Locally Weighted Principal Component Analysis-Based Multimode Modeling for Complex Distributed Parameter Systems

被引:38
作者
Xu, Kangkang [1 ]
Fan, Bi [2 ]
Yang, Haidong [1 ]
Hu, Luoke [3 ]
Shen, Wenjing [4 ]
机构
[1] Guangdong Univ Technol, Sch Electromech Engn, Guangzhou 510006, Peoples R China
[2] Shenzhen Univ, Coll Management, Res Inst Business Analyt & Supply Chain Managemen, Shenzhen 518060, Peoples R China
[3] Zhejiang Univ, Sch Mech Engn, Key Lab Adv Mfg Technol Zhejiang Prov, State Key Lab Fluid Power & Mechatron Syst, Hangzhou 310027, Peoples R China
[4] Shenzhen Technol Univ, Sino German Coll Intelligent Mfg, Shenzhen 518118, Peoples R China
基金
中国国家自然科学基金;
关键词
Spatiotemporal phenomena; Principal component analysis; Analytical models; Mathematical model; Numerical models; Reduced order systems; Nonlinear dynamical systems; Distributed parameter systems (DPSs); finite Gaussian mixture model (FGMM); locally weighted principal component analysis (PCA); multimode modeling; spatial basis functions (SBFs); KARHUNEN-LOEVE DECOMPOSITION; APPROXIMATION; PCA;
D O I
10.1109/TCYB.2021.3061741
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
Global principal component analysis (PCA) has been successfully introduced for modeling distributed parameter systems (DPSs). In spite of the merits, this method is not feasible due to parameter variations and multiple operating domains. A novel multimode spatiotemporal modeling method based on the locally weighted PCA (LW-PCA) method is developed for large-scale highly nonlinear DPSs with parameter variations, by separating the original dataset into tractable subsets. This method implements the decomposition by making full use of the dependence among subset densities. First, the spatiotemporal snapshots are divided into multiple different Gaussian components by using a finite Gaussian mixture model (FGMM). Once the components are derived, a Bayesian inference strategy is then applied to calculate the posterior probabilities of each spatiotemporal snapshot belonging to each component, which will be regarded as the local weights of the LW-PCA method. Second, LW-PCA is adopted to calculate each locally weighted snapshot matrix, and the corresponding local spatial basis functions (SBFs) can be generated by the PCA method. Third, all the local temporal models are estimated using the extreme learning machine (ELM). Thus, the local spatiotemporal models can be produced with local SBFs and corresponding temporal model. Finally, the original system can be approximated using the sum form of each local spatiotemporal model. Unlike global PCA, which uses global SBFs to construct a global spatiotemporal model, LW-PCA approximates the original system by multiple local reduced SBFs. Numerical simulations verify the effectiveness of the developed multimode spatiotemporal model.
引用
收藏
页码:10504 / 10514
页数:11
相关论文
共 38 条
[1]   Nonlinear model order reduction based on local reduced-order bases [J].
Amsallem, David ;
Zahr, Matthew J. ;
Farhat, Charbel .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2012, 92 (10) :891-916
[2]   Finite-dimensional approximation and control of non-linear parabolic PDE systems [J].
Baker, J ;
Christofides, PD .
INTERNATIONAL JOURNAL OF CONTROL, 2000, 73 (05) :439-456
[3]  
Bartlett P. L., 2003, Journal of Machine Learning Research, V3, P463, DOI 10.1162/153244303321897690
[4]  
Canuto C., 1988, Spectral Methods in Fluid Dynamics
[5]   Spectral-approximation-based intelligent modeling for distributed thermal processes [J].
Deng, H ;
Li, HX ;
Chen, GR .
IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, 2005, 13 (05) :686-700
[6]   Detection and Spatial Identification of Fault for Parabolic Distributed Parameter Systems [J].
Feng, Yun ;
Li, Han-Xiong .
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, 2019, 66 (09) :7300-7309
[7]   Nonlinear process monitoring based on linear subspace and Bayesian inference [J].
Ge, Zhiqiang ;
Zhang, Muguang ;
Song, Zhihuan .
JOURNAL OF PROCESS CONTROL, 2010, 20 (05) :676-688
[8]   Unified iterative learning control for flexible structures with input constraints [J].
He, Wei ;
Meng, Tingting ;
He, Xiuyu ;
Ge, Shuzhi Sam .
AUTOMATICA, 2018, 96 :326-336
[9]   Iterative Learning Control for a Flapping Wing Micro Aerial Vehicle Under Distributed Disturbances [J].
He, Wei ;
Meng, Tingting ;
He, Xiuyu ;
Sun, Changyin .
IEEE TRANSACTIONS ON CYBERNETICS, 2019, 49 (04) :1524-1535
[10]   Low-order control-relevant models for a class of distributed parameter systems [J].
Hoo, KA ;
Zheng, DG .
CHEMICAL ENGINEERING SCIENCE, 2001, 56 (23) :6683-6710