×

Dual extreme learning machines-based spatiotemporal modeling for nonlinear distributed thermal processes. (English) Zbl 07342025

Summary: Many industrial thermal processes belong to distributed parameter systems (DPSs), which have two coupled nonlinear blocks. Dual least square support vector machines (LS-SVM) has been proposed to model such systems. However, due to the use of two LS-SVM, this method often leads to heavy computation and long learning time, which does not suit for online application. In this study, a dual extreme learning machine (ELM)-based spatiotemporal modeling method is proposed for such two nonlinearities embedded DPSs. Firstly, the KL method is applied to reduce the dimension of the original system and obtain the spatial basis functions (BFs). Then, dual ELM is designed to match the two nonlinear structures. Finally, through the reconstruction of space-time synthesis, the approximate spatiotemporal distribution model of the original system is obtained. In addition, simulations on a curing process is studied to confirm the effectiveness of the proposed method.

MSC:

93-XX Systems theory; control
68-XX Computer science
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Atwell, J. A. and King, B. B. [2001] “ Proper orthogonal decomposition for reduced basis feedback controllers for parabolic equations,” Math. Computer Modeling33(1-3), 1-19. · Zbl 0964.93032
[2] Boyd, J. P., Marilyn, T. and Paraphrasing, T. S. [2001] Chebyshev and Fourier Spectral Methods (Dover Publications. New York). · Zbl 0994.65128
[3] Canuto, C. [1988] Spectral Methods in Fluid Dynamics (Springer, New York). · Zbl 0658.76001
[4] Chen, I. L., Lee, Y. T., Kuo, P. S. and Chen, J. T. [2013] “ On the true and spurious eigenvalues by using the real or the imaginary-part of the method of fundamental solutions,” Int. J. Comput. Methods10(2), 1341003. · Zbl 1359.65241
[5] Coca, D. and Billings, S. A. [2002] “ Identification of finite dimensional models of infinite dimensional dynamical systems,” Automatica38(11), 1851-1865. · Zbl 1011.93026
[6] Deng, H., Li, H. X. and Chen, G. [2005] “ Spectral-approximation-based intelligent modeling for distributed thermal processes,” IEEE Trans. Control Syst. Technol.13(5), 686-700.
[7] Deng, H., Jiang, M. and Huang, C. Q. [2012] “ New spatial basis functions for the model reduction of nonlinear distributed parameter systems,” J. Process Control22(2), 404-411.
[8] Ding, S., Mirza, B., Lin, Z., Cao, J., Lai, X., Nguyen, T. and Sepulveda, J. [2017] “ Kernel based online learning for imbalance multiclass classification,” Neurocomputing277, 139-148.
[9] Fletcher, C. A. J. [1984] Computational Galerkin Methods (Springer, New York). · Zbl 0533.65069
[10] Gong, B., Sun, T., Shen, W. and Liu, W. [2016] “ A priori error estimate of stochastic Galerkin method for optimal control problem governed by random parabolic PDE with constrained control,” Int. J. Comput. Methods13(5), 1650028. · Zbl 1359.49007
[11] Hoo, K. A. and Zheng, D. [2001] “ Low-order control-relevant models for a class of distributed parameter systems,” Chem. Eng. Sci.56(23), 6683-6710.
[12] Huang, G. B., Zhu, Q. Y. and Siew, C. K. [2006] “ Extreme learning machine: Theory and applications,” Neurocomputing70(1-3), 489-501.
[13] Huang, G. B., Wang, D. H. and Lan, Y. [2011] “ Extreme learning machines: A survey,” Int. J. Mach. Learning Cybernetics2(2), 107-122.
[14] Huang, G. B., Zhou, H., Ding, X. and Zhang, R. [2011] “ Extreme learning machine for regression and multiclass classification,” IEEE Trans. Syst. Man Cybernetics42(2), 513-529.
