Adaptive experimental design for construction of response surface approximations

Abstract

Sequential Approximate Optimization (SAO) is a class of methods available for the multidisciplinary design optimization (MDO) of complex systems that are composed of several disciplines coupled together. One of the approaches used for SAO, is based on a quadratic response surface approximation, where zero and first order information are required. In these methods, designers must generate and query a database of order O(n2) in order to compute the second order terms of the quadratic response surface approximation. As the number of design variables grows, the computational cost of generating the required database becomes a concern. In this paper, we present an new approach in which we require just O(ri) parameters for constructing a second order approximation. This is accomplished by transforming the matrix of second order terms into the canonical form. The method periodically requires an order O(n2) update of the second order approximation to maintain accuracy. Results show that the proposed approach is practical and convenient for engineering design problems by dramatically reducing the total number of calls to the simulation tools.