复杂作用关系过程的区域显著性实验设计及全局建模方法

崔庆安

系统工程理论与实践 ›› 2013, Vol. 33 ›› Issue (9) : 2249-2262.

PDF(1387 KB)
PDF(1387 KB)
系统工程理论与实践 ›› 2013, Vol. 33 ›› Issue (9) : 2249-2262. DOI: 10.12011/1000-6788(2013)9-2249
研究论文

复杂作用关系过程的区域显著性实验设计及全局建模方法

    崔庆安
作者信息 +

Design of experiments and global modeling approach based on sub-domains significance for complicated relationship process

    CUI Qing-an
Author information +
文章历史 +

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.

Abstract

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 characteristics 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 quality 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 traditional 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 changing 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.

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

Key words

design of experiments / modeling / complicated relationship process / support vector regression / parameter optimization

引用本文

导出引用
崔庆安. 复杂作用关系过程的区域显著性实验设计及全局建模方法. 系统工程理论与实践, 2013, 33(9): 2249-2262 https://doi.org/10.12011/1000-6788(2013)9-2249
CUI Qing-an. Design of experiments and global modeling approach based on sub-domains significance for complicated relationship process. Systems Engineering - Theory & Practice, 2013, 33(9): 2249-2262 https://doi.org/10.12011/1000-6788(2013)9-2249
中图分类号: F406.3   

参考文献

[1] Box G, Woodall W. Innovation, quality engineering, and statistics[J]. Quality Engineering, 2012, 24(1): 20-29.

[2] Eichner G, Stute W. Kernel adjusted nonparameteric regression[J]. Journal of Statistical Planning and Inference, 2012, 142(9): 2537-2544.

[3] Deng H S, Shao W, Ma Y, et al. Bayesian metamodeling for computer experiments using the Gaussian Kriging models[J]. Quality and Reliability Engineering International, 2012, 28(4): 455-466.

[4] Khayet M, Cojocaru C, Essalhi M. Artificial neural network modeling and response surface methodology of desalination by reverse osmosis[J]. Journal of Membrane Science, 2012, 368(1-2): 202-214.

[5] 孙林, 杨世元. 基于SVM的柔性生产模式下生产过程质量智能预测[J]. 系统工程理论与实践, 2009, 29(6): 139-146.Sun L, Yang S Y. Intelligent prediction for process quality of flexible manufacturing system based on SVM[J]. Systems Engineering-Theory & Practice, 2009, 29(6): 139-146.

[6] Pronzato L, Müller W. Design of computer experiments: Space filling and beyond[J]. Statistics and Computing, 2012, 22(3): 681-701.

[7] Husslage B, Rennen G, Van Dam E R, et al. Space-filling Latin hypercube designs for computer experiments[J]. Optimization and Engineering, 2011, 12(4): 611-630.

[8] Sun F, Liu M Q, Lin D K J. Construction of orthogonal Latin hypercube designs with flexible run sizes[J]. Journal of Statistical Planning and Inference, 2010, 140(11): 3236-3242.

[9] Fang K T, Lin D. Uniform design in computer and physical experiments[M]//The Grammar of Technology Development. Japan: Springer, 2008, 105-125.

[10] Mühlenstädt. Simplex based space filling designs[J]. Journal of Statistical Planning and Inference, 2009, 140(3): 585-596.

[11] Loeppky J, Moore L M, William B J. Batch sequential designs for computer experiments[J]. Journal of Statistical Planning and Inference, 2010, 140(6): 1452-1464.

[12] Gramacy R, Polson N. Particle learning of Gaussian process models for sequential design and optimization[J]. Journal of Computational and Graphical Statistics, 2011, 20(1): 102-118.

[13] Zhao Z, Yao W. Sequential design for nonparametric inference[J]. Canadian Journal of Statistics, 2012, 40(2): 362-377.

[14] Fang K T, Wang Y. A sequential algorithm for optimization and its applications to regression analysis[M]. Lecture Notes in Contemporary Mathematics, Beijing: Science Press, 1990: 17-28.

[15] 陈纪波, 王桂芝, 赵靖, 等. 二维序贯均匀设计方法的拓展研究[J]. 数学的实践与认识, 2010, 40(1): 127-131.Chen J B, Wang G Z, Zhao J, et al. An extended study in sequential uniform design[J]. Mathematics in Practice and Theory, 2010, 40(1): 127-131.

[16] 黄寒砚, 王正明, 陈璇, 等. 基于不平稳假设的序贯近似建模方法[J]. 系统工程理论与实践, 2010, 30(11): 2089-2098.Huang H J, Wang Z M, Chen X, et al. Non-stationary covariance-based sequential meta-modeling of engineering design simulation[J]. Systems Engineering-Theory & Practice, 2010, 30(11): 2089-2098.

[17] 崔庆安. 面向多极值质量特性的全局式序贯性实验设计方法[J]. 系统工程理论与实践, 2012, 32(10): 2143-2153.Cui Q A. Global sequential design for multi-extreme quality characteristics process[J]. Systems Engineering-Theory & Practice, 2012, 32(10): 2143-2153.

[18] 崔庆安, 何桢, 崔楠. 基于SVM的RSM模型拟合方法研究[J]. 管理科学学报, 2008, 11(1): 31-41.Cui Q A, He Z, Cui N. SVM-based RSM model fitting approach[J]. Journal of Management Sciences in China, 2008, 11(1): 31-41.

[19] 汪建均, 马义中, 汪新. 两阶段的贝叶斯模型选择与筛选试验分析[J]. 系统工程理论与实践, 2011, 31(8): 1447-1453.Wang J J, Ma Y Z, Wang X. Two-stage Bayesian model choice and analysis of screening experiments[J]. Systems Engineering-Theory & Practice, 2011, 32(8): 1447-1453.

[20] Kleijnen J. Factor screening in simulation experiments: Review of sequential bifurcation[J]. Operations Research & Management Science, 2009, 133(1): 153-167.

基金

国家自然科学基金(71171180)

PDF(1387 KB)

250

Accesses

0

Citation

Detail

段落导航
相关文章

/