Time/Space-Separation-Based SVM Modeling for Nonlinear Distributed Parameter Processes

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• 作者：Chenkun Qi ; Han-Xiong Li ; Xianxia Zhang ; Xianchao Zhao ; Shaoyuan Li ; Feng Gao
• 刊名：Industrial & Engineering Chemistry Research
• 出版年：2011
• 出版时间：January 5, 2011
• 年：2011
• 卷：50
• 期：1
• 页码：332-341
• 全文大小：444K
• 年卷期：v.50,no.1(January 5, 2011)
• ISSN：1520-5045

文摘

Modeling of distributed parameter systems (DPSs) is difficult because of their infinite-dimensional spatiotemporal nature and complex nonlinearities. Data-based modeling is necessary because there are usually some unknown uncertainties in first-principles modeling. In practice, a low-dimensional spatiotemporal model is often required for real-time implementations. In this study, a time/space-separation-based support-vector-machine (SVM) model identification approach is proposed for unknown nonlinear DPSs. The spatiotemporal output of the system is measured at a finite number of spatial locations, and for easy implementation, the input is assumed to be a finite-dimensional temporal variable. First, Karhunen鈭扡o猫ve (KL) decomposition is used for time/space separation and dimension reduction. Subsequently, the spatiotemporal output is expanded onto a low-dimensional Karhunen鈭扡o猫ve space with temporal coefficients. Finally, the least-squares support-vector-machine (LS-SVM) approach is used to model the system dynamics in a low-dimensional temporal domain. After the time/space synthesis, the nonlinear spatiotemporal dynamics can be reconstructed. Simulations are presented to demonstrate the effectiveness of this spatiotemporal modeling method.