#! /usr/bin/env python from __future__ import print_function from openturns import * #from math import * TESTPREAMBLE() RandomGenerator.SetSeed(0) try: # # Physical model # inputFunction = Description(2) inputFunction[0] = "X1" inputFunction[1] = "X2" outputFunction = Description(1) outputFunction[0] = "G" formulas = Description(outputFunction.getSize()) formulas[0] = "2.5 + 0.1*(X1-X2)^2.0 - (X1+X2)/sqrt(2.0)" EtatLimite = NumericalMathFunction(inputFunction, outputFunction, formulas) dim = EtatLimite.getInputDimension() print(dim) # # Probabilistic model # mean = NumericalPoint(dim, 0.0) mean[0] = 0.0 mean[1] = 0.0 sigma = NumericalPoint(dim, 0.0) sigma[0] = 1.0 sigma[1] = 1.0 R = IdentityMatrix(dim) myDistribution = Normal(mean, sigma, R) start = myDistribution.getMean() Covariance = myDistribution.getCovariance() # # Limit state # vect = RandomVector(myDistribution) output = RandomVector(EtatLimite, vect) myEvent = Event(output, Less(), 0.0) # # Calculs # # # FORM/SORM Cobyla myCobyla = Cobyla() myCobyla.setMaximumIterationNumber(100 * dim) myCobyla.setMaximumAbsoluteError(1.0e-10) myCobyla.setMaximumRelativeError(1.0e-10) myCobyla.setMaximumResidualError(1.0e-10) myCobyla.setMaximumConstraintError(1.0e-10) myAlgoC = FORM(myCobyla, myEvent, start) myAlgoC2 = SORM(myCobyla, myEvent, start) myAlgoC.run() myAlgoC2.run() resultC = FORMResult(myAlgoC.getResult()) resultC2 = SORMResult(myAlgoC2.getResult()) # # FORM/SORM Abdo Rackwitz myAbdoRackwitz = AbdoRackwitz() myAbdoRackwitz.setMaximumIterationNumber(100 * dim) myAbdoRackwitz.setMaximumAbsoluteError(1.0e-10) myAbdoRackwitz.setMaximumRelativeError(1.0e-10) myAbdoRackwitz.setMaximumResidualError(1.0e-10) myAbdoRackwitz.setMaximumConstraintError(1.0e-10) myAlgoAR = FORM(myAbdoRackwitz, myEvent, start) myAlgoAR2 = SORM(myAbdoRackwitz, myEvent, start) myAlgoAR.run() myAlgoAR2.run() resultAR = FORMResult(myAlgoAR.getResult()) resultAR2 = SORMResult(myAlgoAR2.getResult()) # # Monte Carlo CoV_MC = 0.5 myMC = MonteCarlo(myEvent) myMC.setMaximumOuterSampling(100000) myMC.setBlockSize(1) myMC.setMaximumCoefficientOfVariation(CoV_MC) myMC.run() # # LHS CoV_LHS = 0.1 myLHS = LHS(myEvent) myLHS.setMaximumOuterSampling(100000) myLHS.setBlockSize(1) myLHS.setMaximumCoefficientOfVariation(CoV_LHS) myLHS.run() # # # Outputs # print("") print("") print( "************************************************************************************************") print( "***************************************** FORM COBYLA *****************************************") print( "************************************************************************************************") print("event probability = %.5e" % PfC) print("generalized reliability index = %.5f" % Beta_generalizedC) print( "************************************************************************************************") for i in range(u_starC.getDimension()): print("standard space design point = %.5f" % u_starC[i]) print( "************************************************************************************************") for i in range(x_starC.getDimension()): print("physical space design point = %.5f" % x_starC[i]) print( "************************************************************************************************") print("is standard point origin in failure space? ", PtC) print( "************************************************************************************************") for i in range(gammaC.getDimension()): print("importance factors = %.5f" % gammaC[i]) print( "************************************************************************************************") print("Hasofer reliability index = %.5f" % beta_hasoferC) print( "************************************************************************************************") for i in range(SensitivityC.getSize()): for j in range(SensitivityC[i].getDimension()): print("Pf sensitivity = %.5f" % SensitivityC[i][j]) print( "************************************************************************************************") print("") print( "************************************************************************************************") print( "************************************** FORM ABDO RACKWITZ **************************************") print( "************************************************************************************************") print("event probability = %.5e" % PfAR) print("generalized reliability index = %.5f" % Beta_generalizedAR) print( "************************************************************************************************") for i in range(u_starAR.getDimension()): print("standard space design point = %.5f" % u_starAR[i]) print( "************************************************************************************************") for i in range(x_starAR.getDimension()): print("physical space design point = %.5f" % x_starAR[i]) print( "************************************************************************************************") print("is standard point origin in failure space? ", PtAR) print( "************************************************************************************************") for i in range(gammaAR.getDimension()): print("importance factors = %.5f" % gammaAR[i]) print( "************************************************************************************************") print("Hasofer reliability index = %.5f" % beta_hasoferAR) print( "************************************************************************************************") for i in range(SensitivityAR.getSize()): for j in range(SensitivityAR[i].getDimension()): print("Pf sensitivity = %.5f" % SensitivityAR[i][j]) print( "************************************************************************************************") print("") print( "************************************************************************************************") print( "***************************************** SORM COBYLA *****************************************") print( "************************************************************************************************") print("Breitung event probability = %.5e" % PFBreitC2) print("Breitung generalized reliability index = %.5f" % BetaBreitC2) print("HohenBichler event probability = %.5e" % PFHBC2) print("HohenBichler generalized reliability index = %.5f" % BetaHBC2) print("Tvedt event probability = %.5e" % PFTvedtC2) print("Tvedt generalized reliability index = %.5f" % BetaTvedtC2) print( "************************************************************************************************") for i in range(CurvC2.getDimension()): print("sorted curvatures = %.5f" % cleanScalar(CurvC2[i])) print( "************************************************************************************************") for i in range(u_starC2.getDimension()): print("standard space design point = %.5f" % u_starC2[i]) print( "************************************************************************************************") for i in range(x_starC2.getDimension()): print("physical space design point = %.5f" % x_starC2[i]) print( "************************************************************************************************") print( "************************************************************************************************") print("is standard point origin in failure space? ", PtC2) print( "************************************************************************************************") for i in range(gammaC2.getDimension()): print("importance factors = %.5f" % gammaC2[i]) print( "************************************************************************************************") print("Hasofer reliability index = %.5f" % beta_hasoferC2) print( "************************************************************************************************") print("") print( "************************************************************************************************") print( "************************************** SORM ABDO RACKWITZ **************************************") print( "************************************************************************************************") print("Breitung event probability = %.5e" % PFBreitAR2) print("Breitung generalized reliability index = %.5f" % BetaBreitAR2) print("HohenBichler event probability = %.5e" % PFHBAR2) print("HohenBichler generalized reliability index = %.5f" % BetaHBAR2) print("Tvedt event probability = %.5e" % PFTvedtAR2) print("Tvedt generalized reliability index = %.5f" % BetaTvedtAR2) print( "************************************************************************************************") for i in range(CurvAR2.getDimension()): print("sorted curvatures = %.5f" % cleanScalar(CurvAR2[i])) print( "************************************************************************************************") for i in range(u_starAR2.getDimension()): print("standard space design point = %.5f" % u_starAR2[i]) print( "************************************************************************************************") for i in range(x_starAR2.getDimension()): print("physical space design point = %.5f" % x_starAR2[i]) print( "************************************************************************************************") print( "************************************************************************************************") print("is standard point origin in failure space? ", PtAR2) print( "************************************************************************************************") for i in range(gammaAR2.getDimension()): print("importance factors = %.5f" % gammaAR2[i]) print( "************************************************************************************************") print("Hasofer reliability index = %.5f" % beta_hasoferAR2) print( "************************************************************************************************") print("") print( "************************************************************************************************") print( "**************************************** MONTE CARLO *******************************************") print( "************************************************************************************************") print("Pf estimation = %.5e" % PFMC) print("Pf Variance estimation = %.5e" % Variance_PF_MC) print("CoV = %.5f" % CVMC) print("90% Confidence Interval =", "%.5e" % length90MC) print("CI at 90% =[", "%.5e" % (PFMC - 0.5 * length90MC), "; %.5e" % (PFMC + 0.5 * length90MC), "]") print( "************************************************************************************************") print("") print( "************************************************************************************************") print( "******************************************* L H S **********************************************") print( "************************************************************************************************") print("Pf estimation = %.5e" % PFLHS) print("Pf Variance estimation = %.5e" % Variance_PF_LHS) print("CoV = %.5f" % CVLHS) print("90% Confidence Interval =", "%.5e" % length90LHS) print("CI at 90% =[", "%.5e" % (PFLHS - 0.5 * length90LHS), "; %.5e" % (PFLHS + 0.5 * length90LHS), "]") print( "************************************************************************************************") print("") except: import sys print("t_Waarts_convex.py", sys.exc_info()[0], sys.exc_info()[1])