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#! /usr/bin/env python
from __future__ import print_function
from openturns import *
from math import *
def printNumericalPoint(point, digits):
oss = "["
eps = pow(0.1, digits)
for i in range(point.getDimension()):
if i == 0:
sep = ""
else:
sep = ","
if fabs(point[i]) < eps:
oss += sep + '%.6f' % fabs(point[i])
else:
oss += sep + '%.6f' % point[i]
sep = ","
oss += "]"
return oss
TESTPREAMBLE()
try:
# We create a numerical math function
myFunction = NumericalMathFunction(
["E", "F", "L", "I"], ["d"], ["-F*L^3/(3*E*I)"])
dim = myFunction.getInputDimension()
# We create a normal distribution point of dimension 1
mean = NumericalPoint(dim, 0.0)
# E
mean[0] = 50.0
# F
mean[1] = 1.0
# L
mean[2] = 10.0
# I
mean[3] = 5.0
sigma = NumericalPoint(dim, 1.0)
R = IdentityMatrix(dim)
myDistribution = Normal(mean, sigma, R)
# We create a 'usual' RandomVector from the Distribution
vect = RandomVector(myDistribution)
# We create a composite random vector
output = RandomVector(myFunction, vect)
# We create an Event from this RandomVector
myEvent = Event(output, Less(), -1.5)
# We create a NearestPoint algorithm
myAbdoRackwitz = AbdoRackwitz()
myAbdoRackwitz.setMaximumIterationNumber(100)
myAbdoRackwitz.setMaximumAbsoluteError(1.0e-10)
myAbdoRackwitz.setMaximumRelativeError(1.0e-10)
myAbdoRackwitz.setMaximumResidualError(1.0e-10)
myAbdoRackwitz.setMaximumConstraintError(1.0e-10)
print("myAbdoRackwitz=", myAbdoRackwitz)
# We create a FORM algorithm
# The first parameter is an OptimizationSolver
# The second parameter is an event
# The third parameter is a starting point for the design point research
myAlgo = SORM(myAbdoRackwitz, myEvent, mean)
# Perform the simulation
myAlgo.run()
# Stream out the result
result = myAlgo.getResult()
digits = 5
print("Breitung event probability=%.6f" %
result.getEventProbabilityBreitung())
print("Breitung generalized reliability index=%.6f" %
result.getGeneralisedReliabilityIndexBreitung())
print("HohenBichler event probability=%.6f" %
result.getEventProbabilityHohenBichler())
print("HohenBichler generalized reliability index=%.6f" %
result.getGeneralisedReliabilityIndexHohenBichler())
print("Tvedt event probability=%.6f" % result.getEventProbabilityTvedt())
print("Tvedt generalized reliability index=%.6f" %
result.getGeneralisedReliabilityIndexTvedt())
print("sorted curvatures=", printNumericalPoint(
result.getSortedCurvatures(), digits))
print("standard space design point=", printNumericalPoint(
result.getStandardSpaceDesignPoint(), digits))
print("physical space design point=", printNumericalPoint(
result.getPhysicalSpaceDesignPoint(), digits))
# Is the standard point origin in failure space?
print("is standard point origin in failure space? ",
result.getIsStandardPointOriginInFailureSpace())
print("importance factors=", printNumericalPoint(
result.getImportanceFactors(), digits))
print("Hasofer reliability index=%.6f" %
result.getHasoferReliabilityIndex())
except:
import sys
print("t_SORM_std.py", sys.exc_info()[0], sys.exc_info()[1])
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