FORMv0 {mistral} | R Documentation |
FORM method (old version)
Description
Calculate failure probability by FORM method and important sampling.
Usage
FORMv0(f, u.dep, inputDist, N.calls, eps = 1e-7,
Method = "HLRF", IS = FALSE, q = 0.5, copula = "unif")
Arguments
f |
A failure fonction |
u.dep |
A vector, starting point to the research of the design point |
inputDist |
A list which contains the name of the input distribution and their parameters. For the input "i", inputDistribution[[i]] = list("name_law",c(parameters1,..., parametersN)) |
N.calls |
Number of calls to f allowed |
eps |
Stop criterion : distance of two points between two iterations |
Method |
Choice of the method to research the design point: "AR" for Abdo-Rackwitz and "HLRF" for Hasofer-Lindt-Rackwitz-Fiessler |
IS |
"TRUE" for using importance Sampling method (applied after FORM which provides the importance density). Default = "FALSE". |
q |
Ratio of N.calls for the research of the design point by FORM. Default = 0.5. 1-q = the remaining ratio to use importance sampling. |
copula |
Choice of the copula. Default = "unif" (uniform copula) |
Details
This function estimate the probability that the output of the failure function is negative using FORM algorithm. The importance sampling procedure estimate a probability using a Gaussian distribution centered in the design point with a covariance matrix equal to the indentity.
Value
pf |
Failure probability |
beta |
Reliability index (beta) |
compt.f |
Number of calls to f |
design.point |
Coordinates of the design point |
fact.imp |
Importance factors |
variance |
Standard error of the probability estimator (if IS = TRUE) |
conf |
Confidence interval of the estimator at 0.95 (if IS = TRUE) |
x |
A data frame containing the input design of experiments |
y |
A vector of model responses (corresponding to x) |
dy |
A data frame of model response derivatives (wrt each input and corresponding to x); for the IS sample, the derivatives are not computed |
Author(s)
Vincent Moutoussamy and Bertrand Iooss
References
O. Ditlevsen and H.O. Madsen. Structural reliability methods, Wiley, 1996
M. Lemaire, A. Chateauneuf and J. Mitteau. Structural reliability, Wiley Online Library, 2009.
Examples
## Not run:
distribution = list()
distribution[[1]] = list("gamma",c(2,1))
distribution[[2]] = list("gamma",c(3,1))
f <- function(X){
X[1]/sum(X) - qbeta((1e-5),2,3)
}
res <- mistral:::FORMv0(f, u.dep = c(0,0.1), inputDist = distribution,
N.calls = 1000, eps = 1e-7, Method = "HLRF", IS = "TRUE",
q = 0.1, copula = "unif")
names(res)
print(res)
print(res$pf)
## End(Not run)