased but the value already chosen is sufficient. +The preceding plots confirm that the implementation is correct. If you desire more accuracy, you can further decrease the minimum eigenvalue, but the value already chosen is sufficient. Running the simulations ~~~~~~~~~~~~~~~~~~~~~~~ @@ -359,19 +359,19 @@ to write a workflow that does the following: 5. Solve the model and store :math:`u` for each simulation. .. note:: - One realization continuously varies with :math:`x` but a plane stress element like PLANE182 can only have a constant - young modulus assigned. Therefore, for an element whose :math:`x`-coordinates are between :math:`x_1` and :math:`x_2`, one can simply + One realization continuously varies with :math:`x`, but a plane stress element like PLANE182 can only have a constant + Young's modulus assigned. Therefore, for an element whose :math:`x`-coordinates are between :math:`x_1` and :math:`x_2`, you can simply assign the average value of :math:`E` between these two values or assign the value of :math:`E` at the centroid. The later is chosen for this implementation. The method chosen becomes insignificant with a finer mesh as both methods should produce similar results. -A function implementing the preceding steps follows: +This function implements the preceding steps: .. literalinclude:: sfem.py :language: python :lines: 444-556 -Required arguments can be passed to the defined function to run the simulations: +You can pass the required arguments to the defined function to run the simulations: .. literalinclude:: sfem.py :language: python @@ -388,7 +388,7 @@ simulation results can performed to determine the probability density function o .. figure:: pdf.png - The probability density function of response :math:`u` + The probability density function of response :math:`u`. To answer the second question, simply evaluate the probability that the response :math:`u` is less than :math:`0.2 \: m`: @@ -401,32 +401,32 @@ The computed probability is approximately 99%, which is a measure of how well th requirement. .. note:: - The overall implementation of this example was split into several functions so users can modify practically any aspect of the problem - statement with minimal edits to the code for testing out other scenarios. For example, different structural geometry, - different mesh size, different loading condition etc. + Splitting the overall implementation of this example into several functions lets you modify practically any aspect of the problem + statement with minimal edits to the code for testing out other scenarios. For example, you can use a different structural geometry, mesh size, or loading condition. -Improving simulation speed via multi-threading +Improve simulation speed using multi-threading ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ One of the main drawbacks of MCS is the number of simulations required. In this example, 5000 simulations can take quite -some time to run on a single MAPDL instance. To speed things up, the :class:`~ansys.mapdl.core.pool.MapdlPool` class can be utilized -to run simulations across multiple MAPDL instances. The implementation is as follows: +some time to run on a single MAPDL instance. To speed things up, you can use the +:class:`~ansys.mapdl.core.pool.MapdlPool` class to run simulations across multiple +MAPDL instances: .. literalinclude:: sfem.py :language: python :lines: 589-738 -To run simulations over 10 MAPDL instances, the preceding function is simply called with appropriate arguments: +To run simulations over 10 MAPDL instances, call the preceding function with appropriate arguments: .. literalinclude:: sfem.py :language: python :lines: 741-758 -Now the simulations can be completed much faster. +The simulations are completed much faster. .. tip:: - In a local test, using the MapdlPool approach (with 10 MAPDL instances) took about 38 minutes to run, while a single instance run - lasted for about 3 hours. The simulation speed depends on a multitude of factors but this comparison provides an idea of the speed - gain to expect when utilizing multiple instances. + In a local test, using the MapdlPool approach (with 10 MAPDL instances) takes about 38 minutes to