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class=FORMImportanceSamplingAnalysis name=myIS limitState=class=LimitStateImplementation name=aLimitState physicalModel=aModelPhys outputName=Y0 operator=class=Greater name=Unnamed threshold=20 maximumCalls=1000 maximumCoefficientOfVariation=0.1 maximumElapsedTime=60 seed=2 blockSize=10 standardSpaceDesignPoint=class=Point name=Unnamed dimension=2 values=[0,0] optimization algorithm=class=OptimizationAlgorithm implementation=class=AbdoRackwitz class=OptimizationAlgorithmImplementation problem=class=OptimizationProblem implementation=class=OptimizationProblemImplementation objective=class=Function name=Unnamed implementation=class=FunctionImplementation name=Unnamed description=[] evaluationImplementation=class=NoEvaluation name=Unnamed gradientImplementation=class=NoGradient name=Unnamed hessianImplementation=class=NoHessian name=Unnamed equality constraint=none inequality constraint=none bounds=none minimization=true dimension=0 startingPoint=class=Point name=Unnamed dimension=2 values=[1,1] maximumIterationNumber=100 maximumCallsNumber=1000 maximumAbsoluteError=1e-05 maximumRelativeError=1e-05 maximumResidualError=1e-05 maximumConstraintError=1e-05 tau=0.5 omega=0.0001 smooth=1.2 physicalStartingPoint=class=Point name=Unnamed dimension=2 values=[1,1]
result= class=SimulationReliabilityResult name=Unnamed simulationResult=probabilityEstimate=8.638291e-02 varianceEstimate=7.114811e-05 standard deviation=8.43e-03 coefficient of variation=9.76e-02 confidenceLength(0.95)=3.31e-02 outerSampling=20 blockSize=10
class=FORMImportanceSamplingAnalysis name=myIS2 limitState=class=LimitStateImplementation name=aLimitState physicalModel=aModelPhys outputName=Y0 operator=class=Greater name=Unnamed threshold=20 maximumCalls=inf maximumCoefficientOfVariation=0.02 maximumElapsedTime=100000 seed=0 blockSize=100 standardSpaceDesignPoint=class=Point name=Unnamed dimension=2 values=[0,0] optimization algorithm=class=OptimizationAlgorithm implementation=class=AbdoRackwitz class=OptimizationAlgorithmImplementation problem=class=OptimizationProblem implementation=class=OptimizationProblemImplementation objective=class=Function name=Unnamed implementation=class=FunctionImplementation name=Unnamed description=[] evaluationImplementation=class=NoEvaluation name=Unnamed gradientImplementation=class=NoGradient name=Unnamed hessianImplementation=class=NoHessian name=Unnamed equality constraint=none inequality constraint=none bounds=none minimization=true dimension=0 startingPoint=class=Point name=Unnamed dimension=2 values=[1,1] maximumIterationNumber=100 maximumCallsNumber=1000 maximumAbsoluteError=1e-05 maximumRelativeError=1e-05 maximumResidualError=1e-05 maximumConstraintError=1e-05 tau=0.5 omega=0.0001 smooth=1.2 physicalStartingPoint=class=Point name=Unnamed dimension=2 values=[1,1]
result= class=SimulationReliabilityResult name=Unnamed simulationResult=probabilityEstimate=7.237985e-02 varianceEstimate=2.086018e-06 standard deviation=1.44e-03 coefficient of variation=2.00e-02 confidenceLength(0.95)=5.66e-03 outerSampling=50 blockSize=100
