一种基于支持向量机的非参数双响应曲面法

现有非参数双响应曲面法只注重提高模型的拟合性能而忽视提高泛化性能，对于复杂工业过程的质量优化和稳健设计应用效果不佳．为此提出了一种新的非参数双响应曲面法．首先采用均匀空间网格形式取样，然后利用支持向量机来拟合过程的均值和方差响应，并且通过比较不同拟合模型的泛化误差上界来优化支持向量机的参数．与基于核函数和基于人工神经网络的非参数双响应曲面法对比结果表明：实验设计方式相同时，该方法的平均泛化误差分别降低了31．0％和51．8％；而泛化误差相近时，平均样本量分别降低了35．0％和48．6％；对不同取样方法的泛化性能研究表明，在没有先验知识时，均匀空间网格是一种可接受的实验设计方式．由此说明了该方法的适用性与优越性.

SVM-Based Nonparametric Dual Response Surface Methodology

Current researches on nonparametric dual response surface methodology (NPDRSM) focus on impro- ving fitting performance,but lose sight of improving generalization performance of models.Thus NPDRSM does not work well for the quality optimization and robustness design under the constraints of real industrial proces- ses.A new NPRSM was presented,which collected data by using equal intervals space filling,and then fitted process response mean and variance models by support vector machines (SVM).Meanwhile,it optimized pa- rameters in SVM by comparing the upper bounds of generalized error of different SVM models.The experiments show that,with the same design of experiment,the average generalized error of SVM-based NPDRSM decreases by 31.0% compared with kernel based NPDRSM,and by 51.8% compared with artificial neural networks (ANN)-based NPDRSM;when the generalized errors are close,the average sample size of SVM-based NP- DRSM decreases by 35.0% compared with kernel-based NPDRSM,and by 48.6% compared with ANN-based NPDRSM.The generalization researches with different sampling manners show that the equal intervals space filling is an acceptable design method under the situations without prior knowledge about the processes.All of these results demonstrate the adaptability and superiority of the method proposed.