基于SVM的RSM模型拟合方法研究

对于多极值、存在高阶交互作用和约束的复杂过程,参数RSM整体代表性差,难以达到全局最优;而非参数RSM在样本量有限时泛化性差,模型难以优化.将RSM模型拟合归结为一类有限制条件、可主动获取样本点的小样本学习问题;提出一种基于SVM的复杂过程RSM模型拟合方法,并提出了适用于RSM的实用性SVM核函数及参数选择方法.算例研究表明,所提的核函数及参数选择方法得到的泛化误差与其最小值的平均偏离率在20%以内;基于SVM的RSM拟合模型对因子约束、误差分布无严格限制,泛化性能、曲面重现能力均优于现有RSM,其平均泛化误差与样本量分别比非参数RSM降低约20%和30%,说明了所提方法的有效性与优越性.

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.