Response Surface Modeling by Local Kernel Partial Least Squares

Abstract

Partial Least Squares are introduced to build the response surface for multi-collinearity problems, which can effectively work on the problems of small sized samples and multiple correlations. However, this approach is a linear method, which is not capable to deal with the non-linear response surface model. To solve this problem, in this paper, we propose two improved algorithms called Local Partial Least Squares (LPLS) and Local Kernel Partial Least Squares (LKPLS). LKPLS is an improved LPLS method. It provides a non-linear transformation by mapping the data in the original space into a feature kernel space and builds a local algebraic model for each estimated point. We examine the approach in both Three-dimensional and Multi-dimensional response surface experiments to verify the correctness and usefulness of the proposed method. Moreover, the simulation results show that the proposed method works well when occurring extreme value missing phenomenon.