Probability estimation: directional simulation¶
In this example we estimate a failure probability with the directional simulation algorithm provided by the DirectionalSampling class.
The directional simulation algorithm operates in the standard space based on:
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
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 here.
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 :
from openturns.usecases import cantilever_beam as cantilever_beam cb = cantilever_beam.CantileverBeam()
We load the joint probability distribution of the input parameters :
distribution = cb.distribution
We load the model giving the displacement at the end of the beam :
model = cb.model
We create the event whose probability we want to estimate.
vect = ot.RandomVector(distribution) G = ot.CompositeRandomVector(model, vect) event = ot.ThresholdEvent(G, ot.Greater(), 0.30)
Root finding algorithm.
solver = ot.Brent() rootStrategy = ot.MediumSafe(solver)
Direction sampling algorithm.
samplingStrategy = ot.OrthogonalDirection()
Create a simulation algorithm.
algo = ot.DirectionalSampling(event, rootStrategy, samplingStrategy) algo.setMaximumCoefficientOfVariation(0.1) algo.setMaximumOuterSampling(40000) algo.setConvergenceStrategy(ot.Full()) algo.run()
result = algo.getResult() probability = result.getProbabilityEstimate() print('Pf=', probability)
Total running time of the script: ( 0 minutes 0.686 seconds)