Use a randomized QMC algorithm

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

from __future__ import print_function
from openturns.usecases import cantilever_beam as cantilever_beam
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.

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