run, while a single instance runs + for about 3 hours. The simulation speed depends on a multitude of factors, but this comparison provides an idea of the speed + gain to expect when using multiple instances. .. warning:: Ensure there are enough licenses available to run multiple MAPDL instances concurrently. From 1ab852c80639a3dcb3918d73bdcf5798ce58715a Mon Sep 17 00:00:00 2001 From: moe-ad Date: Wed, 22 Jan 2025 09:44:49 +0100 Subject: [PATCH 21/26] fix: more review comments --- .../examples/extended_examples/sfem/sfem.py | 4 +- .../extended_examples/sfem/stochastic_fem.rst | 40 +++++++++---------- 2 files changed, 20 insertions(+), 24 deletions(-) diff --git a/doc/source/examples/extended_examples/sfem/sfem.py b/doc/source/examples/extended_examples/sfem/sfem.py index b37f5fae594..429e57c14f6 100644 --- a/doc/source/examples/extended_examples/sfem/sfem.py +++ b/doc/source/examples/extended_examples/sfem/sfem.py @@ -242,7 +242,7 @@ def stochastic_field_realization( Returns ------- float - The value of the realization at a given point within the domain + Value of the realization at a given point within the domain. """ # Shift parameter -> Because terms are solved in a symmetric domain [-A, A] T = (domain[0] + domain[1]) / 2 @@ -708,7 +708,7 @@ def run_simulations_over_multple_instances( from ansys.mapdl.core import MapdlPool - # First determine the number of simulations to run per instance + # Determine the number of simulations to run per instance if no_of_simulations % no_of_instances == 0: # Simulations can be split equally across instances simulations_per_instance = no_of_simulations // no_of_instances diff --git a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst index 902f643aa1f..0071c8afe75 100644 --- a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst +++ b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst @@ -29,7 +29,7 @@ Random variables versus stochastic processes This section attempts to explain how random variables and stochastic processes differ. Because these concepts are used for modeling the system randomness, explaining them is important. Random variables are easier to understand from elementary probability theory, which isn't the case for stochastic processes. If the following -explanations are too brief, consult books on SFEM. Both [1]_and [2]_are recommended resources. +explanations are too brief, consult books on SFEM. Both [1]_ and [2]_ are recommended resources. Random variables ~~~~~~~~~~~~~~~~ @@ -94,8 +94,8 @@ this equation: Here :math:`\sigma_E^2` is the variance, and :math:`\ell` is the correlation length parameter. -To aid understanding, the following diagram depicts two equivalent ways of visualizing a -stochastic process/random field, that is as an infinite collection of random variables or as a +To aid understanding, the figure below is a diagram depicting two equivalent ways of visualizing a +stochastic process or random field, that is, as an infinite collection of random variables or as a realization/sample function assigned to each outcome of an experiment. .. figure:: realizations.png @@ -104,8 +104,8 @@ realization/sample function assigned to each outcome of an experiment. .. note:: The concepts in the preceding sections generalize to more dimensions, for example, a random vector instead of a random - variable, or an :math:`\mathbb{R}^d`-valued stochastic process. The preceding presentation is however - sufficient for this example. + variable, or an :math:`\mathbb{R}^d`-valued stochastic process. A detailed discussion of these generalizations can be + found in [1]_and [2]_. Series expansion of stochastic processes ---------------------------------------- @@ -223,14 +223,10 @@ random field given by this expression: .. math:: E(x) = 10^5(1+0.10f(x)) (kN/m^2) -Here :math:`f(x)` is a zero mean stationary Gaussian field with unit variance. The covariance function for :math:`f` follows: - -.. math:: C_f(x_r,x_s)=e^{-\frac{\lvert x_r-x_s \rvert}{3}} - -The following are required: +with :math:`f(x)` being a zero mean stationary Gaussian field with unit variance. The covariance function for :math:`f` is :math:`C_f(x_r,x_s)=e^{-\frac{\lvert x_r-x_s \rvert}{3}}`. 