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class=FORMAnalysis name=myFORM limitState=class=LimitStateImplementation name=aLimitState physicalModel=aModelPhys outputName=Y0 operator=class=Greater name=Unnamed threshold=20 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=FORMResult class=AnalyticalResult standardSpaceDesignPoint=class=Point name=Standard Space Design Point dimension=2 values=[0.0819089,1.38964] physicalSpaceDesignPoint=class=Point name=Physical Space Design Point dimension=2 values=[1.08191,2.38964] limitStateVariable=class=RandomVector implementation=class=ThresholdEventImplementation antecedent=class=CompositeRandomVector function=class=Function name=Unnamed implementation=class=FunctionImplementation name=Unnamed description=[X0,X1,Y0] evaluationImplementation=MemoizeEvaluation(class=SymbolicEvaluation name=Unnamed inputVariablesNames=[X0,X1] outputVariablesNames=[y0] formulas=[sin(X0) + 8*X1]) gradientImplementation=class=SymbolicGradient name=Unnamed evaluation=class=SymbolicEvaluation name=Unnamed inputVariablesNames=[X0,X1] outputVariablesNames=[y0] formulas=[sin(X0) + 8*X1] hessianImplementation=class=SymbolicHessian name=Unnamed evaluation=class=SymbolicEvaluation name=Unnamed inputVariablesNames=[X0,X1] outputVariablesNames=[y0] formulas=[sin(X0) + 8*X1] antecedent=class=UsualRandomVector distribution=class=JointDistribution name=JointDistribution dimension=2 copula=class=BlockIndependentCopula name=BlockIndependentCopula dimension=2 copula[0]=class=IndependentCopula name=IndependentCopula dimension=2 marginal[0]=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[1] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] marginal[1]=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[1] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] operator=class=Greater name=Unnamed threshold=20 isStandardPointOriginInFailureSpace=false hasoferReliabilityIndex=1.39205 importanceFactors=class=PointWithDescription name=Unnamed dimension=0 description=[] values=[] classicalImportanceFactors=class=PointWithDescription name=Unnamed dimension=0 description=[] values=[] hasoferReliabilityIndexSensitivity=[[mu_0_marginal_0 : -0.0586046, sigma_0_marginal_0 : -0.00480024],[mu_0_marginal_1 : -0.998281, sigma_0_marginal_1 : -1.38725],[]] eventProbability=0.0819529 generalisedReliabilityIndex=1.39205 eventProbabilitySensitivity=[[mu_0_marginal_0 : 0.00887259, sigma_0_marginal_0 : 0.000726744],[mu_0_marginal_1 : 0.151137, sigma_0_marginal_1 : 0.210027],[]]
class=FORMAnalysis name=myFORM2 limitState=class=LimitStateImplementation name=aLimitState physicalModel=aModelPhys outputName=Y0 operator=class=Greater name=Unnamed threshold=20 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=FORMResult class=AnalyticalResult standardSpaceDesignPoint=class=Point name=Standard Space Design Point dimension=2 values=[0.0687464,1.14043] physicalSpaceDesignPoint=class=Point name=Physical Space Design Point dimension=2 values=[1.06875,2.14043] limitStateVariable=class=RandomVector implementation=class=ThresholdEventImplementation antecedent=class=CompositeRandomVector function=class=Function name=Unnamed implementation=class=FunctionImplementation name=Unnamed description=[X0,X1,Y0] evaluationImplementation=class=ParametricEvaluation function=class=Function name=Unnamed implementation=class=FunctionImplementation name=Unnamed description=[X0,X1,X2,Y0] evaluationImplementation=MemoizeEvaluation(class=SymbolicEvaluation name=Unnamed inputVariablesNames=[X0,X1,X2] outputVariablesNames=[y0] formulas=[sin(X0) + 8*X1 + X2]) gradientImplementation=class=SymbolicGradient name=Unnamed evaluation=class=SymbolicEvaluation name=Unnamed inputVariablesNames=[X0,X1,X2] outputVariablesNames=[y0] formulas=[sin(X0) + 8*X1 + X2] hessianImplementation=class=SymbolicHessian name=Unnamed evaluation=class=SymbolicEvaluation name=Unnamed inputVariablesNames=[X0,X1,X2] outputVariablesNames=[y0] formulas=[sin(X0) + 8*X1 + X2] parameters positions=[2] parameters=class=PointWithDescription name=Unnamed dimension=1 description=[X2] values=[2] input positions=[0,1] gradientImplementation=class=ParametricGradient