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浙江大学学报(工学版)  2019, Vol. 53 Issue (11): 2154-2162    DOI: 10.3785/j.issn.1008-973X.2019.11.013
计算机技术与控制工程     
基于低维约束嵌入的分布参数系统建模
周朝君(),黄明辉,陆新江*()
中南大学 机电工程学院,湖南 长沙 410083
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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摘要:

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    
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
收稿日期: 2018-07-30 出版日期: 2019-11-21
CLC:  TP 301  
基金资助: 国家自然科学基金资助项目(51675539);中南大学创新驱动计划资助项目(2016CX009,2015CX002);湖南省科技领先人才资助项目(2016RS2015)
通讯作者: 陆新江     E-mail: jun9196@csu.edu.cn;luxj@csu.edu.cn
作者简介: 周朝君(1994—),男,硕士生,从事数据建模研究. orcid.org/0000-0002-6768-3163. E-mail: jun9196@csu.edu.cn
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引用本文:

周朝君,黄明辉,陆新江. 基于低维约束嵌入的分布参数系统建模[J]. 浙江大学学报(工学版), 2019, 53(11): 2154-2162.

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.

链接本文:

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

图 1  数据间的非线性联系
图 2  低维约束嵌入建模策略的空间基函数学习过程
图 3  低维约束嵌入方法的时空建模框架
图 4  加热炉构成示意图
图 5  12个温度传感器的位置分布
图 6  输入信号 ${u_3}$的幅值
图 7  不同位置处模型预测值与真实值的温度对比
图 8  模型预测与真实值的相对误差
建模方法 建模误差 测试误差
KL 1.177 7 1.267 5
LLE 0.276 1 0.736 1
本研究方法 0.114 2 0.584 0
表 1  3种方法下模型的均方根误差
建模方法 RMSE
s3 s6
KL 2.361 4 0.744 6
LLE 0.631 9 0.643 7
本研究方法 0.457 1 0.562 8
表 2  3种方法下未训练点的均方根误差
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