Use a randomized QMC algorithm

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

from openturns.usecases import stressed_beam
import openturns as ot

We load the data class containing the probabilistic modeling of the beam.

sm = stressed_beam.AxialStressedBeam()

We load the joint probability distribution of the input parameters :

distribution = sm.distribution

We load the model as well,

model = sm.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.Less(), 0.0)

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(1e4))
algo.run()

Retrieve results.

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

Pf= 0.02970000000000001