.. only:: html

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

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

    .. _sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_directional_sampling.py:


Probability estimation: directional simulation
==============================================

In this example we estimate a failure probability with the directional simulation algorithm provided by the `DirectionalSampling` class.

Introduction
------------

The directional simulation algorithm  operates in the standard space based on:

1. a *root strategy* to evaluate the nearest failure point along each direction and take the contribution of each direction to the failure event probability into account. The available strategies are:
   - `RiskyAndFast`
   - `MediumSafe`
   - `SafeAndSlow`

2. a *sampling strategy* to choose directions in the standard space. The available strategies are:
   - `RandomDirection`
   - `OrthogonalDirection`

Let us consider the analytical example of the cantilever beam described :ref:`here <use-case-cantilever-beam>`.



.. 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 model from the usecases module :


.. code-block:: default

    from openturns.usecases import cantilever_beam as cantilever_beam
    cb = cantilever_beam.CantileverBeam()








We load the joint probability distribution of the input parameters :


.. code-block:: default

    distribution = cb.distribution








We load the model giving the displacement at the end of the beam :


.. code-block:: default

    model = cb.model








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(), 0.30)








Root finding algorithm.


.. code-block:: default

    solver = ot.Brent()
    rootStrategy = ot.MediumSafe(solver)








Direction sampling algorithm.


.. code-block:: default

    samplingStrategy = ot.OrthogonalDirection()








Create a simulation algorithm.


.. code-block:: default

    algo = ot.DirectionalSampling(event, rootStrategy, samplingStrategy)
    algo.setMaximumCoefficientOfVariation(0.1)
    algo.setMaximumOuterSampling(40000)
    algo.setConvergenceStrategy(ot.Full())
    algo.run()








Retrieve results.


.. code-block:: default

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




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

 Out:

 .. code-block:: none

    Pf= 4.0070181504701335e-07





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

   **Total running time of the script:** ( 0 minutes  0.686 seconds)


.. _sphx_glr_download_auto_reliability_sensitivity_reliability_plot_estimate_probability_directional_sampling.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_estimate_probability_directional_sampling.py <plot_estimate_probability_directional_sampling.py>`



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

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


.. only:: html

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