## -----------------------------------------------------------------------------
## Calcul de probabilite associe a des evenemenrs rares
## * Limit State Function (LSF) :
## !!! DEFINITION DANS ESPACE NORME CENTRE : LSF DOIT COMPORTER DES TRANSFO
## ISO-PROBABILISTES SI NECESSAIRES
## * Methode : MP
## * Reference : WAARTS
## -----------------------------------------------------------------------------
## Copyright (C) 2015
## Gilles DEFAUX
## CEA / DAM / DIF
## gilles.defaux@cea.fr
## -----------------------------------------------------------------------------
## On efface toutes les donnees
rm(list=ls(all=TRUE))
library(mistral)
## -----------------------------------
## PARAMETRES ET OPTIONS
## -----------------------------------
set.seed(123456)
NbSim = 200
## -----------------------------------
## DEFINITION DU PROBLEME
## -----------------------------------
Dim = 2
## Modele Stochastique
distX1 <- list(type='Norm', MEAN=0.0, STD=1.0, P1=NULL, P2=NULL, NAME='X1')
distX2 <- list(type='Norm', MEAN=0.0, STD=1.0, P1=NULL, P2=NULL, NAME='X2')
input.margin <- list(distX1,distX2)
input.Rho <- diag(Dim)
L0 <- chol(input.Rho)
## Fonction de performance
lsf = function(U) {
X <- UtoX(U, input.margin, L0)
G <- 5.0 - 0.2*(X[1,]-X[2,])^2.0 - (X[1,]+X[2,])/sqrt(2.0)
return(G)
}
## TEST
U0 <- c(1.0,1.0)
lsf(U0)
## -----------------------------------
## CALCUL
## -----------------------------------
myMP = MP( dimension = Dim,
lsf = lsf,
N = NbSim,
q = 0.0,
lower.tail = TRUE,
N.batch = 2,
plot = FALSE,
verbose = 1)
# check validity range
myMP$ecdf_MP(myMP$L_max + 0.1)
# plot the empirical cdf
plot(xplot <- seq(myMP$L_max, 10.0, l = 1000), sapply(xplot, myMP$ecdf_MP))
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