1. Using the K-L series expansion, generate 5000 realizations for :math:`E(x)` and perform Monte - Carlo simulation to determine the probability density function of the response :math:`u`, at the bottom right corner + Carlo simulation to determine the PDF of the response :math:`u`, at the bottom right corner of the cantilever. 2. If some design code stipulates that the displacement :math:`u` must not exceed :math:`0.2 \: m`, how confident can @@ -266,8 +262,8 @@ The function for evaluating the Young's modulus itself is straight forward: :language: python :lines: 268-295 -Realizations of the young modulus -+++++++++++++++++++++++++++++++++++++++++++++ +Realizations of the Young's modulus ++++++++++++++++++++++++++++++++++++ You can now generate sample realizations of the Young's modulus to see what they look like: .. literalinclude:: sfem.py @@ -344,17 +340,17 @@ The preceding plots confirm that the implementation is correct. If you desire mo Running the simulations ~~~~~~~~~~~~~~~~~~~~~~~ -Now focus shifts to the PyMAPDL part of this example. Remember that the problem requires running 5000 simulations. Therefore, there is need -to write a workflow that does the following: +Focus now shifts to the PyMAPDL part of this example. Remember that the problem requires running 5000 simulations. Therefore, +you must write a workflow that performs these actions: -1. Create the geometry of the cantilever model +1. Create the geometry of the cantilever model. -2. Mesh the model. For this, 4-node PLANE182 elements is going to be used +2. Mesh the model. The following code uses the four-node PLANE182 elements. -3. Generate one realization of :math:`E` and one sample of :math:`P` for each simulation +3. For each simulation, generate one realization of :math:`E` and one sample of :math:`P`. 4. For each simulation, loop through the elements and for each element, use the generated - realization to assign the value of the young's modulus. Also assign the load for each simulation. + realization to assign the value of the Young's modulus. Also assign the load for each simulation. 5. Solve the model and store :math:`u` for each simulation. @@ -379,8 +375,8 @@ You can pass the required arguments to the defined function to run the simulatio Answering problem questions ~~~~~~~~~~~~~~~~~~~~~~~~~~~ -To finish answering the first question (simulations have already been run), a statistical post-processing of -simulation results can performed to determine the probability density function of the response :math:`u`: +To determine the PDF of the response :math:`u`, you can perform a statistical post-processing of +simulation results: .. literalinclude:: sfem.py :language: python @@ -388,7 +384,7 @@ simulation results can performed to determine the probability density function o .. figure:: pdf.png - The probability density function of response :math:`u`. + The PDF of response :math:`u` To answer the second question, simply evaluate the probability that the response :math:`u` is less than :math:`0.2 \: m`: From 10c16031d43cb933d632e4f0163f31e717f31622 Mon Sep 17 00:00:00 2001 From: moe-ad Date: Wed, 22 Jan 2025 10:10:49 +0100 Subject: [PATCH 22/26] fix: more review suggestions --- .../extended_examples/sfem/stochastic_fem.rst | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst index 0071c8afe75..9d614b2ef50 100644 --- a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst +++ b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst @@ -25,7 +25,7 @@ the Monte Carlo simulation (MCS) stands out as the most prominent method. Renown ease of implementation, MCS can be applied to virtually any type of problem in stochastic analysis. Random variables versus stochastic processes --------------------------------------------------- +-------------------------------------------- This section attempts to explain how random variables and stochastic processes differ. Because these concepts are used for modeling the system randomness, explaining them is important. Random variables are easier to understand from elementary probability theory, which isn't the case for stochastic processes. If the following @@ -96,7 +96,7 @@ Here :math:`\sigma_E^2` is the variance, and :math:`\ell` is the correlation