class=FORMImportanceSamplingAnalysis name=myIS3 limitState=class=LimitStateImplementation name=aLimitState physicalModel=aModelPhys outputName=Y0 operator=class=Greater name=Unnamed threshold=20 maximumCalls=1000 maximumCoefficientOfVariation=-1 maximumElapsedTime=60 seed=0 blockSize=10 standardSpaceDesignPoint=class=Point name=Unnamed dimension=2 values=[0,0] optimization algorithm=class=OptimizationAlgorithm implementation=class=AbdoRackwitz class=OptimizationAlgorithmImplementation problem=class=OptimizationProblem implementation=class=OptimizationProblemImplementation objective=class=Function name=Unnamed implementation=class=FunctionImplementation name=Unnamed description=[] evaluationImplementation=class=NoEvaluation name=Unnamed gradientImplementation=class=NoGradient name=Unnamed hessianImplementation=class=NoHessian name=Unnamed equality constraint=none inequality constraint=none bounds=none minimization=true dimension=0 startingPoint=class=Point name=Unnamed dimension=2 values=[1.08161,2.38966] maximumIterationNumber=100 maximumCallsNumber=1000 maximumAbsoluteError=1e-05 maximumRelativeError=1e-05 maximumResidualError=1e-05 maximumConstraintError=1e-05 tau=0.5 omega=0.0001 smooth=1.2 physicalStartingPoint=class=Point name=Unnamed dimension=2 values=[1.08161,2.38966]
result= class=SimulationReliabilityResult name=Unnamed simulationResult=probabilityEstimate=1.124241e-01 varianceEstimate=2.365458e-05 standard deviation=4.86e-03 coefficient of variation=4.33e-02 confidenceLength(0.95)=1.91e-02 outerSampling=100 blockSize=10
#!/usr/bin/env python
import openturns as ot
import persalys
myStudy = persalys.Study('myStudy')
persalys.Study.Add(myStudy)
dist_X0 = ot.Normal(1, 1)
X0 = persalys.Input('X0', 0, dist_X0, '')
dist_X1 = ot.Normal(1, 1)
X1 = persalys.Input('X1', 0, dist_X1, '')
X2 = persalys.Input('X2', 2, '')
Y0 = persalys.Output('Y0', '')
inputs = [X0, X1, X2]
outputs = [Y0]
formulas = ['sin(X0) + 8*X1 + X2']
aModelPhys = persalys.SymbolicPhysicalModel('aModelPhys', inputs, outputs, formulas)
myStudy.add(aModelPhys)
aLimitState = persalys.LimitState('aLimitState', aModelPhys, 'Y0', ot.Greater(), 20)
myStudy.add(aLimitState)
myIS = persalys.FORMImportanceSamplingAnalysis('myIS', aLimitState)
myIS.setMaximumCalls(1000)
myIS.setMaximumCoefficientOfVariation(0.1)
myIS.setMaximumElapsedTime(60)
myIS.setBlockSize(10)
myIS.setSeed(2)
myIS.setPhysicalStartingPoint([1, 1])
optimizationAlgo = ot.AbdoRackwitz()
optimizationAlgo.setMaximumCallsNumber(1000)
optimizationAlgo.setMaximumAbsoluteError(1e-05)
optimizationAlgo.setMaximumRelativeError(1e-05)
optimizationAlgo.setMaximumResidualError(1e-05)
optimizationAlgo.setMaximumConstraintError(1e-05)
myIS.setOptimizationAlgorithm(optimizationAlgo)
myStudy.add(myIS)
myIS2 = persalys.FORMImportanceSamplingAnalysis('myIS2', aLimitState)
myIS2.setMaximumCoefficientOfVariation(0.02)
myIS2.setMaximumElapsedTime(100000)
myIS2.setBlockSize(100)
myIS2.setSeed(0)
myIS2.setPhysicalStartingPoint([1, 1])
optimizationAlgo = ot.AbdoRackwitz()
optimizationAlgo.setMaximumCallsNumber(1000)
optimizationAlgo.setMaximumAbsoluteError(1e-05)
optimizationAlgo.setMaximumRelativeError(1e-05)
optimizationAlgo.setMaximumResidualError(1e-05)
optimizationAlgo.setMaximumConstraintError(1e-05)
myIS2.setOptimizationAlgorithm(optimizationAlgo)
myStudy.add(myIS2)
myIS3 = persalys.FORMImportanceSamplingAnalysis('myIS3', aLimitState)
myIS3.setMaximumCalls(1000)
myIS3.setMaximumCoefficientOfVariation(-1)
myIS3.setMaximumElapsedTime(60)
myIS3.setBlockSize(10)
myIS3.setSeed(0)
myIS3.setPhysicalStartingPoint([1.08161, 2.38966])
optimizationAlgo = ot.AbdoRackwitz()
optimizationAlgo.setMaximumCallsNumber(1000)
optimizationAlgo.setMaximumAbsoluteError(1e-05)
optimizationAlgo.setMaximumRelativeError(1e-05)
optimizationAlgo.setMaximumResidualError(1e-05)
optimizationAlgo.setMaximumConstraintError(1e-05)
myIS3.setOptimizationAlgorithm(optimizationAlgo)
myStudy.add(myIS3)
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