SMART {mistral}R Documentation

Support-vector Margin Algoritm for Reliability esTimation

Description

Calculate a failure probability with SMART method. This should not be used by itself but only through S2MART.

Usage

SMART(
  dimension,
  lsf,
  N1 = 10000,
  N2 = 50000,
  N3 = 2e+05,
  Nu = 50,
  lambda1 = 7,
  lambda2 = 3.5,
  lambda3 = 1,
  tune_cost = c(1, 10, 100, 1000),
  tune_gamma = c(0.5, 0.2, 0.1, 0.05, 0.02, 0.01),
  clusterInMargin = TRUE,
  alpha_margin = 1,
  k1 = round(6 * (dimension/2)^(0.2)),
  k2 = round(12 * (dimension/2)^(0.2)),
  k3 = k2 + 16,
  X = NULL,
  y = NULL,
  failure = 0,
  limit_fun_MH = NULL,
  sampling_strategy = "MH",
  seeds = NULL,
  seeds_eval = NULL,
  burnin = 20,
  thinning = 4,
  plot = FALSE,
  limited_plot = FALSE,
  add = FALSE,
  output_dir = NULL,
  z_MH = NULL,
  z_lsf = NULL,
  verbose = 0
)

Arguments

dimension

the dimension of the input space

lsf

the limit-state function

N1

Number of samples for the (L)ocalisation step

N2

Number of samples for the (S)tabilisation step

N3

Number of samples for the (C)onvergence step

Nu

Size of the first Design of Experiments

lambda1

Relaxing parameter for MH algorithm at step L

lambda2

Relaxing parameter for MH algorithm at step S

lambda3

Relaxing parameter for MH algorithm at step C

tune_cost

Input for tuning cost paramter of the SVM

tune_gamma

Input for tuning gamma parameter of the SVM

clusterInMargin

Enforce selected clusterised points to be in margin

alpha_margin

a real value defining the margin. While 1 is the ‘real’ margin for a SVM, one can decide here to stretch it a bit.

k1

Rank of the first iteration of step S

k2

Rank of the first iteration of step C

k3

Rank of the last iteration of step C

X

Coordinates of alredy known points

y

Value of the LSF on these points

failure

Failure threshold

limit_fun_MH

Define an area of exclusion with a limit function

sampling_strategy

Either MH for Metropolis-Hastings of AR for accept-reject

seeds

If some points are already known to be in the subdomain defined by limit_fun_MH

seeds_eval

Value of the metamodel on these points

burnin

Burnin parameter for MH

thinning

Thinning parameter for MH

plot

Set to TRUE for a full plot, ie. refresh at each iteration

limited_plot

Set to TRUE for a final plot with final DOE, metamodel and LSF

add

If plots are to be added to the current device

output_dir

If plots are to be saved in jpeg in a given directory

z_MH

For plots, if the limit_fun_MH has already been evaluated on the grid

z_lsf

For plots, if LSF has already been evaluated on the grid

verbose

Either 0 for almost no output, 1 for medium size output and 2 for all outputs

Details

SMART is a reliability method proposed by J.-M. Bourinet et al. It makes uses of a SVM-based metamodel to approximate the limit state function and calculates the failure probability with a crude Monte-Carlo method using the metamodel-based limit state function. As SVM is a classification method, it makes use of limit state function values to create two classes : greater and lower than the failure threshold. Then the border is taken as a surogate of the limit state function.

Concerning the refinement strategy, it distinguishes 3 stages, known as Localisation, Stalibilsation and Convergence stages. The first one is proposed to reduce the margin as much as possible, the second one focuses on switching points while the last one works on the final Monte-Carlo population and is designed to insure a strong margin; see F. Deheeger PhD thesis for more information.

Value

An object of class list containing the failure probability and some more outputs as described below:

proba

The estimated failure probability.

cov

The coefficient of variation of the Monte-Carlo probability estimate.

Ncall

The total number of calls to the limit_state_function.

X

The final learning database, ie. all points where lsf has been calculated.

y

The value of the limit_state_function on the learning database.

meta_fun

The metamodel approximation of the limit_state_function. A call output is a list containing the value and the standard deviation.

meta_model

The final metamodel.

points

Points in the failure domain according to the metamodel.

meta_eval

Evaluation of the metamodel on these points.

z_meta

If plot==TRUE, the evaluation of the metamodel on the plot grid.

Note

Problem is supposed to be defined in the standard space. If not, use UtoX to do so.

Furthermore, each time a set of vector is defined as a matrix, ‘nrow’ = dimension and ‘ncol’ = number of vector.

Author(s)

Clement WALTER clementwalter@icloud.com

References

See Also

SubsetSimulation MonteCarlo svm (in package e1071) S2MART


[Package mistral version 2.2.2 Index]