.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_example/plot_example2.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_example_plot_example2.py>`
        to download the full example code

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

.. _sphx_glr_auto_example_plot_example2.py:


Example 2: Use of AK - IS on Non linear oscillator
--------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 7-16

.. code-block:: default


    import openturns as ot
    from openturns.viewer import View
    import numpy as np
    import otak

    ot.RandomGenerator.SetSeed(1)









.. GENERATED FROM PYTHON SOURCE LINES 17-18

| Definition of Input distribution

.. GENERATED FROM PYTHON SOURCE LINES 18-31

.. code-block:: default


    dist_c1=ot.Normal(1, 0.1)
    dist_c2=ot.Normal(0.1, 0.01)
    dist_m=ot.Normal(1.,0.05 )
    dist_r =ot.Normal(0.5, 0.05)
    dist_t1 =ot.Normal(1., 0.2)
    dist_F1=ot.Normal(1., 0.2)
    std_dev = [dist_c1.getStandardDeviation()[0],dist_c2.getStandardDeviation()[0],dist_m.getStandardDeviation()[0],
               dist_r.getStandardDeviation()[0],dist_t1.getStandardDeviation()[0],dist_F1.getStandardDeviation()[0]]
    dim_inputs=6
    marginals = [dist_c1,dist_c2,dist_m,dist_r,dist_t1,dist_F1]
    dist_x = ot.ComposedDistribution(marginals)








.. GENERATED FROM PYTHON SOURCE LINES 32-33

| Definition of limit state function

.. GENERATED FROM PYTHON SOURCE LINES 33-50

.. code-block:: default


    def non_lin_osc(x):
        c1 = x[0]
        c2  = x[1]
        m = x[2]
        r = x[3]
        t1 = x[4]
        F1= x[5]
    
        omega = np.sqrt((c1+c2)/m)
    
        G = 3*r - np.abs(2*F1/(m*omega**2)*np.sin(omega*t1/2))
        return [G]

    # Definition of pythonfunction
    non_lin_osc = ot.PythonFunction(6, 1, non_lin_osc)








.. GENERATED FROM PYTHON SOURCE LINES 51-52

| Definition of event

.. GENERATED FROM PYTHON SOURCE LINES 52-58

.. code-block:: default


    vect = ot.RandomVector(dist_x)
    G = ot.CompositeRandomVector(non_lin_osc, vect)
    event_osc = ot.ThresholdEvent(G, ot.Less(), 0.0)









.. GENERATED FROM PYTHON SOURCE LINES 59-60

| Run of AK IS

.. GENERATED FROM PYTHON SOURCE LINES 60-85

.. code-block:: default


    dim_osc = 6
    basis = ot.ConstantBasisFactory(dim_inputs).build()
    covarianceModel = ot.SquaredExponential([0.1]*dim_osc, [1.0])

    n_IS_osc = 1000
    n_DoE_osc = 40
    sim_budget_osc = 200
    verbose = False
    my_AK_non_lin_osc = otak.AK_ISAlgorithm(event_osc,
                                        n_IS_osc,
                                        n_DoE_osc,
                                        sim_budget_osc,                                                                   
                                        basis,
                                        covarianceModel,
                                        ot.Cobyla(),
                                        2,
                                        verbose)
									
									
    #computation of probability with AK-IS
    my_AK_non_lin_osc.compute_proba()


    print('Probability of failure:',my_AK_non_lin_osc.getFailureProbability())
    print('Simulation budget:',my_AK_non_lin_osc.getSimBudget())



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

 Out:

 .. code-block:: none

    Probability of failure: 0.02867081530928803
    Simulation budget: 49





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

   **Total running time of the script:** ( 0 minutes  0.394 seconds)


.. _sphx_glr_download_auto_example_plot_example2.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_example2.py <plot_example2.py>`



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

     :download:`Download Jupyter notebook: plot_example2.ipynb <plot_example2.ipynb>`


.. only:: html

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

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