diff --git a/docs/code/reliability/inverse_form/inverse_form_cantilever.py b/docs/code/reliability/inverse_form/inverse_form_cantilever.py index b5bfcb79..54f355e7 100644 --- a/docs/code/reliability/inverse_form/inverse_form_cantilever.py +++ b/docs/code/reliability/inverse_form/inverse_form_cantilever.py @@ -59,7 +59,7 @@ # With everything defined we are ready to run the inverse first-order reliability method and print the results. # The solution to this problem given by Du is :math:`\textbf{U}^*=(1.7367, 0.16376)` with a reliability index of # :math:`\beta_{HL}=||\textbf{U}^*||=1.7444` and probability of failure of -# :math:`p_{fail} = \Phi(-\beta_{HL})=\Phi(-1.7444)=0.04054`. We expect this problem to converge in 4 iterations. +# :math:`p_{fail} = \Phi(-\beta_{HL})=0.04054`. We expect this problem to converge in 4 iterations. # We confirm our design point matches this length, and therefore has a probability of failure specified by our input. # %% diff --git a/docs/source/reliability/inverse_form.rst b/docs/source/reliability/inverse_form.rst index 6dde4b65..f3470823 100644 --- a/docs/source/reliability/inverse_form.rst +++ b/docs/source/reliability/inverse_form.rst @@ -31,9 +31,9 @@ The feasibility criteria :math:`||\textbf{U}||=\beta` may be equivalently define :math:`\beta = -\Phi^{-1}(p_{fail})`, where :math:`\Phi^{-1}(\cdot)` is the inverse standard normal CDF. Algorithm ------------------ +--------- This method implements a gradient descent algorithm to solve the optimization problem within the tolerances specified by -:math:`\text{tolerance}_{\textbf{U}}` (:code:`tolerance_u`) and :math:`\text{tolerance}_{\nabla G(\textbf{U})}` (:code:`tolerance_gradient`). +:code:`tolerance_u` and :code:`tolerance_gradient`. 0. Define :math:`u_0` and :math:`\beta` directly or :math:`\beta=-\Phi^{-1}(p_\text{fail})` 1. Set :math:`u=u_0` and :math:`\text{converged}=False` @@ -50,12 +50,14 @@ The :class:`.InverseFORM` class is imported using the following command: >>> from UQpy.reliability.taylor_series import InverseFORM Methods ------------------ +------- + .. autoclass:: UQpy.reliability.taylor_series.InverseFORM :members: run Attributes ------------------ +---------- + .. autoattribute:: UQpy.reliability.taylor_series.InverseFORM.alpha .. autoattribute:: UQpy.reliability.taylor_series.InverseFORM.alpha_record .. autoattribute:: UQpy.reliability.taylor_series.InverseFORM.beta @@ -68,7 +70,8 @@ Attributes Examples -"""""""""" +-------- + .. toctree:: InverseFORM Examples <../auto_examples/reliability/inverse_form/index> \ No newline at end of file