Parametrization of a simulation algorithmΒΆ

In this basic example we are going to parameterize a simulation algorithm:

  • parameters linked to the number of points generated

  • the precision of the probability estimator

  • the sample storage strategy

  • using callbacks to monitor progress and stopping criteria.

[1]:
from __future__ import print_function
import openturns as ot
[2]:
# create the joint distribution of the parameters
distribution_R = ot.LogNormalMuSigma(300.0, 30.0, 0.0).getDistribution()
distribution_F = ot.Normal(75e3, 5e3)
marginals = [distribution_R, distribution_F]
distribution = ot.ComposedDistribution(marginals)
[3]:
# create the model
model = ot.SymbolicFunction(['R', 'F'], ['R-F/(pi_*100.0)'])
[4]:
# create the event we want to estimate the probability
vect = ot.RandomVector(distribution)
G = ot.CompositeRandomVector(model, vect)
event = ot.Event(G, ot.Less(), 0.0)
[5]:
# create a Monte Carlo algorithm
experiment = ot.MonteCarloExperiment()
algo = ot.ProbabilitySimulationAlgorithm(event, experiment)
[6]:
# Criteria 1: Define the Maximum Coefficient of variation of the probability estimator
algo.setMaximumCoefficientOfVariation(0.05)
[7]:
# Criteria 2: Define the number of iterations of the simulation
algo.setMaximumOuterSampling(int(1e4))
[8]:
# The block size parameter represents the number of samples evaluated per iteration, useful for parallelization
algo.setBlockSize(2)
[9]:
# HistoryStrategy to store the values of the probability used to draw the convergence graph

# Null strategy
algo.setConvergenceStrategy(ot.Null())

# Full strategy
algo.setConvergenceStrategy(ot.Full())

# Compact strategy: N points
N = 1000
algo.setConvergenceStrategy(ot.Compact(N))
[10]:
# Use a callback to display the progress every 10%
def progress(p):
    if p >= progress.t:
        progress.t += 10.0
        print('progress=', p, '%')
    return False
progress.t = 10.0
algo.setProgressCallback(progress)
[11]:
# Use a callback to stop the simulation
def stop():
    # here we never stop, but we could
    return False
algo.setStopCallback(stop)
[12]:
algo.run()
progress= 10.0 %
progress= 20.0 %
progress= 30.0 %
progress= 40.0 %
progress= 50.0 %
progress= 60.0 %
progress= 70.0 %
progress= 80.0 %
progress= 90.0 %
progress= 100.0 %
[13]:
# retrieve results
result = algo.getResult()
probability = result.getProbabilityEstimate()
print('Pf=', probability)
Pf= 0.02859999999999999