Spatio-temporal response robust parameter design based on Gaussian process model

ZHAI Cuihong, WANG Jianjun, MA Yizhong, FENG Zebiao, YANG Shijuan

Systems Engineering - Theory & Practice ›› 2023, Vol. 43 ›› Issue (2) : 537-555.

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Systems Engineering - Theory & Practice ›› 2023, Vol. 43 ›› Issue (2) : 537-555. DOI: 10.12011/SETP2021-1756

Spatio-temporal response robust parameter design based on Gaussian process model

  • ZHAI Cuihong1, WANG Jianjun1, MA Yizhong1, FENG Zebiao2, YANG Shijuan1
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Abstract

A new spatio-temporal response optimization model, combined with multivariate quality loss function in the framework of fast nonseparable Gaussian process (FNSGP) modeling, is constructed for robust parameter design of large-scale spatio-temporal data. Firstly, considering the spatial and temporal correlation, the response surface between the input factors and quality characteristics is constructed by the FNSGP model. The fast and accurate algorithm of forward-filtering and backward-smoothing is used to estimate and predict the model. Secondly, the joint quality loss weights of the spatio-temporal responses are calculated based on the signal-to-noise ratio to construct the multivariate quality loss function. Then, a two-stage parameter optimization scheme is established using the multivariate quality loss function. Finally, the nonlinear optimization algorithm is used to find the joint optimal parameter design values of spatial and temporal factors. The results show that the proposed method can effectively deal with the meta-modeling and robust parameter design problems of large-scale spatio-temporal data. Compared with alternative methods such as the separable Gaussian process, linear regression, and random forest, it can obtain more robust optimization results.

Key words

spatio-temporal data / nonseparable Gaussian process / Kalman filter / quality loss function / robust parameter design

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ZHAI Cuihong , WANG Jianjun , MA Yizhong , FENG Zebiao , YANG Shijuan. Spatio-temporal response robust parameter design based on Gaussian process model. Systems Engineering - Theory & Practice, 2023, 43(2): 537-555 https://doi.org/10.12011/SETP2021-1756

