mistral (version 2.2.2)

FORMv0: 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")

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

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)

Author

Vincent Moutoussamy and Bertrand Iooss

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.

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

if (FALSE) {
 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)
}