Constrained Modeling Using Principal Component Analysis

Abstract

This chapter introduces performance-driven modeling using principal component analysis. The keystone of the technique is in spanning the surrogate model domain by the selected principal components of the reference points. This allows for a reduction of the model dimensionality, a consequence of which is an improved scalability of the surrogate in terms of the dependence between the model predictive power and the number of training data samples. Because the domain is essentially an affinely transformed unity hypercube, both the design of experiments (in particular, uniform sampling) and surrogate model optimization are straightforward. Depending on the setup, the discussed approach may be competitive to previously discussed methods in terms of the computational cost of surrogate model construction. Application case studies and benchmarking against conventional data-driven modeling methods but also nested kriging are given as well.