Documentation
/ User's manual in Python
: 
| XIV.14. Macros Reliability | ||
|---|---|---|
 | Chapter XIV. Use-cases in python |  |
The objective of the macro is to perform a FORM SORM study.
This example comes from De Victor's thesis. The problem has three input variables x, fe and M. Each variable follows a normal distribution with the following mean and standard error: x is N(40, 5), fe is N(50, 2.5) and M is N(1000,200). The safety threshold is calculated with M-x*fe and should be positive for a safe solution.
The Script follows the following steps:
a macro section to choose the optimisation solver;
a namespace section;
the definition of the safety function;
the study procedure.
"""
Example of reliability form / sorm usage
"""
import numpy as np
from rootlogon import DataServer, Reliability, Relauncher, Reoptimizer
def fselect(x_var, fe_var, m_var):
"""Compute the criterion."""
# critere
return [m_var-x_var*fe_var]
# inputs
x = DataServer.TNormalDistribution("x", 40, 5)
fe = DataServer.TNormalDistribution("x2", 50, 2.5)
M = DataServer.TNormalDistribution("M", 1000, 200)
# outputs
cont = DataServer.TAttribute("seuil")
# starting point
start = np.array([-1., -1., 1.], dtype=np.float64)
# code
fobj = Reliability.TSimpleTransform()
fobj.addParameter(x)
fobj.addParameter(fe)
fobj.addParameter(M)
fcont = Relauncher.TPythonEval(fselect)
fcont.addInput(x)
fcont.addInput(fe)
fcont.addInput(M)
fcont.addOutput(cont)
code = Reliability.TFormEval(fobj, fcont)
it = Reoptimizer.TGreaterFit(0.0)
code.addConstraint(cont, it)
# runner
run = Relauncher.TSequentialRun(code)
run.startSlave()
if run.onMaster():
# tds
tds = DataServer.TDataServer("toto", "tds for vizir test")
code.addAllInputs(tds)
# FORM
# optimizer
solv = Reoptimizer.TNloptCobyla()
nlo = Reoptimizer.TNlopt(tds, run, solv)
code.addObjective(nlo)
# resolution
nlo.setStartingPoint(len(start), start)
nlo.solverLoop()
# results
# tds.getTuple().Scan("*")
# SORM
sorm = Reliability.TSorm(tds, run)
sorm.solverLoop()
# results
tds.getTuple().Scan("*")
# cleanup
run.stopSlave()
The study procedure requests the definition of:
variables: input variables with their statistical laws and the output variable;
the starting point for the design point optimisation. Take care that it is defined in the normal space (not in the physical space);
evaluation functions; the transformation function, the safety function, and the composition of both of them;
a standard sequential
TRun;the
TDataServerwith its inputs declaration;the FORM optimisation sequence;
the SORM estimation sequence;
back-up and finalisation.
Processing reliabilityFormSorm.py... |....:....|....:....|....:....|....:....|....:....0050 |....:....|.... :************************************************************************************************************************************************************ * Row * toto__n__ * u_x.u_x * u_x2.u_x2 * u_M.u_M * betaHL.be * form.form * x.x * x2.x2 * M.M * seuil.seu * factor.fa * sorm.sorm * ************************************************************************************************************************************************************ * 0 * 0 * -2.289658 * -0.677000 * 1.8963080 * 3.0490734 * 0.0011477 * 28.551708 * 48.307498 * 1379.2616 * -1.67e-05 * 1.0203699 * 0.0011711 * ************************************************************************************************************************************************************
There are two lines used to show the optimisation progress (evaluation numbers), and then the resulting TDataServer is
shown. Columns start with two indexes, the three normal variables, the Hasofer-Lind indicator, the FORM estimation,
the three physical variables, the FORM correction, and the SORM estimation.
| |  | |
| XIV.13. Macros UncertModeler |  | References |