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#! /usr/bin/env python
import openturns as ot
import math as m
def printPoint(point, digits):
oss = "["
eps = m.pow(0.1, digits)
for i in range(point.getDimension()):
if i == 0:
sep = ""
else:
sep = ","
if abs(point[i]) < eps:
oss += sep + "%.6f" % abs(point[i])
else:
oss += sep + "%.6f" % point[i]
sep = ","
oss += "]"
return oss
ot.TESTPREAMBLE()
# We create a numerical math function
myFunction = ot.SymbolicFunction(["E", "F", "L", "I"], ["-F*L^3/(3*E*I)"])
dim = myFunction.getInputDimension()
# We create a normal distribution point of dimension 1
mean = ot.Point(dim, 0.0)
# E
mean[0] = 50.0
# F
mean[1] = 1.0
# L
mean[2] = 10.0
# I
mean[3] = 5.0
sigma = ot.Point(dim, 1.0)
R = ot.IdentityMatrix(dim)
myDistribution = ot.Normal(mean, sigma, R)
# We create a 'usual' RandomVector from the Distribution
vect = ot.RandomVector(myDistribution)
# We create a composite random vector
output = ot.CompositeRandomVector(myFunction, vect)
# We create an Event from this RandomVector
myEvent = ot.ThresholdEvent(output, ot.Less(), -1.5)
# We create a NearestPoint algorithm
myAbdoRackwitz = ot.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 OptimizationAlgorithm
# The second parameter is an event
# The third parameter is a starting point for the design point research
myAlgo = ot.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=", printPoint(result.getSortedCurvatures(), digits))
print(
"standard space design point=",
printPoint(result.getStandardSpaceDesignPoint(), digits),
)
print(
"physical space design point=",
printPoint(result.getPhysicalSpaceDesignPoint(), digits),
)
# Is the standard point origin in failure space?
print(
"is standard point origin in failure space? ",
result.getIsStandardPointOriginInFailureSpace(),
)
print("importance factors=", printPoint(result.getImportanceFactors(), digits))
print("Hasofer reliability index=%.6f" % result.getHasoferReliabilityIndex())
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