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mistral (version 1.1-1)

MonteCarlo: Crude Monte Carlo method

Description

Estimate a failure probability using crude Monte Carlo method

Usage

MonteCarlo(dimension,
          LimitStateFunction,
          N_max         = 5e+05,
          N_batch       = 1000,
          failure       = 0,
          precision     = 0.05,
          plot          = FALSE,
          output_dir    = NULL,
          verbose       = 0)

Arguments

dimension
an integer giving the dimension of the input space.
LimitStateFunction
the failure function.
N_max
Maximum number of calls to the LimiStateFunction.
N_batch
Size of batch for Monte-Carlo population increase.
failure
the value defining the failure domain F = { x | LimitStateFunction(x) < failure }.
precision
A target maximum value of the coefficient of variation
plot
a boolean parameter specifying if function and samples should be plotted. Note that this option is only to be used when working on light limit state functions as it requires the calculus of this function on a grid of size 161x161 (plot is
output_dir
optional. If plots are to be saved in .jpeg in a given directory. This variable will be pasted with "_Monte_Carlo_brut.jpeg" to get the full output directory.
verbose
Eiher 0 for an almost no output message, or 1 for medium size or 2 for full size

Value

  • An object of class list containing the failure probability and some more outputs as described below:
  • probaThe estimated failure probability.
  • covThe coefficient of variation of the Monte-Carlo probability estimate.
  • NcallThe total number of calls to the LimitStateFunction.

See Also

SubsetSimulation

Examples

Run this code
#Try Naive Monte Carlo on a given function with different failure level
#Limit state function defined by Kiureghian & Dakessian :
kiureghian = function(x, b=5, kappa=0.5, e=0.1) {b - x[2] - kappa*(x[1]-e)^2}

res = list()
res[[1]] = MonteCarlo(2,kiureghian,failure = 0,plot=TRUE)
res[[2]] = MonteCarlo(2,kiureghian,failure = 1,plot=TRUE)
res[[3]] = MonteCarlo(2,kiureghian,failure = -1,plot=TRUE)


#Try Naive Monte Carlo on a given function and change number of points.
#Limit state function defined by Waarts :
waarts = function(u) { min(
  	(3+(u[1]-u[2])^2/10 - (u[1]+u[2])/sqrt(2)),
		(3+(u[1]-u[2])^2/10 + (u[1]+u[2])/sqrt(2)),
		u[1]-u[2]+7/sqrt(2),
		u[2]-u[1]+7/sqrt(2))
}
res = list()
res[[1]] = MonteCarlo(2,waarts,N_max = 10000)
res[[2]] = MonteCarlo(2,waarts,N_max = 100000)
res[[3]] = MonteCarlo(2,waarts,N_max = 500000)

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