Online Spatiotemporal Least-Squares Support Vector Machine Modeling Approach for Time-Varying Distributed Parameter Processes

Lu, XinJiang; Yin, Feng; Huang, Minghui

doi:10.1021/acs.iecr.7b00984

Cited by 13 publications

(5 citation statements)

References 35 publications

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“…The solution of obtained nonlinear dynamic systems will have high-sensitive dependence on perturbations, a slight perturbation (e.g., inappropriate truncation of higher modes) would lead to topological changes of the dynamic system. Thus, the modified EEFs are given by adding an extra weight matrix into (8)…”

Section: Modified Eefs and Its Applications For Model Reductionmentioning

confidence: 99%

“…It is clear that the weights of initial EEFs in (8) are changed from to . And we can find that each modified EEFs is the linear combination of initial EEFs as follows:…”

Section: Modified Eefs and Its Applications For Model Reductionmentioning

confidence: 99%

“…Thus, model reduction for nonlinear STSs at a reasonable cost and accuracy has a great significance in practical engineering applications. Empirical eigenfunctions (EEFs) identified by proper orthogonal decomposition (POD) [1] are widely used as global spatial basis functions in advanced methods for model reduction of nonlinear STSs [2][3][4][5][6][7][8]. Modes obtained from POD can be calculated quite easily as the solutions of an eigenvalue problem involving second-order correlation tensors.…”

Section: Introductionmentioning

confidence: 99%

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Modified Empirical Eigenfunctions and Its Applications for Model Reduction of Nonlinear Spatiotemporal Systems

Jiang

Liu

2018

Mathematical Problems in Engineering

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Model reduction can greatly reduce complexity and difficulty of control design for spatiotemporal systems (STS) in engineering applications. Empirical eigenfunctions (EEFs) are widely used for the model reduction of spatiotemporal systems, however, truncation of higher modes may describe the behaviours of nonlinear spatiotemporal systems inaccurately. In this paper, modified EEFs are proposed and applied to model reduction of nonlinear spatiotemporal systems. Modified EEFs are obtained via modifying the weights matrix in the method of snapshots, which can be rewritten as linear combinations of initial EEFs. The coefficient matrix for combinations is computed according to the nonlinear temporal dynamics of STSs. Thus, the effects of higher modes are considered into modified EEFs with less computational requirements. The reduced model can give a more accurate description for behaviours of the system. The performance of the proposed method is further proved theoretically, and a numerical example demonstrates the effectiveness of the proposed method.

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Section: Modified Eefs and Its Applications For Model Reductionmentioning

confidence: 99%

“…It is clear that the weights of initial EEFs in (8) are changed from to . And we can find that each modified EEFs is the linear combination of initial EEFs as follows:…”

Section: Modified Eefs and Its Applications For Model Reductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modified Empirical Eigenfunctions and Its Applications for Model Reduction of Nonlinear Spatiotemporal Systems

Jiang

Liu

2018

Mathematical Problems in Engineering

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“…Recently, some researchers have attempted to develop spatiotemporal analytic models based on experimental data. − They believe that the thermal processes of LIBs are time-/space-coupled, infinite-dimensional distributed parameter systems (DPSs). − In addressing these problems, a time/space separation strategy that is usually accompanied by separate learning of spatial basis functions and temporal models is an effective model-reduction method in DPSs. , Under this framework, many machine learning algorithms, such as extreme learning machine (ELM), locally linear embedding, and isometric mapping, can be extended to model a battery’s thermal process. These data-driven methods can be performed without any prior knowledge.…”

Section: Introductionmentioning

confidence: 99%

Multiple Spatiotemporal Broad Learning for Real-Time Temperature Estimation of Lithium-Ion Batteries

Yang

Zhu

et al. 2023

Ind. Eng. Chem. Res.

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The temperature estimation of lithium-ion batteries (LIBs) is of great significance to their thermal management and intelligent operation. Due to different working conditions and unknown external disturbance, batteries often need to work at a large operating range with multiple working points. However, direct global modeling and persistently exciting experiment in a large working region are very costly in practical. Complex spatiotemporal coupling and infinite-dimensional nature further make the problem more difficult. To address the above problems, a novel multiple spatiotemporal modeling method is proposed based on incremental spatiotemporal broad learning (ST-BL) and adaptive ensemble learning (EL) for the temperature prediction of batteries. First, the thermal process is identified through several local spatiotemporal domains using density peak clustering. To solve the complex spatiotemporal coupling problem, a novel ST-BL that introduces a spatial kernel function into BL is developed to model each local spatiotemporal domain. Further, the multiple ST-BL model is obtained by adaptive EL of all local models. In addition, to improve the adaptive ability of the model to the current state, incremental learning is performed on local models using newly arrived samples. Since the proposed multiple spatiotemporal modeling method involves a multi-modeling mechanism, it can achieve higher accuracy and efficiency than the traditional global single spatiotemporal modeling method, which is validated by an LIB experiment.

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“…Recently, some nonlinear spatiotemporal methods have been developed for modeling nonlinear DPSs. For example, the spatiotemporal least squares support vector machine (LS-SVM) [31]- [33] used the spatial kernel functions to represent nonlinear relationships on space, and the spatiotemporal extreme learning machine [34], [35] was developed to model nonlinear DPSs due to its strong nonlinear mapping ability and self-learning properties. However, these spatiotemporal modeling methods did not take the intrinsic structure of the data into account, which often makes them less effective for modeling complex DPSs.…”

Section: Introductionmentioning

confidence: 99%

A Modeling Approach With Spatial Basis Functions Learning and Temporal Dynamic Online Modeling for Time-Varying Distributed Parameter Processes

Zhou

2019

IEEE Access

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Currently, most of existing data-driven modeling methods for distributed parameter systems (DPSs) are offline and do not take the intrinsic structure of streaming data into account. This often makes them difficult to model strongly nonlinear and time-varying DPSs. To overcome this, a novel modeling method that integrates the advantages of both manifold-learning-based spatial basis functions learning and temporal dynamic online modeling is proposed. In this method, the original spatiotemporal data are first mapped into high dimensional space using nonlinear mapping function, from which manifold learning is developed to obtain spatial basis functions. This allows the strongly nonlinear relationship on space able to be constructed due to nonlinear mapping, and maintaining the intrinsic data structure due to manifold learning. In addition, the online least squares support vector machine (LS-SVM) is developed to construct the temporal dynamics model. This may make time-varying dynamics of DPSs able to be captured. By integrating spatial basis functions and the online LS-SVM temporal model, a spatiotemporal model is constructed, which allows for the reconstruction of time-varying and nonlinear dynamics of DPSs. The catalytic rod simulation and heating experiments not only demonstrate the effectiveness of the proposed method, but also the better modeling ability as compared to several common modeling methods.INDEX TERMS Distributed parameter systems, strong nonlinearity, time-varying, manifold learning, LS-SVM.

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Online Spatiotemporal Least-Squares Support Vector Machine Modeling Approach for Time-Varying Distributed Parameter Processes

Cited by 13 publications

References 35 publications

Modified Empirical Eigenfunctions and Its Applications for Model Reduction of Nonlinear Spatiotemporal Systems

Modified Empirical Eigenfunctions and Its Applications for Model Reduction of Nonlinear Spatiotemporal Systems

Multiple Spatiotemporal Broad Learning for Real-Time Temperature Estimation of Lithium-Ion Batteries

A Modeling Approach With Spatial Basis Functions Learning and Temporal Dynamic Online Modeling for Time-Varying Distributed Parameter Processes

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