Efficient Response Surface Modeling by Using Moving Least-Squares Method and Sensitivity

Abstract

The response surface method (RSM) has currently become one of the better-known meta-modeling techniques. However, its approximation errors have placed several restrictions on designers as classical RSM uses the leastsquares method (LSM) to find the best-fitting approximation models from the given function data. We discuss how to construct RS models efficiently and accurately using the moving least-squares method (MLSM) combined with sensitivity information. The formulations for incorporating the sensitivity using the MLSM are derived. With this method, several parameters should be determined during the construction of response surfaces. The parametric study and optimization for these parameters are performed. However, because of the discontinuity problem of the optimization, a genetic algorithm is adopted. The correlation coefficient is used for the normalized comparison between the function and gradient errors. Also, the reciprocal condition number is applied to avoid illconditioned approximations. Several difficulties and their respective solutions during the approximation processes are described, and the numerical examples are then demonstrated to verify the accuracy and the efficiency of this method. If the sensitivity of each sampling point can be calculated efficiently by utilizing a cheap computation, the proposed method is recognized as very efficient and accurate.