len To aid understanding, the figure below is a diagram depicting two equivalent ways of visualizing a stochastic process or random field, that is, as an infinite collection of random variables or as a -realization/sample function assigned to each outcome of an experiment. +realization or sample function assigned to each outcome of an experiment. .. figure:: realizations.png @@ -127,7 +127,7 @@ the K-L series expansion is given by this equation: .. math:: X(t) = \sum_{n=1}^\infty \sqrt{\lambda_{c,n}}\cdot\varphi_{c,n}(t)\cdot\xi_{c,n} + \sum_{n=1}^\infty \sqrt{\lambda_{s,n}}\cdot\varphi_{s,n}(t)\cdot\xi_{s,n},\quad t\in\mathbb{D} :label: K-L expansion -where, +The terms in the first summation are given by .. math:: :label: cosine terms @@ -136,12 +136,12 @@ where, k_{c,n} = \frac{1}{\sqrt{a+\frac{\sin(2\omega_{c,n}\cdot a)}{2\omega_{c,n}}}} -where :math:`\omega_{c,n}` is obtained as the solution of +In the preceding terms, :math:`\omega_{c,n}` is obtained as the solution of .. math:: \frac{1}{b} - \omega_{c,n}\cdot\tan(\omega_{c,n}\cdot a) = 0 \quad \text{in the range} \quad \biggl[(n-1)\frac{\pi}{a}, (n-\frac{1}{2})\frac{\pi}{a}\biggr] :label: cosine equation -and, +The terms in the second summation are given by .. math:: :label: sine terms @@ -150,7 +150,7 @@ and, k_{s,n} = \frac{1}{\sqrt{a-\frac{\sin(2\omega_{s,n}\cdot a)}{2\omega_{s,n}}}} -where :math:`\omega_{s,n}` is obtained as the solution of +In the preceding terms, :math:`\omega_{s,n}` is obtained as the solution of .. math:: \frac{1}{b}\cdot\tan(\omega_{s,n}\cdot a) + \omega_{s,n} = 0 \quad \text{in the range} \quad \biggl[(n-\frac{1}{2})\frac{\pi}{a}, n\frac{\pi}{a}\biggr] :label: sine equation From d28cb2cdbd8f4fe35d3bd7d7e867e7dc8e7771e0 Mon Sep 17 00:00:00 2001 From: moe-ad Date: Wed, 22 Jan 2025 10:33:50 +0100 Subject: [PATCH 23/26] fix: final review suggestions --- .../extended_examples/sfem/stochastic_fem.rst | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst index 9d614b2ef50..b86390d661e 100644 --- a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst +++ b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst @@ -105,7 +105,7 @@ realization or sample function assigned to each outcome of an experiment. .. note:: The concepts in the preceding sections generalize to more dimensions, for example, a random vector instead of a random variable, or an :math:`\mathbb{R}^d`-valued stochastic process. A detailed discussion of these generalizations can be - found in [1]_and [2]_. + found in [1]_ and [2]_. Series expansion of stochastic processes ---------------------------------------- @@ -163,7 +163,7 @@ It is worth mentioning that :math:`\lambda` and :math:`\omega` in the series exp .. math:: D' = D - T = \biggl[\frac{t_{min}-t_{max}}{2}, \frac{t_{max}-t_{min}}{2} \biggr] - The series expansion is then defined by this equation: + The series expansion is then defined by this equation: .. math:: X(t) = \sum_{n=1}^\infty \sqrt{\lambda_{c,n}}\cdot\varphi_{c,n}(t-T)\cdot\xi_{c,n} + \sum_{n=1}^\infty \sqrt{\lambda_{s,n}}\cdot\varphi_{s,n}(t-T)\cdot\xi_{s,n},\quad t\in\mathbb{D} @@ -191,11 +191,11 @@ Equation :math:numref:`approximation` is computationally feasible to handle. A s Monte Carlo simulation ---------------------- -For linear static problems in the context of FEM, the system equations that must be solved change. +For linear static problems in the context of FEM, the system equations that must be solved change. The well-known deterministic equation defined by: .. math:: \pmb{K}\pmb{U} = \pmb{F} -to +changes to .. math:: \pmb{K}(\pmb{\xi})\pmb{U}(\pmb{\xi}) = \pmb{F}(\pmb{\xi}) @@ -206,8 +206,8 @@ distribution and for each of these samples solving the deterministic problem: .. math:: \pmb{K}(\pmb{\xi}_{(i)})\pmb{U}(\pmb{\xi}_{(i)}) = \pmb{F}(\pmb{\xi}_{(i)}) The next step is to collect the :math:`N_{sim}` response vectors :math:`\pmb{U} := \pmb{U}(\pmb{\xi}_{(i)})` and perform a statistical -post-processing to extract useful information such as mean value, variance, histogram, -empirical pdf/cdf, etc. +postprocessing to extract useful information such as mean value, variance, histogram, and +empirical PDF. Problem description From 949781d0d4ac0befa22c190823834f68df5d00ab