References

[1] 唐铁球. 中国高端装备制造产业分布特征与发展趋势[J]. 求索, 2015(12):10-14. Tang T Q. Distribution characteristics and development trend of China's high-end equipment manufacturing industry[J]. Seeker, 2015(12):10-14.
[2] 彭中文, 王媚华, 倪佳杰. 政治关系、经营业绩与企业社会责任——基于高端装备制造业上市公司的面板数据[J]. 软科学, 2015, 29(3):19-22. Peng Z W, Wang M H, Ni J J. Political relation, operating performance and corporate social responsibility—Based on panel data of high equipment manufacturing listed companies[J]. Soft Science, 2015, 29(3):19-22.
[3] Nair V N, Taam W, Ye K Q. Analysis of functional responses from robust design studies[J]. Journal of Quality Technology, 2002, 34(4):355-370.
[4] Alshraideh H, Castillo E D. Gaussian process modeling and optimization of profile response experiments[J]. Quality and Reliability Engineering International, 2014, 30(4):449-462.
[5] He Z, Zhou P, Zhang M, et al. A review of analysis of dynamic response in design of experiments[J]. Quality and Reliability Engineering International, 2015, 31(4):535-542.
[6] Yan H, Paynabar K, Shi J J. Real-time monitoring of high-dimensional functional data streams via spatio-temporal smooth sparse decomposition[J]. Technometrics, 2018, 60(2):181-197.
[7] 马义中, 汪建均, 苏国进. 动态多响应系统的稳健参数设计[J]. 系统工程理论与实践, 2012, 32(8):1841-1849.Ma Y Z, Wang J J, Su G J. Robust parameter design for dynamic multi-response system[J]. Systems Engineering-Theory & Practice, 2012, 32(8):1841-1849.
[8] Miller A, Wu C F J. Parameter design for signal-response systems:A different look at Tanguchi's dynamic parameter design[J]. Statistical Science, 1996, 11(2):122-136.
[9] Hsieh K L, Tong L I, Chiu H P, et al. Optimization of a multi-response problem in Taguchi's dynamic system[J]. Computers & Industrial Engineering, 2005, 49(4):556-571.
[10] 汪建均, 马义中, 欧阳林寒, 等. 多响应稳健参数设计的贝叶斯建模与优化[J]. 管理科学学报, 2016, 19(2):85-94.Wang J J, Ma Y Z, Ouyang L H, et al. Bayesian modeling and optimization of multi-response robust parameter design[J]. Journal of Management Sciences in China, 2016, 19(2):85-94.
[11] Castillo E D, Colosimo B M, Alshraideh H. Bayesian modeling and optimization of functional responses affected by noise factors[J]. Journal of Quality Technology, 2012, 44(2):117-135.
[12] Gelfand A E, Diggle P, Guttorp P, et al. Handbook of spatial statistics[M]. New York:CRC Press, 2010.
[13] Cressie N, Wikle C K. Statistics for spatio-temporal data[M]. Hoboken:John Wiley & Sons, 2015.
[14] Datta A, Banerjee S, Finley A O, et al. Nonseparable dynamic nearest neighbor Gaussian process models for large spatio-temporal data with an application to particulate matter analysis[J]. The Annals of Applied Statistics, 2016, 10(3):1286-1316.
[15] Box G E P, Draper N R. Empirical model-building and response surfaces[M]. New York:John Wiley & Sons, 1987.
[16] 冯泽彪, 汪建均, 马义中. 基于多变量高斯过程模型的贝叶斯建模与稳健参数设计[J]. 系统工程理论与实践, 2020, 40(3):703-713.Feng Z B, Wang J J, Ma Y Z. Bayesian modeling and robust parameter design based on multivariate Gaussian process model[J]. Systems Engineering-Theory & Practice, 2020, 40(3):703-713.
[17] Mardia K V, Goodall C R. Spatial-temporal analysis of multivariate environmental monitoring data[J]. Multivariate Environmental Statistics, 1993, 6(76):347-385.
[18] Cressie N A, Huang H C. Classes of nonseparable, spatio-temporal stationary covariance functions[J]. Journal of the American Statistical Association, 1999, 94(448):1330-1339.
[19] Fuentes M. Testing for separability of spatial-temporal covariance functions[J]. Journal of Statistical Planning and Inference, 2006, 136(2):447-466.
[20] Mitchell M W, Genton M G, Gumpertz M L. A likelihood ratio test for separability of covariances[J]. Journal of Multivariate Analysis, 2006, 97(5):1025-1043.
[21] Li B, Genton M G, Sherman M. Testing the covariance structure of multivariate random fields[J]. Biometrika, 2008, 95(4):813-829.
[22] Huang H, Sun Y. Visualization and assessment of spatio-temporal covariance properties[J]. Spatial Statistics, 2019, 34:100272.
[23] Kyriakidis P C, Journel A G. Geostatistical space-time models:A review[J]. Mathematical Geology, 1999, 31(6):651-684.
[24] Gu M, Xu Y. Fast nonseparable Gaussian stochastic process with application to methylation level interpolation[J]. Journal of Computational and Graphical Statistics, 2020, 29(2):250-260.
[25] Gneiting T. Nonseparable, stationary covariance functions for space-time data[J]. Journal of the American Statistical Association, 2002, 97(458):590-600.
[26] Kolovos A, Christakos G, Hristopulos D T, et al. Methods for generating non-separable spatiotemporal covariance models with potential environmental applications[J]. Advances in Water Resources, 2004, 27(8):815-830.
[27] Fricker T E, Oakley J E, Urban N M. Multivariate Gaussian process emulators with nonseparable covariance structures[J]. Technometrics, 2013, 55(1):47-56.
[28] Li Y X, Zhou Q. Pairwise meta-modeling of multivariate output computer models using nonseparable covariance function[J]. Technometrics, 2016, 58(4):483-494.
[29] Goulard M, Voltz M. Linear coregionalization model:Tools for estimation and choice of cross-variogram matrix[J]. Mathematical Geology, 1992, 24(3):269-286.
[30] Gelfand A E, Schmidt A M, Banerjee S, et al. Nonstationary multivariate process modeling through spatially varying coregionalization[J]. Test, 2004, 13(2):263-312.
[31] Higdon D, Gattiker J, Williams B, et al. Computer model calibration using high-dimensional output[J]. Journal of the American Statistical Association, 2008, 103(482):570-583.
[32] Hartikainen J, Särkkä S. Kalman filtering and smoothing solutions to temporal Gaussian process regression models[C]//2010 IEEE International Workshop on Machine Learning for Signal Processing. Kittila, Finland:IEEE, 2010:379-384.
[33] West M, Harrison J. Bayesian forecasting and dynamic models[M]. New York:Springer-Verlag, 1997.
[34] Petris G, Petrone S, Campagnoli P. Dynamic linear models[M]. New York:Springer, 2009.
[35] Gu M Y. Jointly robust prior for Gaussian stochastic process in emulation, calibration and variable selection[J]. Bayesian Analysis, 2019, 14(3):857-885.
[36] Pignatiello J J. Strategies for robust multi-response quality engineering[J]. IIE Transactions, 1993, 25(3):5-15.
[37] 翟翠红, 汪建均, 冯泽彪. 基于高斯过程模型的多响应稳健参数设计[J]. 系统工程与电子技术, 2021, 43(12):3683-3693.Zhai C H, Wang J J, Feng Z B. Multi-response robust parameter design based on Gaussian process model[J]. Systems Engineering and Electronics, 2021, 43(12):3683-3693.
[38] 曹晋华, 程侃. 可靠性数学引论[M]. 北京:高等教育出版社, 2006.Cao J J, Cheng K. Introduction to reliability mathematics[M]. Beijing:Higher Education Press, 2006.
[39] Govaerts B, Noel J. Analysing the results of a designed experiment when the response is a curve:Methodology and application in metal injection moulding[J]. Quality and Reliability Engineering International, 2005, 21(5):509-520.
[40] 尹长春. 温度对化学反应速度和化学平衡的影响[J]. 化学教育, 1980, 1(4):9-12.Yin C C. The effect of temperature on the rate of chemical reactions and chemical equilibrium[J]. Chinese Journal of Chemical Education, 1980, 1(4):9-12.

Funding

National Natural Science Foundation of China (72171118, 71771121, 71931006); Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX21_0361)
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