.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_reliability_sensitivity_reliability_plot_flood_model.py>`     to download the full example code
    .. rst-class:: sphx-glr-example-title

    .. _sphx_glr_auto_reliability_sensitivity_reliability_plot_flood_model.py:


Estimate a flooding probability
===============================

In this example, we estimate the probability that the ouput of a function exceeds a given threshold with the FORM method. We consider the :ref:`flooding model <use-case-flood-model>`.

Define the model
----------------


.. code-block:: default

    from __future__ import print_function
    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt
    ot.Log.Show(ot.Log.NONE)








We load the flooding model from the usecases module :


.. code-block:: default

    from openturns.usecases import flood_model as flood_model
    fm = flood_model.FloodModel()








We load the joint probability distribution of the input parameters. 


.. code-block:: default

    distribution = fm.distribution








We create the model. 


.. code-block:: default

    model = fm.model








Define the event
----------------

Then we create the event whose probability we want to estimate.


.. code-block:: default

    vect = ot.RandomVector(distribution)
    G = ot.CompositeRandomVector(model, vect)
    event = ot.ThresholdEvent(G, ot.Greater(), 0.0)
    event.setName('overflow')








Estimate the probability with FORM
----------------------------------

Define a solver. 


.. code-block:: default

    optimAlgo = ot.Cobyla()
    optimAlgo.setMaximumEvaluationNumber(1000)
    optimAlgo.setMaximumAbsoluteError(1.0e-10)
    optimAlgo.setMaximumRelativeError(1.0e-10)
    optimAlgo.setMaximumResidualError(1.0e-10)
    optimAlgo.setMaximumConstraintError(1.0e-10)








Run FORM. 


.. code-block:: default

    startingPoint = distribution.getMean()
    algo = ot.FORM(optimAlgo, event, startingPoint)
    algo.run()
    result = algo.getResult()
    standardSpaceDesignPoint = result.getStandardSpaceDesignPoint()








Retrieve results. 


.. code-block:: default

    result = algo.getResult()
    probability = result.getEventProbability()
    print('Pf=', probability)





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    Pf= 0.0005340887806479528




Importance factors. 


.. code-block:: default

    graph = result.drawImportanceFactors()
    view = viewer.View(graph)
    plt.show()



.. image:: /auto_reliability_sensitivity/reliability/images/sphx_glr_plot_flood_model_001.png
    :alt: Importance Factors from Design Point - overflow
    :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.051 seconds)


.. _sphx_glr_download_auto_reliability_sensitivity_reliability_plot_flood_model.py:


.. only :: html

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



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

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



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

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


.. only:: html

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

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