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一类非线性离散时间动态系统的交替辨识算法及应用

张亚军 柴天佑 杨杰

杨贵军, 蒋朝辉, 桂卫华, 阳春华, 谢永芳. 基于熵权-可拓理论的高炉软熔带位置状态模糊综合评判方法. 自动化学报, 2015, 41(1): 75-83. doi: 10.16383/j.aas.2015.c140232
引用本文: 张亚军, 柴天佑, 杨杰. 一类非线性离散时间动态系统的交替辨识算法及应用. 自动化学报, 2017, 43(1): 101-113. doi: 10.16383/j.aas.2017.c150759
YANG Gui-Jun, JIANG Zhao-Hui, GUI Wei-Hua, YANG Chun-Hua, XIE Yong-Fang. Fuzzy Synthesis Evaluation Method for Position State of Blast Furnace Cohesive Zone Based on Entropy Weight Extension Theory. ACTA AUTOMATICA SINICA, 2015, 41(1): 75-83. doi: 10.16383/j.aas.2015.c140232
Citation: ZHANG Ya-Jun, CHAI Tian-You, YANG Jie. Alternating Identification Algorithm and Its Application to a Class of Nonlinear Discrete-time Dynamical Systems. ACTA AUTOMATICA SINICA, 2017, 43(1): 101-113. doi: 10.16383/j.aas.2017.c150759

一类非线性离散时间动态系统的交替辨识算法及应用

doi: 10.16383/j.aas.2017.c150759
基金项目: 

辽宁省科技项目自然科学基金 2015020144

国家自然科学基金 61403071, 61603168

中国博士后科学基金 2014M561246

教育部基本科研业务费培育种子基金 N140804001

详细信息
    作者简介:

    张亚军 东北大学博士后.主要研究方向为非线性模糊自适应控制理论,广义预测控制,多模型切换控制,智能解耦控制,数据驱动控制,智能控制系统的大数据建模,工业过程大数据建模及其应用.E-mail:zhangyajun79@gmail.com

    杨杰 流程工业综合自动化国家重点实验室博士研究生.主要研究方向为工业过程数据驱动建模技术及应用.E-mail:yjercou@126.com

    通讯作者:

    柴天佑 中国工程院院士,东北大学教授.IEEE Fellow,IFAC Fellow,欧亚科学院院士.1985年获得东北大学博士学位.主要研究方向为自适应控制,智能解耦控制,流程工业综合自动化理论、方法与技术.本文通信作者. E-mail:tychai@mail.neu.edu.cn

Alternating Identification Algorithm and Its Application to a Class of Nonlinear Discrete-time Dynamical Systems

Funds: 

Natural Science Foundation of Liaon-ing Province 2015020144

Supported by National Natural Science Foundation of China 61403071, 61603168

China Postdoctoral Science Foundation 2014M561246

Fundamental Research Funds for the Seed Foundation N140804001

More Information
    Author Bio:

    ZHANG Ya-Jun Postdoctoral at Northeastern University. His research interest covers nonlinear fuzzy adaptive control theory, gen-eralized predictive control, multiple models and switchingsystems, intelligent decoupling control, data-based driven control, big data-driven modelling theory, method and technology of intelligent control systems, process industries and their applications.E-mail:

    YANG Jie Ph. D. candidate at the State Key Laboratory of Synthet-ical Automation for Process Industries.His research interest covers data driven modeling technology and application for industrial pro-cess.E-mail:

    Corresponding author: CHAI Tian-You Academician of Chinese Academy of Engineering, professor at Northeast-ern University, IEEE Fellow, IFAC Fellow, IEAS Fellow.He received his Ph. D. degree from Northeastern Univer-sity in 1985. His research interest covers adaptive control,intelligent decoupling control, and integrated automation theory, method and technology of industrial process. Cor-responding author of this paper.). E-mail:tychai@mail.neu.edu.cn
  • 摘要: 表征产品在工业过程加工的质量、效率、成本、能耗或物耗等的运行指标与过程控制系统的输出密切相关,它们之间的动态模型往往机理不清,具有强非线性,难以用精确数学模型描述,但运行指标的预报对运行操作具有重要意义.本文利用工业过程在工作点附近工作的特点,将过程控制系统的输出与运行指标之间的动态模型描述成线性模型与高阶非线性项即未建模动态组成,对线性模型以及未建模动态提出了一种由改进的投影算法与未建模动态估计算法组成的交替辨识算法.最后,通过数值仿真实验和电熔镁炉的真实数据进行功率预报实验,实验结果表明了所提方法的有效性.
  • 图  1  BP神经网络估计$v[\varphi (k)]$的结构

    Fig.  1  The structure of the estimation for $v[\varphi (\text{k})]$ by BP neural networks[

    图  2  输入信号u

    Fig.  2  Control input signal u

    图  3  未建模动态(星线)及其估计值(圈线)

    Fig.  3  The un-modeled dynamics (star line) and its estimation value (circle line)

    图  4  采用BP神经网络估计未建模动态的误差

    Fig.  4  Estimation error for the un-modeled dynamics which produced by BP neural networks

    图  5  采用BP神经网络的估计误差(残差)的概率密度函数

    Fig.  5  The probability density functions of prediction errors (residuals) by BP neural networks

    图  6  BP神经网络的性能、训练状况和相关系数

    Fig.  6  The performance,training state,and regression of BP neural networks

    图  7  $A({z^{ - 1}})$ 中的参数和$B({z^{ - 1}})$中的参数

    Fig.  7  Parameters in A(z-1) and parameters in B(z-1)

    图  8  未建模动态(星线)及其估计值(圈线)

    Fig.  8  The un-modeled dynamics (star line) and its estimation value (circle line) by BP neural networks

    图  9  采用BP神经网络估计未建模动态的误差

    Fig.  9  Estimation error for the un-modeled dynamics which produced by BP neural networks with he proposed method

    图  10  采用BP神经网络的估计误差(残差)的概率密度函数

    Fig.  10  The probability density functions of prediction errors (residuals) by BP neural networks

    图  11  BP 神经网络的性能、训练状况和相关系数

    Fig.  11  The performance, training state, and regression of BP neural networks

    图  12  电熔镁炉结构示意图

    Fig.  12  The structure of electric-melting magnesia furnace

    图  13  功率的相关性分析

    Fig.  13  The correlation analysis of power

    图  14  功率(星线) 及其估计值(圈线)

    Fig.  14  The power (star line) and its estimation value (circle line) by the proposed method

    图  15  功率的估计误差

    Fig.  15  Estimation error of power

    图  16  估计误差(残差) 的概率密度函数

    Fig.  16  The probability density functions of prediction errors (residuals)

    图  17  BP 神经网络的性能、训练状况和相关系数

    Fig.  17  The performance, training state, and regression of BP neural networks

    表  1  辨识的平均绝对值误差、方差以及标准差

    Table  1  The average absolute error,variance and the standard deviation which produced by the proposed method

    平均绝对值误差方差标准差
    432.6477311320557.9634
    下载: 导出CSV
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