Estimate a probability using randomized QMC

In this example we are going to estimate a failure probability on the cantilever beam.

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 data class containing the probabilistic modeling of the beam.

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 as well,

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(), 0.3)

Define the low discrepancy sequence.

sequence = ot.SobolSequence()

Create a simulation algorithm.

experiment = ot.LowDiscrepancyExperiment(sequence, 1)
experiment.setRandomize(True)
algo = ot.ProbabilitySimulationAlgorithm(event, experiment)
algo.setMaximumCoefficientOfVariation(0.05)
algo.setMaximumOuterSampling(int(1e5))
algo.run()

Retrieve results.

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

Out:

Pf= 0.0