Modeling for distributed parameter systems based on low-dimensional constrained embedding

doi:10.3785/j.issn.1008-973X.2019.11.013

Journal of ZheJiang University (Engineering Science)

2019, Vol. 53

Issue (11): 2154-2162 DOI: 10.3785/j.issn.1008-973X.2019.11.013

Computer Technology and Control Engineering

Modeling for distributed parameter systems based on low-dimensional constrained embedding

Chao-jun ZHOU(

),Ming-hui HUANG,Xin-jiang LU*(

)

College of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China

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Abstract

It is difficult to establish a precise model for the distributed parameter systems (DPSs), which is affected by spatiotemporal coupling characteristic, strong nonlinearity, complex energy exchange and unknown factors. Aiming at this problem, a data-driven based low-dimensional constrained embedding modeling method was proposed. The data local nonlinearity and the global nonlinearity were considered based on the data manifold distribution. By nonlinear mapping and manifold learning methods, the nonlinear connection of local manifold structure was guaranteed and the nonlocal manifold structure was constrained to avoid data chaos in the low-dimensional space. The least squares support vector machine (LS-SVM) was used to establish the temporal series model to obtain the dynamic features in time direction. A complete predictive model of the system was reconstructed by spatiotemporal integration. Experimental results of thermal process show that the proposed method can effectively establish a model of strongly nonlinear DPS. Compared with the traditional method, the proposed method has stronger modeling performance and predictive ability.

Key words： distributed parameter system strong nonlinearity manifold learning kernel method low-dimensional constraint least squares support vector machine

Received: 30 July 2018 Published: 21 November 2019

CLC:

TP 301

Corresponding Authors: Xin-jiang LU E-mail: jun9196@csu.edu.cn;luxj@csu.edu.cn

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Cite this article:

Chao-jun ZHOU,Ming-hui HUANG,Xin-jiang LU. Modeling for distributed parameter systems based on low-dimensional constrained embedding. Journal of ZheJiang University (Engineering Science), 2019, 53(11): 2154-2162.

URL:

http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2019.11.013 OR http://www.zjujournals.com/eng/Y2019/V53/I11/2154

基于低维约束嵌入的分布参数系统建模

针对分布参数系统受时空耦合特性、强非线性、复杂的能量交换以及未知因素等的影响，难以精确建模的问题，提出基于数据驱动的低维约束嵌入建模方法. 以数据流形分布为基础，考虑数据局部非线性和全局非线性；通过非线性映射和流形学习方法，保证数据局部流形结构的非线性联系；约束非局部流形结构，避免数据在低维空间内发生混乱现象；采用最小二乘支持向量机建立时序模型，获得时间方向上的动态特征，并通过时空整合，重构系统完整的预测模型. 热过程的实验结果表明，所提出的方法能有效建立强非线性分布参数系统的模型，与传统方法对比，具有更强的建模性能与预测能力.

关键词： 分布参数系统, 强非线性, 流形学习, 核方法, 低维约束, 最小二乘支持向量机

Fig.1 Nonlinear relation between data

Fig.2 Learning process for spatial basis functions of low-dimensional constrained embedding modeling strategy

Fig.3 Spatiotemporal modeling framework of low-dimensional constrained embedding method

Fig.4 Schematic diagram of composition of heating furnace

Fig.5 Position distribution of twelve temperature sensors

Fig.6 Amplitude of input signal

${u_3}$

Fig.7 Temperature contrast between model predictive value and real value in different positions

Fig.8 Relative error between model predictive and real values

Tab.1 Root mean square errors of model by three methods

Tab.2 Root mean square errors of untrained points modeling by three methods


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