Response Surface Model Using the Sorted -Fold Approach

Abstract

Complex engineering problems are represented by surrogate models in order to find the optimum design points with greater computational efficiency. The least-squares response surface methodology is one of the most commonly used approximation models and has been widely applied to optimization problems in the field of aerospace. In this paper, we propose a new surrogate modeling technique called the sorted -fold approach with which the entire sample points are sorted based on the residuals and then grouped into data sets. Multiple response surfaces are constructed while one data set used for cross-validating the representative response surface is omitted. Each response surface is weighted based on how well it can predict the cross-validating data response. Our investigations reveal that this approach has a higher ability of obtaining accurate predictions than the least-squares response surface methodology when tested at a large number of validation points. When the method is applied to benchmark problems and the numerical simulation of residual stress prediction (done by laser peening in order to improve the fatigue life of aircraft structures), the results maintain validity.