Response Surface Approximation using Gradient Information

摘要

Response surface techniques have originally been developed for the construction of approximations on the basis of function values only. In many cases however, derivative information is available inexpensively, and can be used to improve the accuracy and reduce the cost of the response surface. This is, for example, the case when efficient procedures for design sensitivity analysis are available. In the present paper, a framework is given for the construction of response surfaces (RS) using both function values and derivatives. The basis is a weighted least squares formulation, which also includes derivatives. Of particular interest is the estimation of the covariance matrix for use as the weight matrix in an iterative procedure of Weighted Least Squares regression. Examples of Response Surface Approximations on simple polynomials and on structural optimization problems will be presented.