.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/reliability/sorm/SORM_nonlinear_function.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_reliability_sorm_SORM_nonlinear_function.py>`
        to download the full example code or to run this example in your browser via Binder

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_reliability_sorm_SORM_nonlinear_function.py:


4. SORM - Nonlinear function - Two Random variables
=====================================================

In the fourth example we have the limit state to be a nonlinear function of two (:math:`d=2`) random variables

.. math:: g(X_1, X_2) = X_1X_1 - 80

where :math:`X_1` follows a normal distribution with mean :math:`\mu_{X_1}=20` and standard deviation
:math:`\sigma_{X_1}=7` and :math:`X_2` follows a lognormal distribution with mean :math:`\mu_{X_2}=7` and
standard deviation :math:`\sigma_{X_2}=1.4`.

.. GENERATED FROM PYTHON SOURCE LINES 16-17

Initially we have to import the necessary modules.

.. GENERATED FROM PYTHON SOURCE LINES 20-47

.. code-block:: default

    import numpy as np
    from UQpy.run_model.RunModel import RunModel
    from UQpy.run_model.model_execution.PythonModel import PythonModel
    from UQpy.distributions import Normal
    from UQpy.reliability import FORM
    from UQpy.reliability import SORM
    from UQpy.distributions import Lognormal

    m0 = 7
    v0 = 1.4
    mu = np.log(m0) - np.log(np.sqrt(1 + (v0 / m0) ** 2))
    scale = np.exp(mu)
    s = np.sqrt(np.log(1 + (v0 / m0) ** 2))
    loc_ = 0.0

    dist1 = Normal(loc=20., scale=2)
    dist2 = Lognormal(s=s, loc=0.0, scale=scale)
    model = PythonModel(model_script='local_model4.py', model_object_name="example4")
    RunModelObject4 = RunModel(model=model)
    form = FORM(distributions=[dist1, dist2], runmodel_object=RunModelObject4)
    form.run()
    sorm = SORM(form_object=form)


    # print results
    print('SORM probability of failure: %s' % sorm.failure_probability)



.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  0.000 seconds)


.. _sphx_glr_download_auto_examples_reliability_sorm_SORM_nonlinear_function.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example


    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/SURGroup/UQpy/master?urlpath=lab/tree/notebooks/auto_examples/reliability/sorm/SORM_nonlinear_function.ipynb
        :alt: Launch binder
        :width: 150 px



    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: SORM_nonlinear_function.py <SORM_nonlinear_function.py>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: SORM_nonlinear_function.ipynb <SORM_nonlinear_function.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_