LSFM: LSFM

In ShinsukeSakai0321/LimitState: Package supporting FORM approach

Description

Base class for the analysis using limit state function method.

Usage

Arbitrary limit state function subjects are inherited from this base class

Public function

Standard reference class is R6 class
Public function

function	contents	variable(s)
initialize(name,n,Mu,sigmmaX,dist)	initializes the object	name: name of the subject,n:number of variables, Mu:list of mean values of variables, sigmmaX: list of std. values of variables,dist: list of distribution names(characters)
GetN()	returns the number of variables
DefineG(glim)	difines control class for G-calculation	glim: object of g-definition class which is inheritted class of Lbase
GetMu()	returns list of mean values of variables
GetSigm() \ tab returns list of std. values of variables
GetBeta()	retuns reliability index
GetAlpha()	returns the list of differential vector
GetPOF()	returns value of probability of failure
GetDP()	returns list of DP vector
GetConv()	returns number of convergence
GetG()	returns g value at the mean vector of the variables
SetMu(Xm)	sets mean values of variables from list Xm	Xm:list of mean values of variables
RF()	searches the design point usein modified Rackwitz-Fiessler algorithm

Author(s)

Shinsuke Sakai, Takuyo Kaida

Examples

# Most simple example
# Definition of G and dGdX
GRS <- R6::R6Class("GRS",
                       inherit=Lbase,
                       public=list(
                         gcalc = function(){
                           X <- super$GetX()
                           R <- X[1]
                           S <- X[2]
                           g<- R-S
                           super$SetG(g)
                         },
                         dGdXcalc = function(){
                           X <- super$GetX()
                           dGdX <- super$GetdGdX()
                           dGdX[1] <- 1
                           dGdX[2] <- -1
                           super$SetdGdX(dGdX)
                         }
                       )
                       )
# Reliability Analysis
Sexample <- R6::R6Class("Sexample",
                        inherit=LSFM,
                        public= list(
                          Calc=function(){
                            super$DefineG(GRS$new(super$GetN()))
                            super$RF()
                          }
                        )
                        )
####main###
muX<-c(200,100)
sigmmaX<-c(10,20)
dist <- c("normal", "normal")
exam <- Sexample$new("Sexample",2,muX,sigmmaX,dist)
exam$Calc()
exam$GetPOF()
# correct answer  3.872108e-06


#Example of Lbase must be executed before this example.
# Example
#"Probability, Reliability and Statistical Methods in
#  Engineering Design"
# Achintya Haldar  & Sankaran Mahadevan
#  P.218 Table 7.5, 7.6
GPRSMED <- R6::R6Class("GPRSMED",
                       inherit=Lbase,
                       public = list(
                         gcalc = function(){
                           X <- super$GetX()
                           As <- X[1]
                           fy <- X[2]
                           fcd <- X[3]
                           b <- X[4]
                           d <- X[5]
                           eta <- X[6]
                           M <- X[7]
                           g <- As*fy*d*(1.0-eta*As*fy/b/d/fcd)-M
                           super$SetG(g)
                         } ,
                         dGdXcalc = function(){
                           X <- super$GetX()
                           dGdX <- super$GetdGdX()
                           As <- X[1]
                           fy <- X[2]
                           fcd <- X[3]
                           b <- X[4]
                           d <- X[5]
                           eta <- X[6]
                           M <- X[7]
                           dd<-expression(As*fy*d*(1.0-eta*As*fy/b/d/fcd)-M)
                           dGdX[1] <- eval(D(dd,"As"))
                           dGdX[2] <- eval(D(dd,"fy"))
                           dGdX[3] <- eval(D(dd,"fcd"))
                           dGdX[4] <- eval(D(dd,"b"))
                           dGdX[5] <- eval(D(dd,"d"))
                           dGdX[6] <- eval(D(dd,"eta"))
                           dGdX[7] <- eval(D(dd,"M"))
                           super$SetdGdX(dGdX)
                         }
                       )

)
PRSMED <- R6::R6Class("PRSMED",
                     inherit=LSFM,
                     public = list(
                       Calc = function(){
                         super$DefineG(GPRSMED$new(super$GetN()))
                         super$RF()
                       }
                     )
)
############### Main Program #######################
##################### Input Data (mean value and COV) ##################
Ay <- 1.56 ; Aycov <- 0.036
fy <- 47.7; fycov <- 0.15
fcd <- 3.5; fcdcov <- 0.21
b <- 8.0; bcov <- 0.045
d <- 13.2; dcov <- 0.086
eta <- 0.59; etacov <- 0.05
M <- 326.25; Mcov <- 0.17

##list of mean values
muX <-  c(Ay,fy,fcd,b,d,eta,M)
##list of COV values
COVX <- c(Aycov,fycov,fcdcov,bcov,dcov,etacov,Mcov)
sigmmaX <- muX * COVX
##sets names of distribution
dist <- c("normal", "normal", "normal", "normal" ,"normal" ,"normal" ,"normal" )

robj <- PRSMED$new("PRSMDE",7,muX,sigmmaX,dist)
robj$Calc()
cat('Reliability index beta = ', robj$GetBeta(), '\n')
dist[7] <- "lognormal"
robj <- PRSMED$new("PRSMDE",7,muX,sigmmaX,dist)
robj$Calc()
cat('Reliability index beta = ', robj$GetBeta(), '\n')
dist <- c("lognormal", "lognormal", "lognormal", "lognormal" ,"lognormal" ,"lognormal" ,"normal" )
robj <- PRSMED$new("PRSMDE",7,muX,sigmmaX,dist)
robj$Calc()
cat('Reliability index beta = ', robj$GetBeta(), '\n')
dist <- c("lognormal", "lognormal", "lognormal", "lognormal" ,"lognormal" ,"lognormal" ,"lognormal" )
robj <- PRSMED$new("PRSMDE",7,muX,sigmmaX,dist)
robj$Calc()
cat('Reliability index beta = ', robj$GetBeta(), '\n')

#######################################################
#### expected results of the example program ####
#Reliability index beta =  3.833028
#Reliability index beta =  3.761254
#Reliability index beta =  4.387684
#Reliability index beta =  4.090647

ShinsukeSakai0321/LimitState documentation built on Dec. 26, 2019, 11:31 a.m.