基于样本点显著性及嵌套正交设计的序贯设计及建模方法

针对高度非线性且存在多极值质量特性的复杂作用关系过程,采用最小二乘支持向量回归(LS-SVR)和嵌套正交设计进行序贯设计及建模.首先给出了LS-SVR支持向量的统计分布,构造了显著性检验统计量,以此反映样本点的显著性;其次,以正交设计为初始设计,建立过程的LSSVR模型,而后在显著性较高的样本点附近子区域,嵌套入与初始设计不同的正交设计,再拟合新的LS-SVR模型.研究表明,对样本点的显著性检验,更贴合支持向量的波动特性;嵌套正交设计提供了较为规则的子区域划分和实验点添加方法,降低了序贯设计难度.与一次性LHS设计和传统路径式序贯设计相比,方法的预测均方误差降低27%以上,最大预测偏差降低2%以上;方法在发现更多极值点的基础上,得到了更优的质量特性,且样本量降低了13%.

Sequential design and modeling based on significance of samples and nested orthogonal design

A complicated manufacturing process is mainly characterized by the high nonlinear relationship between its input factors and output response. Moreover, the response usually has more than one local extremum. This paper proposed a sequential design and modeling approach for parameter optimization of the complicated processes by using least squares support vector regression and nested orthogonal design. Firstly, the statistical distribution of support vector is given, and therefore a hypothesis test for the significant of corresponding sample point is developed. Secondly, by using an orthogonal design as the initial design, a LS-SVR model is built and the significant samples are detected out. Furthermore, a nested orthogonal design with different run numbers and factor levels is located around the significant samples, and a new LS-SVR model is set up iteratively. The theoretical and numerical researches show that, the significant test for sample point is fit for the statistical dispersion of support vector. The nested orthogonal design provides an easy way to regular partition the sub-regions where the new design points are to be added. Compared with those of the "one-shot" LHS and traditional "path-oriented" sequential design, the mean squared predictive errors and max predictive deviation of the proposed approach decreases 27% and 2% respectively; Furthermore, the proposed approach reaches a better response by finding many local extremums as well as a 13% decrease of sample size.