tmse_optim: Targeted MSE criterion

Description

Evaluation of the Targeted MSE criterion. To be used in optimization routines, like in max.infill.criterion

Usage

tmse_optim(x, T, method.param=0, model, type="UK")

Arguments

the input vector at which one wants to evaluate the criterion

the targeted (scalar) output value

method.param

the (scalar) tolerance around the target T

model

An object of class km (Kriging model)

type

Kriging type (string): "SK" or "UK" (default)

Value

targeted MSE value

References

Picheny, V., Ginsbourger, D., Roustant, O., Haftka, R.T., Adaptive designs of experiments for accurate approximation of a target region, J. Mech. Des. - July 2010 - Volume 132, Issue 7, http://dx.doi.org/10.1115/1.4001873 Picheny V., Improving accuracy and compensating for uncertainty in surrogate modeling, Ph.D. thesis, University of Florida and Ecole Nationale Superieure des Mines de Saint-Etienne

Examples

Run this code

####################################################################
#a 9-point full factorial initial design
design.fact <- expand.grid(seq(0,1,length=3), seq(0,1,length=3))

design.fact <- data.frame(design.fact)
names(design.fact) <- c ( "x1","x2")
testfun <- camelback2			#our test function

#the response
response <- testfun(design.fact)

#the initial km model
model <- km(formula=~., design = design.fact, response = response, 
covtype="matern5_2")

#the integration points
n.grid <- 30
x.grid <- y.grid <- seq(0,1,length=n.grid)
design.grid <- expand.grid(x.grid, y.grid)

#evaluate criterion on the grid
T <- 0
tmse.EI.grid <- apply(design.grid, 1, tmse_optim, T=T, method.param=
0.1, model=model)
z.grid <- matrix(tmse.EI.grid, n.grid, n.grid)

#plots: contour of the criterion, doe points and new point
contour(x.grid,y.grid,z.grid,25)
points(design.fact, col="black", pch=20, lwd=4)

i.best <- which.max(tmse.EI.grid)
points(design.grid[i.best,], col="blue", pch=20, lwd=4)

#plots: contour of the actual function at threshold
testfun.grid <- testfun(design.grid)
z.grid.2 <- matrix(testfun.grid, n.grid, n.grid)
contour(x.grid,y.grid,z.grid.2,levels=T,col="blue",add=TRUE)
title("Contour lines of tmse criterion (black) and of 
f(x)=T (blue)")
#####################################################################