evaluation=class=ParametricEvaluation function=class=Function name=Unnamed implementation=class=FunctionImplementation name=Unnamed description=[X0,X1,X2,Y0] evaluationImplementation=MemoizeEvaluation(class=SymbolicEvaluation name=Unnamed inputVariablesNames=[X0,X1,X2] outputVariablesNames=[y0] formulas=[sin(X0) + 8*X1 + X2]) gradientImplementation=class=SymbolicGradient name=Unnamed evaluation=class=SymbolicEvaluation name=Unnamed inputVariablesNames=[X0,X1,X2] outputVariablesNames=[y0] formulas=[sin(X0) + 8*X1 + X2] hessianImplementation=class=SymbolicHessian name=Unnamed evaluation=class=SymbolicEvaluation name=Unnamed inputVariablesNames=[X0,X1,X2] outputVariablesNames=[y0] formulas=[sin(X0) + 8*X1 + X2] parameters positions=[2] parameters=class=PointWithDescription name=Unnamed dimension=1 description=[X2] values=[2] input positions=[0,1] hessianImplementation=class=ParametricHessian evaluation=class=ParametricEvaluation function=class=Function name=Unnamed implementation=class=FunctionImplementation name=Unnamed description=[X0,X1,X2,Y0] evaluationImplementation=MemoizeEvaluation(class=SymbolicEvaluation name=Unnamed inputVariablesNames=[X0,X1,X2] outputVariablesNames=[y0] formulas=[sin(X0) + 8*X1 + X2]) gradientImplementation=class=SymbolicGradient name=Unnamed evaluation=class=SymbolicEvaluation name=Unnamed inputVariablesNames=[X0,X1,X2] outputVariablesNames=[y0] formulas=[sin(X0) + 8*X1 + X2] hessianImplementation=class=SymbolicHessian name=Unnamed evaluation=class=SymbolicEvaluation name=Unnamed inputVariablesNames=[X0,X1,X2] outputVariablesNames=[y0] formulas=[sin(X0) + 8*X1 + X2] parameters positions=[2] parameters=class=PointWithDescription name=Unnamed dimension=1 description=[X2] values=[2] input positions=[0,1] antecedent=class=UsualRandomVector distribution=class=JointDistribution name=JointDistribution dimension=2 copula=class=BlockIndependentCopula name=BlockIndependentCopula dimension=2 copula[0]=class=IndependentCopula name=IndependentCopula dimension=2 marginal[0]=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[1] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] marginal[1]=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[1] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] operator=class=Greater name=Unnamed threshold=20 isStandardPointOriginInFailureSpace=false hasoferReliabilityIndex=1.1425 importanceFactors=class=PointWithDescription name=Unnamed dimension=0 description=[] values=[] classicalImportanceFactors=class=PointWithDescription name=Unnamed dimension=0 description=[] values=[] hasoferReliabilityIndexSensitivity=[[mu_0_marginal_0 : -0.0600444, sigma_0_marginal_0 : -0.00412783],[mu_0_marginal_1 : -0.998196, sigma_0_marginal_1 : -1.13837],[],[ : -0.124774]] eventProbability=0.126624 generalisedReliabilityIndex=1.1425 eventProbabilitySensitivity=[[mu_0_marginal_0 : 0.0124721, sigma_0_marginal_0 : 0.000857415],[mu_0_marginal_1 : 0.207341, sigma_0_marginal_1 : 0.236456],[],[ : 0.0259176]]
class=FORMAnalysis name=myFORM3 limitState=class=LimitStateImplementation name=aLimitState physicalModel=aModelPhys outputName=Y0 operator=class=Greater name=Unnamed threshold=20 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=FORMResult class=AnalyticalResult standardSpaceDesignPoint=class=Point name=Standard Space Design Point dimension=2 values=[0.0688187,1.14042] physicalSpaceDesignPoint=class=Point name=Physical Space Design Point dimension=2 values=[1.06882,2.14042] limitStateVariable=class=RandomVector implementation=class=ThresholdEventImplementation antecedent=class=CompositeRandomVector function=class=Function name=Unnamed implementation=class=FunctionImplementation name=Unnamed description=[X0,X1,Y0] evaluationImplementation=class=ParametricEvaluation function=class=Function name=Unnamed implementation=class=FunctionImplementation name=Unnamed description=[X0,X1,X2,Y0] evaluationImplementation=MemoizeEvaluation(class=SymbolicEvaluation name=Unnamed inputVariablesNames=[X0,X1,X2] outputVariablesNames=[y0] formulas=[sin(X0) + 8*X1 + X2]) gradientImplementation=class=SymbolicGradient name=Unnamed evaluation=class=SymbolicEvaluation