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class=SORMAnalysis name=mySORM 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= Probability estimate (Breitung)=0.0763276
Generalised reliability (Breitung)=1.43022
Probability estimate (Hohenbichler)=0.0747247
Generalised reliability (Hohenbichler)=1.44148
Probability estimate (Tvedt)=0.0745014
Generalised reliability (Tvedt)1.44306
class=SORMAnalysis name=mySORM2 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= Probability estimate (Breitung)=0.119408
Generalised reliability (Breitung)=1.17795
Probability estimate (Hohenbichler)=0.116627
Generalised reliability (Hohenbichler)=1.19202
Probability estimate (Tvedt)=0.116275
Generalised reliability (Tvedt)1.19381
class=SORMAnalysis name=mySORM3 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= Probability estimate (Breitung)=0.119408
Generalised reliability (Breitung)=1.17795
Probability estimate (Hohenbichler)=0.116627
Generalised reliability (Hohenbichler)=1.19202
Probability estimate (Tvedt)=0.116275
Generalised reliability (Tvedt)1.19382
#!/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)
mySORM = persalys.SORMAnalysis('mySORM', aLimitState)
mySORM.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)
mySORM.setOptimizationAlgorithm(optimizationAlgo)
myStudy.add(mySORM)
mySORM2 = persalys.SORMAnalysis('mySORM2', aLimitState)
mySORM2.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)
mySORM2.setOptimizationAlgorithm(optimizationAlgo)
myStudy.add(mySORM2)
mySORM3 = persalys.SORMAnalysis('mySORM3', aLimitState)
mySORM3.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)
mySORM3.setOptimizationAlgorithm(optimizationAlgo)
myStudy.add(mySORM3)
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