Regional sensitivity analysis for exceedance probability

Function for conducting the regional sensitivity analysis developed by (Rohmer and Verdel, 2014) to identiy the range of input values that influence the most the exceedance probability.

Usage

sensi_regional_prob(Z, T, input, w = 0.5, PLOT = FALSE)

Arguments

Z: Output of the propag function with argument return.r= TRUE
T: Exceedance threshold.
input: List of inputs as provided by the function create_input().
w: Weight value used to summarise the pairs of CDFs with the function summary_1cdf()
PLOT: Option for plotting the results

Details

The approach relies on an adaptation of the contribution to sample probability of failure denoted CFP plot, which provides the evolution of the exceedance probability of interest as a function of the quantile level or alpha-cut of the input variable. The higher the deviation from the first bissector, the higher the influence of the corresponding input.

Value

A liste of elements

The matrix of CFP values
The quantile level or alpha-cut
The exceedance probability for the threshold T

References

Rohmer, J., & Verdel, T. (2014). Joint exploration of regional importance of possibilistic and probabilistic uncertainty in stability analysis. Computers and Geotechnics, 61, 308-315.

Examples

if (FALSE) {

#### Model function
FUN = function(X){
  UER = X[1]
  EF = X[2]
  I = X[3]
  C = X[4]
  ED = X[5]
  return(UER*I*C*EF*ED/(70*70*365))
}

ninput = 5 #Number of input parameters
input = vector(mode="list", length=ninput) # Initialisation

input[[1]] = create_input(
  name = "UER",
  type = "possi",
  distr = "triangle",
  param = c(2.e-2, 5.7e-2, 1.e-1),
  monoton = "incr"
)
input[[2]] = create_input(
  name = "EF",
  type = "possi",
  distr = "triangle",
  param = c(200,250,350),
  monoton = "incr"
)
input[[3]] = create_input(
  name = "I",
  type = "possi",
  distr = "triangle",
  param = c(1,1.5,2.5),
  monoton = "incr"
)
input[[4]]=create_input(
  name = "C",
  type = "proba",
  distr = "triangle",
  param = c(5e-3,20e-3,10e-3)
)
input[[5]] = create_input(
  name = "ED",
  type = "proba",
  distr = "triangle",
  param = c(10,50,30)
)

####CREATION OF THE DISTRIBUTIONS ASSOCIATED TO THE PARAMETERS
input = create_distr(input)

#### PROPAGATION
Z0_IRS = propag(N = 500, input, FUN, choice_opt, param_opt, mode = "IRS", sampler="strauss", return.r=TRUE)

#### CFP PLOT
S = sensi_regional_prob(Z0_IRS, T=1e-5,input, w = 0.7, PLOT = TRUE)

}