Mon Sep 17 00:00:00 2001 From: moe-ad Date: Thu, 23 Jan 2025 10:53:54 +0100 Subject: [PATCH 24/26] fix: final review comments --- .../examples/extended_examples/index.rst | 2 +- .../examples/extended_examples/sfem/sfem.py | 14 +++--- .../extended_examples/sfem/stochastic_fem.rst | 50 +++++++++---------- 3 files changed, 33 insertions(+), 33 deletions(-) diff --git a/doc/source/examples/extended_examples/index.rst b/doc/source/examples/extended_examples/index.rst index a0b37325928..34cdf88a19d 100644 --- a/doc/source/examples/extended_examples/index.rst +++ b/doc/source/examples/extended_examples/index.rst @@ -25,7 +25,7 @@ with other programs, libraries, and features in development. +------------------------------------------------------+--------------------------------------------------------------------------------------------+ | :ref:`hpc_ml_ga_example` | Demonstrates how to use PyMAPDL in a high-performance computing system managed by SLURM. | +------------------------------------------------------+--------------------------------------------------------------------------------------------+ -| :ref:`stochastic_fem_example` | Demonstrates using PyMAPDL for stochastic FEA via the Monte Carlo simulation. | +| :ref:`stochastic_fem_example` | Demonstrates using PyMAPDL for stochastic FEA using Monte Carlo simulation. | +------------------------------------------------------+--------------------------------------------------------------------------------------------+ diff --git a/doc/source/examples/extended_examples/sfem/sfem.py b/doc/source/examples/extended_examples/sfem/sfem.py index 429e57c14f6..90c651d5dfd 100644 --- a/doc/source/examples/extended_examples/sfem/sfem.py +++ b/doc/source/examples/extended_examples/sfem/sfem.py @@ -92,7 +92,7 @@ def evaluate_KL_cosine_terms( correl_length_param : float Correlation length parameter of the autocorrelation function of the process. min_eigen_value : float - Minimum eigenvalue to achieve require accuracy. + Minimum eigenvalue to achieve required accuracy. Returns ------- @@ -153,7 +153,7 @@ def evaluate_KL_sine_terms( correl_length_param : float Correlation length parameter of the autocorrelation function of the process. min_eigen_value : float - Minimum eigenvalue to achieve require accuracy. + Minimum eigenvalue to achieve required accuracy. Returns ------- @@ -295,7 +295,7 @@ def young_modulus_realization( ) -# Generation of K-L expansion parameters +# Generate K-L expansion parameters import matplotlib.pyplot as plt domain = (0, 4) @@ -509,7 +509,7 @@ def run_simulations( "S", "CENT", "X", element_centroid_x_coord ) # Select all elements having this coordinate as centroid - # Evaluate young's modulus at this material point + # Evaluate Young's modulus at this material point young_modulus_value = young_modulus_realization( cosine_frequency_list, cosine_eigen_values, @@ -525,7 +525,7 @@ def run_simulations( mapdl.mp( "EX", f"{material_property}", young_modulus_value - ) # Define property ID, assign young's modulus + ) # Define property ID and assign Young's modulus mapdl.mp( "NUXY", f"{material_property}", poisson_ratio ) # Assign poisson ratio @@ -551,7 +551,7 @@ def run_simulations( mapdl.exit() print() - print("All simulations completed!") + print("All simulations completed.") return simulation_results @@ -621,7 +621,7 @@ def run_simulations_threaded( element_ids = mapdl.esel( "S", "CENT", "Y", 0, mesh_size - ) # Select bottom row elements and store the ids + ) # Select bottom row elements and store the IDs # Generate quantities required to define the Young's modulus stochastic process cosine_frequency_list, cosine_eigen_values, cosine_constants = ( diff --git a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst index b86390d661e..ae8ad368b9d 100644 --- a/doc/source/examples/extended_examples/sfem/stochastic_fem.rst +++ b/doc/source/examples/extended_examples/sfem/stochastic_fem.rst @@ -3,7 +3,7 @@ Stochastic finite element method with PyMAPDL ============================================= -This example leverages PyMAPDL for stochastic finite element analysis using the Monte Carlo simulation. +This example leverages PyMAPDL for stochastic finite element method (SFEM) analysis using the Monte Carlo simulation. This extended example demonstrates numerous advantages and workflow possibilities that PyMAPDL provides. It explains important theoretical concepts before presenting the example. @@ -17,16 +17,16 @@ To obtain a more accurate representation of a physical system, it is essential t in system parameters and loading conditions, along with the uncertainty in their estimation and their spatial variability. The finite element method is undoubtedly the most widely used tool for solving deterministic physical problems today. To account for randomness and uncertainty in the modeling of engineering systems, -the stochastic finite element method (SFEM) was introduced. +the SFEM was introduced. SFEM extends the classical deterministic finite element approach to a stochastic framework, offering various techniques for calculating response variability. Among these, -the Monte Carlo simulation (MCS) stands out as the most prominent method. Renowned for its versatility and +Monte Carlo simulation (MCS) stands out as the most prominent method. Renowned for its versatility and ease of implementation, MCS can be applied to virtually any type of problem in stochastic analysis. Random variables versus stochastic processes -------------------------------------------- -This section attempts to explain how random variables and stochastic processes differ. Because these +This section explains how random variables and stochastic processes differ. Because these concepts are used for modeling the system randomness, explaining them is important. Random variables are easier to understand from elementary probability theory, which isn't the case for stochastic processes. If the following explanations are too brief, consult books on SFEM. Both [1]_ and [2]_ are recommended resources. @@ -40,13 +40,13 @@ random variable is written as :math:`X`. Practical example +++++++++++++++++ Imagine a beam with a concentrated load :math:`P` applied at a specific point. The value of :math:`P` -is uncertain. It could vary due to manufacturing tolerances, loading conditions, or measurement errors. Mathematically, +is uncertain. It could vary due to manufacturing tolerances, loading conditions, or measurement errors. Here is a mathematical representation: .. math:: P : \Theta \longrightarrow \mathbb{R} In the preceding equation, :math:`\Theta` is the sample space of all possible loading scenarios, and :math:`\mathbb{R}` represents the set of possible load magnitudes. For example, :math:`P` could be modeled as a random variable with a probability density -function (PDF) such as: +function (PDF): .. math:: f_P(p) = \frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{(p-\mu)^2}{2\sigma^2}}, @@ -61,7 +61,7 @@ which belongs to an interval :math:`I`. For example, this occurs in an engineeri over a time interval :math:`I \subseteq \mathbb{R}^+`. In such cases, the system's response at a specific material point is described not by a single random variable but by a collection of random variables :math:`\{X(t)\}` indexed by :math:`t \in I`. -This 'infinite' collection of random variables over the interval :math:`I` is called a stochastic process and is denoted as +This `infinite` collection of random variables over the interval :math:`I` is called a stochastic process and is denoted as :math:`\{X(t), t \in I\}` or simply :math:`X`. In this way, a stochastic process generalizes the concept of a random variable as it assigns to each outcome :math:`\theta` of the experiment a function :math:`X(t, \theta)`, known as a realization or sample function. Lastly, if :math:`X` is indexed by some spatial coordinate :math:`s \in D \subseteq \mathbb{R}^n` rather than time :math:`t`, @@ -84,7 +84,7 @@ Here: For example, :math:`E(x)` could be a Gaussian random field, in which case it has the stationarity property, making its statistics completely defined by its mean (:math:`\mu_E`), standard deviation -(:math:`\sigma_E`) and covariance function :math:`C_E(x_i,x_j)`. This 'stationarity' simply means +(:math:`\sigma_E`), and covariance function :math:`C_E(x_i,x_j)`. This `stationarity` simply means that the mean and standard deviation of every random variable :math:`E(x)` is constant and equal to :math:`\mu_E` and :math:`\sigma_E` respectively. :math:`C_E(x_i,x_j)` describes how random variables :math:`E(x_i)` and :math:`E(x_j)` are related. For a zero-mean Gaussian random field, the covariance function is given by @@ -94,7 +94,7 @@ this equation: Here :math:`\sigma_E^2` is the variance, and :math:`\ell` is the correlation length parameter. -To aid understanding, the figure below is a diagram depicting two equivalent ways of visualizing a +To aid understanding, the figure following diagram depicts two equivalent ways of visualizing a stochastic process or random field, that is, as an infinite collection of random variables or as a realization or sample function assigned to each outcome of an experiment. @@ -103,7 +103,7 @@ realization or sample function assigned to each outcome of an experiment. A random field :math:`E(x)` viewed as a collection of random variables or as realizations. .. note:: - The concepts in the preceding sections generalize to more dimensions, for example, a random vector instead of a random + The concepts in the preceding topics generalize to more dimensions, for example, a random vector instead of a random variable, or an :math:`\mathbb{R}^d`-valued stochastic process. A detailed discussion of these generalizations can be found in [1]_ and [2]_. @@ -111,7 +111,7 @@ Series expansion of stochastic processes ---------------------------------------- Since a stochastic process involves an infinite number of random variables, most engineering applications involving stochastic processes are mathematically and computationally intractable if there isn't a way of -approximating them with a series of a finite number of random variables. The next section explains +approximating them with a series of a finite number of random variables. The next topic explains the series expansion method used in this example. Karhunen-Loève (K-L) series expansion for a Gaussian process @@ -119,7 +119,6 @@ Karhunen-Loève (K-L) series expansion for a Gaussian process The K-L expansion of any process is based on a spectral decomposition of its covariance function. Analytical solutions are possible in a few cases, and such is the case of a Gaussian process. - For a zero-mean stationary Gaussian process, :math:`X(t)`, with covariance function :math:`C_X(t_i,t_j)=\sigma_X^2e^{-\frac{\lvert t_i-t_j \rvert}{b}}` defined on a symmetric domain :math:`\mathbb{D}=[-a,a]`, the K-L series expansion is given by this equation: @@ -168,7 +167,7 @@ It is worth mentioning that :math:`\lambda` and :math:`\omega` in the series exp .. math:: X(t) = \sum_{n=1}^\infty \sqrt{\lambda_{c,n}}\cdot\varphi_{c,n}(t-T)\cdot\xi_{c,n} + \sum_{n=1}^\infty \sqrt{\lambda_{s,n}}\cdot\varphi_{s,n}(t-T)\cdot\xi_{s,n},\quad t\in\mathbb{D} The K-L expansion of a Gaussian process has the property that :math:`\xi_{c,n}` and :math:`\xi_{s,n}` are independent -standard normal variables, that is they follow the :math:`\mathcal{N}(0,1)` distribution. The other great property is +standard normal variables, that is they follow the :math:`\mathcal{N}(0,1)` distribution. Another property is that :math:`\lambda_{c,n}` and :math:`\lambda_{s,n}` converge to zero fast (in the mean square sense). For practical implementation, this means that the infinite series of the K-L expansion is truncated after a finite number of terms, giving the approximation: @@ -223,17 +222,17 @@ random field given by this expression: .. math:: E(x) = 10^5(1+0.10f(x)) (kN/m^2) -with :math:`f(x)` being a zero mean stationary Gaussian field with unit variance. The covariance function for :math:`f` is :math:`C_f(x_r,x_s)=e^{-\frac{\lvert x_r-x_s \rvert}{3}}`. +Here :math:`f(x)` is a zero mean stationary Gaussian field with unit variance. The covariance function for :math:`f` is :math:`C_f(x_r,x_s)=e^{-\frac{\lvert x_r-x_s \rvert}{3}}`. 1. Using the K-L series expansion, generate 5000 realizations for :math:`E(x)` and perform Monte Carlo simulation to determine the PDF of the response :math:`u`, at the bottom right corner of the cantilever. 