SVM-based RSM model fitting approach

When a complex process is featured with multi-extreme of quality responses as well as high order interactions and constraints among influential factors,parametric response surface method(RSM) fails to fit the real surface and is hard to achieve global optimization;While non-parametric RSM results in poor generalization performance when the sample size is finite and is hard to optimize the response as well.In this paper,the model fitting phase of RSM is described as a sort of restricted small-sample learning problem which is able to actively gain sample points.Then,a Support Vector Machine(SVM) based method is proposed for the model fitting phase of RSM.A practical method for selecting SVM kernel functions and parameters is put forward for RSM as well.The simulations show that,by using the proposed method to select kernel functions and parameters,the average deviation ratio of SVM generalized error from the exhaustively searched minimum is less than 20%.The SVM based RSM model fitting approach has no rigid restriction for the normality of the response and non-constraints among the factors.Furthermore,it outperforms the existing RSM approaches in generalization and surface reconstruction performance.Compared with non-parametric RSM,the average generalized error and the sample size of the proposed approach decrease by about 20% and 30% respectively.All these demonstrate the adaptability and superiority of the proposed approach.