[15] Hu, J. and Zhang, H. [2015] “ Numerical methods of Karhunen-Loève expansion for spatial data,” Economic Qual. Control30(1), 49-58. · Zbl 1388.65186
[16] Li, H. X., Qi, C. and Yu, Y. [2009] “ A spatio-temporal Volterra modeling approach for a class of distributed industrial processes,” J. Process Control19(7), 1126-1142.
[17] Li, H. X. and Qi, C. K. [2010] “ Modeling of distributed parameter systems for applications — A synthesized review from time-space separation,” J. Process Control20(8), 891-901.
[18] Li, H. X. and Qi, C. K. [2011] Spatio-Temporal Modeling of Nonlinear Distributed Parameter Systems (Springer, New York). · Zbl 1223.93001
[19] Liu, G. R. [2016] “ An overview on meshfree methods: For computational solid mechanics,” Int. J. Comput. Methods13(5), 1630001. · Zbl 1359.74388
[20] Liu, G. R. [2018] “ A novel pick-out theory and technique for constructing the smoothed derivatives of functions for numerical methods,” Int. J. Comput. Methods15(3), 1850070. · Zbl 1404.74162
[21] Lu, X., Zhou, C., Huang, M. and Lv, W. [2016] “ Regularized online sequential extreme learning machine with adaptive regulation factor for time-varying nonlinear system,” Neurocomputing174, 617-626.
[22] Mitchell, A. R. and Griffiths, D. F. [1980] The Finite Difference Method in Partial Differential Equations (Wiley, Chichester). · Zbl 0417.65048
[23] Mirza, B. and Lin, Z. [2016] “ Meta-cognitive online sequential extreme learning machine for imbalanced and concept-drifting data classification,” Neural Netw.80, 79-94.
[24] Nguyen, T. V., Song, Z. and Yan, S. [2015] “ Stap: Spatial-temporal attention-aware pooling for action recognition,” IEEE Trans. Circ. Syst. Video Technol.25(1), 77-86.
[25] Nguyen, T. V. and Mirza, B. [2017] “ Dual-layer kernel extreme learning machine for action recognition,” Neurocomputing260, 123-130.
[26] Nguyen, T. V., Nguyen, K. and Do, T. T. [2019] “ Semantic prior analysis for salient object detection,” IEEE Trans. Image Processing28(6), 3130-3141. · Zbl 07122893
[27] Park, H. M. and Cho, D. H. [1996] “ The use of the Karhunen-Loève decomposition for the modeling of distributed parameter systems,” Chem. Eng. Sci.51(1), 81-98.
[28] Ray and Harmon, W. [1981] Advanced Process Control (Butterworths, New York).
[29] Ritto, T. G., Buezas, F. S. and Sampaio, R. [2012] “ Proper orthogonal decomposition for model reduction of a vibroimpact system,” J. Brazilian Soc. Mech. Sci. Eng.34(3), 330-340.
[30] Wang, M., Li, N. and Li, S. [2010] “ Local modeling approach for spatially distributed system based on interval type-2 T-S fuzzy sets,” Ind. Eng. Chem. Res.49(9), 4352-4359.
[31] Wu, H. N. and Li, H. X. [2012] “ A multiobjective optimization based fuzzy control for nonlinear spatially distributed processes with application to a catalytic rod,” IEEE Trans. Ind. Informatics8(4), 860-868.
[32] Xiong, W., Yang, X., Ke, L. and Xu, B. [2015] “ EM algorithm-based identification of a class of nonlinear Wiener systems with missing output data,” Nonlinear Dyn.80(1-2), 329-339. · Zbl 1345.93151
[33] Xu, K. K., Li, H. X. and Yang, H. D. [2017] “ Dual least squares support vector machines based spatiotemporal modeling for nonlinear distributed thermal processes,” J. Process Control54, 81-89.
[34] Yuan, Z., Jin, L., Chi, W. and Tian, H. [2014] “ Finite difference method for solving the nonlinear dynamic equation of underwater towed system,” Int. J. Comput. Methods11(4), 1350060. · Zbl 1359.74471
[35] Zhang, L., Hua, C. and Guan, X. [2015] “ Structure and parameter identification for Bayesian Hammerstein system,” Nonlinear Dyn.79(3), 1847-1861. · Zbl 1331.93215
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.