Comparison of response surface and kriging models for multidisciplinary design optimization

Abstract

In this paper, we compare and contrast the use of second-order response surface models and kriging models for approximating non-random, deterministic computer analyses. After reviewing the response surface method for constructing polynomial approximations, kriging is presented as an alternative approximation method for the design and analysis of computer experiments. Both methods are applied to the multidisciplinary design of an aerospike nozzle which consists of a computational fluid dynamics model and a finite-element model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations, and four optimization problems are formulated and solved using both sets of approximation models. The second-order response surface models and kriging models—using a constant underlying global model and a Gaussian correlation function—yield comparable results. NOMENCLATURE β- constant underlying global portion of kriging model β i, β ij, β ii,- linear, interaction, and quadratic coefficients of polynomial equation in response surface DOE- design of experiments GLOW- gross lift off weight MSE- mean square error n s- number of sample points R- correlation matrix in kriging model R(x i,x j)- correlation function between points x i and x j RS- response surface ˆσ 2- variance estimate θ k- correlation parameters in kriging model ˆy- predicted response value at untried x