Estimate a probability with Latin Hypercube Sampling

In this example we show how to use the LHS algorithm to estimate the probability of an event. We consider the axial stressed beam example.

from __future__ import print_function
from openturns.usecases import stressed_beam as stressed_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 model from the usecases module :

sm = stressed_beam.AxialStressedBeam()

We get the input parameter distribution :

distribution = sm.distribution

and get the model :

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)

Create a LHS algorithm.

algo = ot.LHS(event)
algo.setMaximumCoefficientOfVariation(0.05)
algo.setMaximumOuterSampling(int(1e5))
algo.run()

Retrieve results.

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

Out:

Pf= 0.029342988609791055