2. If some design code stipulates that the displacement :math:`u` must not exceed :math:`0.2 \: m`, how confident can - one be that the structure meets this requirement? + you be that the structure meets this requirement? .. note:: - This example strongly emphasizes how PyMAPDL can help to supercharge workflows. At a very high level, subsequent sections + This example strongly emphasizes how PyMAPDL can help to supercharge workflows. At a very high level, subsequent topics use Python libraries to handle computations related to the stochasticity of the problem and use MAPDL to run the necessary simulations all within the comfort of a Python environment. @@ -343,16 +342,16 @@ Running the simulations Focus now shifts to the PyMAPDL part of this example. Remember that the problem requires running 5000 simulations. Therefore, you must write a workflow that performs these actions: -1. Create the geometry of the cantilever model. +#. Create the geometry of the cantilever model. -2. Mesh the model. The following code uses the four-node PLANE182 elements. +#. Mesh the model. The following code uses the four-node PLANE182 elements. -3. For each simulation, generate one realization of :math:`E` and one sample of :math:`P`. +#. For each simulation, generate one realization of :math:`E` and one sample of :math:`P`. -4. For each simulation, loop through the elements and for each element, use the generated +#. For each simulation, loop through the elements and for each element, use the generated realization to assign the value of the Young's modulus. Also assign the load for each simulation. -5. Solve the model and store :math:`u` for each simulation. +#. Solve the model and store :math:`u` for each simulation. .. note:: One realization continuously varies with :math:`x`, but a plane stress element like PLANE182 can only have a constant @@ -375,7 +374,7 @@ You can pass the required arguments to the defined function to run the simulatio Answering problem questions ~~~~~~~~~~~~~~~~~~~~~~~~~~~ -To determine the PDF of the response :math:`u`, you can perform a statistical post-processing of +To determine the PDF of the response :math:`u`, you can perform a statistical postprocessing of simulation results: .. literalinclude:: sfem.py @@ -384,9 +383,10 @@ simulation results: .. figure:: pdf.png - The PDF of response :math:`u` + The PDF of response :math:`u`. -To answer the second question, simply evaluate the probability that the response :math:`u` is less than +To determine whether the structure meets the requirement of the design code, simply evaluate the +probability that the response :math:`u` is less than :math:`0.2 \: m`: .. literalinclude:: sfem.py @@ -420,7 +420,7 @@ To run simulations over 10 MAPDL instances, call the preceding function with app The simulations are completed much faster. .. tip:: - In a local test, using the MapdlPool approach (with 10 MAPDL instances) takes about 38 minutes to run, while a single instance runs + In a local test, using the ``MapdlPool`` approach (with 10 MAPDL instances) takes about 38 minutes to run, while a single instance runs for about 3 hours. The simulation speed depends on a multitude of factors, but this comparison provides an idea of the speed gain to expect when using multiple instances. From 59f109d4de5529c0eefc144c98da9b6f7128a417 Mon Sep 17 00:00:00 2001 From: German <28149841+germa89@users.noreply.github.com> Date: Thu, 23 Jan 2025 12:40:06 +0100 Subject: [PATCH 25/26] ci: skipping non-student versions when running on remote --- .ci/build_matrix.sh | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/.ci/build_matrix.sh b/.ci/build_matrix.sh index 506b8c6c303..67189fda443 100755 --- a/.ci/build_matrix.sh +++ b/.ci/build_matrix.sh @@ -101,8 +101,8 @@ for version in "${versions[@]}"; do fi # Skipping if on remote and on student - if [[ "$ON_STUDENT" == "true" && "$ON_REMOTE" == "true" ]]; then - echo "Skipping student versions when running on remote" + if [[ "$ON_STUDENT" != "true" && "$ON_REMOTE" == "true" ]]; then + echo "Skipping non-student versions when running on remote" echo "" continue fi From df9d6909debe48b053dd54ff94eabd738c77f522 Mon Sep 17 00:00:00 2001 From: moe-ad Date: Thu, 23 Jan 2025 13:01:08 +0100 Subject: [PATCH 26/26] ci: empty commit to trigger CICD

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