def test_UseCaseMonteCarlo(self):
problem = otb.ReliabilityProblem14()
event = problem.getEvent()
# Create a Monte Carlo algorithm
experiment = ot.MonteCarloExperiment()
algo = ot.ProbabilitySimulationAlgorithm(event, experiment)
algo.setMaximumCoefficientOfVariation(0.01)
algo.setBlockSize(int(1.0e3))
algo.setMaximumOuterSampling(int(1e3))
algo.run()
# Retrieve results
result = algo.getResult()
computed_pf = result.getProbabilityEstimate()
exact_pf = problem.getProbability()
print("exact_pf=", exact_pf)
print("computed_pf=", computed_pf)
samplesize = result.getOuterSampling() * result.getBlockSize()
alpha = 0.05
pflen = result.getConfidenceLength(1 - alpha)
print(
"%.2f%% confidence interval = [%f,%f]"
% ((1 - alpha) * 100, computed_pf - pflen / 2, computed_pf + pflen / 2)
)
print("Sample size : ", samplesize)
atol = 1.0e2 / np.sqrt(samplesize)
np.testing.assert_allclose(computed_pf, exact_pf, atol=atol)
def test_SubsetSampling(self):
problem = otb.ReliabilityProblem14()
algo = otb.SubsetSampling(problem)
algo.run()
result = algo.getResult()
pf = result.getProbabilityEstimate()
exactPf = problem.getProbability()
np.testing.assert_almost_equal(pf, exactPf, decimal=2)
def test_FORM(self):
problem = otb.ReliabilityProblem14()
nearestPointAlgorithm = ot.AbdoRackwitz()
algo = otb.FORM(problem, nearestPointAlgorithm)
algo.run()
result = algo.getResult()
pf = result.getEventProbability()
exactPf = problem.getProbability()
np.testing.assert_almost_equal(pf, exactPf, decimal=2)
def test_FORMIS(self):
problem = otb.ReliabilityProblem14()
nearestPointAlgorithm = ot.AbdoRackwitz()
factory = otb.ProbabilitySimulationAlgorithmFactory()
algo = factory.buildFORMIS(problem, nearestPointAlgorithm)
algo.run()
result = algo.getResult()
pf = result.getProbabilityEstimate()
exactPf = problem.getProbability()
np.testing.assert_almost_equal(pf, exactPf, decimal=2)
def test_MonteCarlo(self):
problem = otb.ReliabilityProblem14()
factory = otb.ProbabilitySimulationAlgorithmFactory()
algo = factory.buildMonteCarlo(problem)
algo.setMaximumOuterSampling(100000)
algo.run()
result = algo.getResult()
pf = result.getProbabilityEstimate()
exactPf = problem.getProbability()
np.testing.assert_almost_equal(pf, exactPf, decimal=2)
def test_ReliabilityBenchmarkProblem14(self):
problem = otb.ReliabilityProblem14()
print(problem)
# Check probability
pf = problem.getProbability()
pf_exacte = 0.00752
np.testing.assert_allclose(pf, pf_exacte, rtol=1.0e-15)
# Check function
event = problem.getEvent()
function = event.getFunction()
X = [0.0, 1.0, 0.0, 0.0, 0.0]
Y = function(X)
assert type(Y) is ot.Point
np.testing.assert_allclose(Y[0], 0.0)
def test_UseCaseFORM(self):
problem = otb.ReliabilityProblem14()
event = problem.getEvent()
distribution = event.getAntecedent().getDistribution()
# We create a NearestPoint algorithm
myCobyla = ot.Cobyla()
# Resolution options:
eps = 1e-3
myCobyla.setMaximumEvaluationNumber(100)
myCobyla.setMaximumAbsoluteError(eps)
myCobyla.setMaximumRelativeError(eps)
myCobyla.setMaximumResidualError(eps)
myCobyla.setMaximumConstraintError(eps)
# For statistics about the algorithm
algo = ot.FORM(myCobyla, event, distribution.getMean())
algo.run()
resultFORM = algo.getResult()
# Combine with Importance Sampling
standardSpaceDesignPoint = resultFORM.getStandardSpaceDesignPoint()
dimension = distribution.getDimension()
myImportance = ot.Normal(dimension)
myImportance.setMean(standardSpaceDesignPoint)
experiment = ot.ImportanceSamplingExperiment(myImportance)
standardEvent = ot.StandardEvent(event)
algo = ot.ProbabilitySimulationAlgorithm(standardEvent, experiment)
algo.setMaximumCoefficientOfVariation(0.01)
algo.setBlockSize(int(1.0e3))
algo.setMaximumOuterSampling(int(1e3))
algo.run()
result = algo.getResult()
computed_pf = result.getProbabilityEstimate()
exact_pf = problem.getProbability()
print("exact_pf=", exact_pf)
print("computed_pf=", computed_pf)
samplesize = result.getOuterSampling() * result.getBlockSize()
alpha = 0.05
pflen = result.getConfidenceLength(1 - alpha)
print(
"%.2f%% confidence interval = [%f,%f]"
% ((1 - alpha) * 100, computed_pf - pflen / 2, computed_pf + pflen / 2)
)
print("Sample size : ", samplesize)
atol = 1.0e1 / np.sqrt(samplesize)
np.testing.assert_allclose(computed_pf, exact_pf, atol=atol)
def ReliabilityBenchmarkProblemList():
"""
Returns the list of reliability benchmark problems.
Returns
-------
problems : list
A list of ReliabilityProblem.
"""
p8 = otb.ReliabilityProblem8()
p14 = otb.ReliabilityProblem14()
p22 = otb.ReliabilityProblem22()
p24 = otb.ReliabilityProblem24()
p25 = otb.ReliabilityProblem25()
p28 = otb.ReliabilityProblem28()
p31 = otb.ReliabilityProblem31()
p33 = otb.ReliabilityProblem33()
p35 = otb.ReliabilityProblem35()
p38 = otb.ReliabilityProblem38()
p53 = otb.ReliabilityProblem53()
p55 = otb.ReliabilityProblem55()
p54 = otb.ReliabilityProblem54()
p57 = otb.ReliabilityProblem57()
p75 = otb.ReliabilityProblem75()
p89 = otb.ReliabilityProblem89()
p107 = otb.ReliabilityProblem107()
p110 = otb.ReliabilityProblem110()
p111 = otb.ReliabilityProblem111()
p63 = otb.ReliabilityProblem63()
p91 = otb.ReliabilityProblem91()
p60 = otb.ReliabilityProblem60()
p77 = otb.ReliabilityProblem77()
pFBS = otb.FourBranchSerialSystemReliability()
pRS = otb.RminusSReliability()
pBeam = otb.AxialStressedBeamReliability()
problemslist = [
p8,
p14,
p22,
p24,
p25,
p28,
p31,
p33,
p35,
p38,
p53,
p55,
p54,
p57,
p75,
p89,
p107,
p110,
p111,
p63,
p91,
p60,
p77,
pFBS,
pRS,
pBeam,
]
return problemslist