摘要
针对参数与质量特性之间作用关系复杂过程的参数优化,提出一种基于质量特性变化显著程度的序贯设计及全局建模方法.首先以均匀设计为基础,将其拆分形成一系列的设计点集和添加点集;其次利用初始设计点集建立过程的支持向量回归(SVR)模型,并对建模样本点进行Ward聚类,由此将可行域划分成若干子区域,并以各子区域支持向量的比率反映该子区域质量特性变化的显著程度;而后以欧氏距离为判别依据,将添加点集中的实验点划分至合适的子区域,根据"子区域间区别对待,子区域内均匀分散"的原则,调整各子区域内添加实验点的数目,在支持向量率较高的子区域添加较多实验点;上述步骤迭代进行直至满足终止准则,再拟合过程最终的SVR模型.仿真与实证研究表明,与基于"均匀分散"原则的传统均匀设计和超拉丁方抽样相比,所提方法的实验设计效率与模型性能均有较大提高:实验点可以有针对性地集中分布于质量特性变化较为显著的子区域,模型预测误差降低了29.8%以上,而且能够以较小的样本量发现过程的多个极值,得到更优的参数优化结果.
For the parameter optimization of process featured with multi-extreme quality characteristics and complicated relationship between parameters and quality characteristics, a sequential experimental design and global modelling approach is proposed considering the significance of changing of quality char acteristics in the sub-domains of the process. First, a succession of design sets and appending sets are derived from a certain set of uniform design. Second, a support vector regression （SVR） model is set up based on the initial design set. Then the whole process domain is partitioned into several sub-domains after Ward＇s clustering of the sample points. Furthermore, the significance of quMity characteristics＇ changing is measured by the corresponding support vector （SV） rate in each sub-domain. Third, each point in the appending set is allocated into a sub-domain according to the Euclidean distance discriminant analysis. Based on the principle of ＂non-uniformity among different sub-domains and uniformity within a single sub-domain＇, the number of appended points to each sub-domain are adjusted by the corresponding SV rate, with more points appended to sub-domains with higher SV rates, and less points appended to sub- domains with low SV rates. Finally, the above steps are iterated until termination condition is reached and consequently, the final SVR model is set up. The simulation studies show that, comparing with tradi- tional uniform design and Latin hypercube sampling （LHS） which are based on the principle of ＂uniform dispersion＂, experimental design efficiency and model performance of the proposed approach are improved. Design points of the approach congregate in the sub-domains correspondingly to the significance of chang- ing of quality characteristic, and the model prediction error decline at least 29.8% as well. Moreover, the approach can find multi-extreme of the process and therefore get better optimization of parameters by using a smaller sample size.
出处
《系统工程理论与实践》
EI
CSSCI
CSCD
北大核心
2013年第9期2249-2262,共14页
Systems Engineering-Theory & Practice
基金
国家自然科学基金(71171180)
关键词
实验设计
建模
复杂作用关系
支持向量回归机
参数优化
design of experiments
modeling
complicated relationship process
support vector regression
parameter optimization
