ENBIS: European Network for Business and Industrial Statistics

Iterative Designs of experiments for constraint approximation

Abstract

Submitted by

Victor Picheny

Authors

Picheny V., Ginsbourger D., Roustant O., Haftka R.T.

Affiliation

Ecole Nationale Superieure des Mines de Saint Etienne / University of Florida

Abstract

This article presents a new criterion for design of experiments, when a metamodel (Kriging) is used to approximate a function that must be known accurately at a particular level-set. Such context occurs for instance in surrogate-based optimization when the constraint function is approximated by a surrogate, or in propagation of uncertainty, when a surrogate is used to compute a probability of failure.
We propose a modification of the classical IMSE criterion, based on an explicit trade-off between reduction of global uncertainty and exploration of target regions, by using the statistical information given by the Kriging model. Sequential strategies are then used to build optimal designs of experiments.
The method is illustrated on several test-problems of dimensions one, two and six. It is shown that compared to classical space-filling strategies, the error on target regions can be reduced very significantly, with reasonable pay-off on the global accuracy.
Finally, the method is tested on a propagation of uncertainty problem, resulting with a gain in accuracy of several orders of magnitude on the probability of failure compared to space-filling designs.

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