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#!/usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
# ot.Log.Show(ot.Log.ALL)
dim = 7
# root cause
mean = [200.0] * dim
mean[-1] = 60
mean[-2] = 60
sigma = [30.0] * dim
sigma[-1] = 15.0
R = ot.CorrelationMatrix(dim)
for i in range(5):
for j in range(i):
R[i, j] = 0.5
dist = ot.Normal(mean, sigma, R)
# leaf events
X = ot.RandomVector(dist)
inputs = ["M1", "M2", "M3", "M4", "M5", "H", "V"]
e0 = ot.ThresholdEvent(
ot.CompositeRandomVector(ot.SymbolicFunction(inputs, ["M1+M2+M4+M5-5*H"]), X),
ot.Less(),
0.0,
)
e1 = ot.ThresholdEvent(
ot.CompositeRandomVector(ot.SymbolicFunction(inputs, ["M2+2*M3+M4-5*V"]), X),
ot.Less(),
0.0,
)
e2 = ot.ThresholdEvent(
ot.CompositeRandomVector(
ot.SymbolicFunction(inputs, ["M1+2*M3+2*M4+M5-5*H-5*V"]), X
),
ot.Less(),
0.0,
)
e3 = ot.ThresholdEvent(
ot.CompositeRandomVector(ot.SymbolicFunction(inputs, ["-(M1+M2+M4+M5-5*80.0)"]), X),
ot.Less(),
0.0,
)
e4 = ot.ThresholdEvent(
ot.CompositeRandomVector(ot.SymbolicFunction(inputs, ["-(M2+2*M3+M4-5*70.0)"]), X),
ot.Less(),
0.0,
)
e5 = ot.ThresholdEvent(
ot.CompositeRandomVector(
ot.SymbolicFunction(inputs, ["-(M1+2*M3+2*M4+M5-5*80.0-5*70.0)"]), X
),
ot.Less(),
0.0,
)
# solver
solver = ot.AbdoRackwitz()
solver.setMaximumIterationNumber(1000)
solver.setMaximumAbsoluteError(1.0e-3)
solver.setMaximumRelativeError(1.0e-3)
solver.setMaximumResidualError(1.0e-3)
solver.setMaximumConstraintError(1.0e-3)
for event in [e0, e3, e4, e5, e1, e2]:
algo = ot.FORM(solver, event, mean)
algo.run()
result = algo.getResult()
print("beta = %.6g" % result.getGeneralisedReliabilityIndex())
# system event in DNF form (union of intersections)
event = ot.UnionEvent(
[
ot.IntersectionEvent([e0, e3, e4, e5]),
ot.IntersectionEvent([e1, e3, e4, e5]),
# ot.IntersectionEvent([e2, e3, e4, e5]),
]
)
# sampling test
pf_sim = event.getSample(10000).computeMean()[0]
print("pf_sim = %.6g" % pf_sim)
ott.assert_almost_equal(pf_sim, 0.0023, 1e-3, 1e-3)
# system FORM
algo = ot.SystemFORM(solver, event, mean)
algo.run()
result = algo.getResult()
pf_sysform = result.getEventProbability()
print("pf_sysform = %.6g" % pf_sysform)
ott.assert_almost_equal(pf_sysform, 0.00234983, 1e-4, 1e-4)
for form_result in result.getFORMResultCollection():
print(" beta=", form_result.getGeneralisedReliabilityIndex())
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