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.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_reliability_sensitivity/reliability/plot_estimate_probability_directional_sampling.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. 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:


Use the Directional Sampling Algorithm
======================================

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

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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>`.


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.. code-block:: default

    from openturns.usecases import cantilever_beam
    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt
    ot.Log.Show(ot.Log.NONE)








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We load the model from the usecases module :

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.. code-block:: default

    cb = cantilever_beam.CantileverBeam()








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We load the joint probability distribution of the input parameters :

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.. code-block:: default

    distribution = cb.distribution








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

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.. code-block:: default

    model = cb.model








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We create the event whose probability we want to estimate.

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.. code-block:: default

    vect = ot.RandomVector(distribution)
    G = ot.CompositeRandomVector(model, vect)
    event = ot.ThresholdEvent(G, ot.Greater(), 0.30)








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Root finding algorithm.

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.. code-block:: default

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








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Direction sampling algorithm.

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.. code-block:: default

    samplingStrategy = ot.OrthogonalDirection()








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Create a simulation algorithm.

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.. code-block:: default

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








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Retrieve results.

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.. code-block:: default

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





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

 Out:

 .. code-block:: none

    Pf= 4.7022072258716404e-07




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We can observe the convergence history with the `drawProbabilityConvergence`
method.

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.. code-block:: default

    graph = algo.drawProbabilityConvergence()
    graph.setLogScale(ot.GraphImplementation.LOGX)
    view = viewer.View(graph)



.. image-sg:: /auto_reliability_sensitivity/reliability/images/sphx_glr_plot_estimate_probability_directional_sampling_001.png
   :alt: DirectionalSampling convergence graph at level 0.95
   :srcset: /auto_reliability_sensitivity/reliability/images/sphx_glr_plot_estimate_probability_directional_sampling_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.710 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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