name=Unnamed inputVariablesNames=[X0,X1,X2] outputVariablesNames=[y0] formulas=[sin(X0) + 8*X1 + X2] hessianImplementation=class=SymbolicHessian name=Unnamed evaluation=class=SymbolicEvaluation name=Unnamed inputVariablesNames=[X0,X1,X2] outputVariablesNames=[y0] formulas=[sin(X0) + 8*X1 + X2] parameters positions=[2] parameters=class=PointWithDescription name=Unnamed dimension=1 description=[X2] values=[2] input positions=[0,1] gradientImplementation=class=ParametricGradient evaluation=class=ParametricEvaluation function=class=Function name=Unnamed implementation=class=FunctionImplementation name=Unnamed description=[X0,X1,X2,Y0] evaluationImplementation=MemoizeEvaluation(class=SymbolicEvaluation name=Unnamed inputVariablesNames=[X0,X1,X2] outputVariablesNames=[y0] formulas=[sin(X0) + 8*X1 + X2]) gradientImplementation=class=SymbolicGradient name=Unnamed evaluation=class=SymbolicEvaluation name=Unnamed inputVariablesNames=[X0,X1,X2] outputVariablesNames=[y0] formulas=[sin(X0) + 8*X1 + X2] hessianImplementation=class=SymbolicHessian name=Unnamed evaluation=class=SymbolicEvaluation name=Unnamed inputVariablesNames=[X0,X1,X2] outputVariablesNames=[y0] formulas=[sin(X0) + 8*X1 + X2] parameters positions=[2] parameters=class=PointWithDescription name=Unnamed dimension=1 description=[X2] values=[2] input positions=[0,1] hessianImplementation=class=ParametricHessian evaluation=class=ParametricEvaluation function=class=Function name=Unnamed implementation=class=FunctionImplementation name=Unnamed description=[X0,X1,X2,Y0] evaluationImplementation=MemoizeEvaluation(class=SymbolicEvaluation name=Unnamed inputVariablesNames=[X0,X1,X2] outputVariablesNames=[y0] formulas=[sin(X0) + 8*X1 + X2]) gradientImplementation=class=SymbolicGradient name=Unnamed evaluation=class=SymbolicEvaluation name=Unnamed inputVariablesNames=[X0,X1,X2] outputVariablesNames=[y0] formulas=[sin(X0) + 8*X1 + X2] hessianImplementation=class=SymbolicHessian name=Unnamed evaluation=class=SymbolicEvaluation name=Unnamed inputVariablesNames=[X0,X1,X2] outputVariablesNames=[y0] formulas=[sin(X0) + 8*X1 + X2] parameters positions=[2] parameters=class=PointWithDescription name=Unnamed dimension=1 description=[X2] values=[2] input positions=[0,1] antecedent=class=UsualRandomVector distribution=class=JointDistribution name=JointDistribution dimension=2 copula=class=BlockIndependentCopula name=BlockIndependentCopula dimension=2 copula[0]=class=IndependentCopula name=IndependentCopula dimension=2 marginal[0]=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[1] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] marginal[1]=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[1] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] operator=class=Greater name=Unnamed threshold=20 isStandardPointOriginInFailureSpace=false hasoferReliabilityIndex=1.1425 importanceFactors=class=PointWithDescription name=Unnamed dimension=0 description=[] values=[] classicalImportanceFactors=class=PointWithDescription name=Unnamed dimension=0 description=[] values=[] hasoferReliabilityIndexSensitivity=[[mu_0_marginal_0 : -0.0600365, sigma_0_marginal_0 : -0.00413164],[mu_0_marginal_1 : -0.998196, sigma_0_marginal_1 : -1.13836],[],[ : -0.124775]] eventProbability=0.126624 generalisedReliabilityIndex=1.1425 eventProbabilitySensitivity=[[mu_0_marginal_0 : 0.0124705, sigma_0_marginal_0 : 0.000858205],[mu_0_marginal_1 : 0.207341, sigma_0_marginal_1 : 0.236456],[],[ : 0.0259176]]
#!/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)
myFORM = persalys.FORMAnalysis('myFORM', aLimitState)
myFORM.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)
myFORM.setOptimizationAlgorithm(optimizationAlgo)
myStudy.add(myFORM)
myFORM2 = persalys.FORMAnalysis('myFORM2', aLimitState)
myFORM2.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)
myFORM2.setOptimizationAlgorithm(optimizationAlgo)
myStudy.add(myFORM2)
myFORM3 = persalys.FORMAnalysis('myFORM3', aLimitState)
myFORM3.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)
myFORM3.setOptimizationAlgorithm(optimizationAlgo)
myStudy.add(myFORM3)
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