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

CUI Qingan, JI Ze, DUAN Huanjiao

Systems Engineering - Theory & Practice ›› 2019, Vol. 39 ›› Issue (9) : 2398-2411.

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Systems Engineering - Theory & Practice ›› 2019, Vol. 39 ›› Issue (9) : 2398-2411. DOI: 10.12011/1000-6788-2018-2268-14

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

  • CUI Qingan1,2, JI Ze1, DUAN Huanjiao1
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Abstract

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.

Key words

sequential design / multi-extremums quality characteristics / parameter optimization / least squares support vector regression

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CUI Qingan , JI Ze , DUAN Huanjiao. Sequential design and modeling based on significance of samples and nested orthogonal design. Systems Engineering - Theory & Practice, 2019, 39(9): 2398-2411 https://doi.org/10.12011/1000-6788-2018-2268-14

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Funding

National Natural Science Foundation of China (71571168, U1604262); Support Plan for Scientific and Technological Innovation Talents in Colleges and Universities of Henan Province (Humanities and Social Sciences) (2019-cx-007); Foundation for Outstanding Teachers from School of Management Engineering of Zhengzhou University
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