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基于WTFMC算法的递归模糊神经网络结构设计

乔俊飞 丁海旭 李文静

乔俊飞, 丁海旭, 李文静. 基于 WTFMC 算法的递归模糊神经网络结构设计. 自动化学报, 2020, 46(11): 2367−2378 doi: 10.16383/j.aas.c180847
引用本文: 乔俊飞, 丁海旭, 李文静. 基于 WTFMC 算法的递归模糊神经网络结构设计. 自动化学报, 2020, 46(11): 2367−2378 doi: 10.16383/j.aas.c180847
Qiao Jun-Fei, Ding Hai-Xu, Li Wen-Jing. Structure design for recurrent fuzzy neural network based on wavelet transform fuzzy Markov chain. Acta Automatica Sinica, 2020, 46(11): 2367−2378 doi: 10.16383/j.aas.c180847
Citation: Qiao Jun-Fei, Ding Hai-Xu, Li Wen-Jing. Structure design for recurrent fuzzy neural network based on wavelet transform fuzzy Markov chain. Acta Automatica Sinica, 2020, 46(11): 2367−2378 doi: 10.16383/j.aas.c180847

基于WTFMC算法的递归模糊神经网络结构设计

doi: 10.16383/j.aas.c180847
基金项目: 

国家自然科学基金 61533002

国家自然科学基金 61603009

北京市自然科学基金 4182007

北京市教委科技一般项目 KM201910005023

北京工业大学日新人计划 2017-RX(1)-04

详细信息
    作者简介:

    丁海旭  北京工业大学信息学部硕士研究生.主要研究方向为神经网络结构设计与优化, 污水处理过程特征建模. E-mail: dinghaixu@emails.bjut.edu.cn

    李文静  北京工业大学信息学部副教授. 2013年于中国科学院自动化研究所获得博士学位.主要研究方向为神经计算, 污水处理过程智能建模. E-mail: wenjing.li@bjut.edu.cn

    通讯作者:

    乔俊飞  北京工业大学信息学部教授.主要研究方向为污水处理过程智能控制, 神经网络结构设计与优化.本文通信作者. E-mail: junfeq@bjut.edu.cn

Structure Design for Recurrent Fuzzy Neural Network Based on Wavelet Transform Fuzzy Markov Chain

Funds: 

National Natural Science Foundation of China 61533002

National Natural Science Foundation of China 61603009

Beijing Natural Science Foundation 4182007

General Science and Technology Project of Beijing Education Commission KM201910005023

Beijing University of Technology0s New Day Program 2017-RX(1)-04

More Information
    Author Bio:

    DING Hai-Xu   Master student at the Faculty of Information Technology, Beijing University of Technology. His research interest covers structure design and optimization of neural networks, feature modelling in wastewater treatment process

    LI Wen-Jing   Associate professor at the Faculty of Information Technology, Beijing University of Technology. She received her Ph. D. degree from Institute of Automation, Chinese Academy of Sciences in 2013. Her research interest covers neural computation and intelligent modelling in wastewater treatment process

    Corresponding author: QIAO Jun-Fei   Professor at the Faculty of Information Technology, Beijing University of Technology. His research interest covers intelligent control of wastewater treatment process, structure design and optimization of neural networks. Corresponding author of this paper
  • 摘要: 针对递归模糊神经网络(Recurrent fuzzy neural network, RFNN)的递归量难以自适应的问题, 提出一种基于小波变换–模糊马尔科夫链(Wavelet transform fuzzy Markov chain, WTFMC)算法的RFNN模型.首先, 在时间维度上记录隐含层神经元的模糊隶属度, 并采用小波变换将该时间序列进行分解, 通过模糊马尔科夫链对子序列的未来时段进行预测, 之后将各预测量合并后代入递归函数中得到具有自适应性的递归量.其次, 利用梯度下降算法更新RFNN的参数来保证神经网络的精度.最后, 通过非线性系统建模中几个基准问题和实际污水处理中关键水质参数的预测实验, 证明了该神经网络模型的可行性和有效性.
    Recommended by Associate Editor LIU Yan-Jun
    1)  本文责任编委  刘艳军
  • 图  1  WTFMC-RFNN预测模型

    Fig.  1  WTFMC-RFNN prediction model

    图  2  Henon混沌系统训练样本RMSE

    Fig.  2  RMSE values in the training process of the Henon chaotic system

    图  3  Henon混沌系统测试样本拟合效果

    Fig.  3  Desired and predicted outputs of the Henon chaotic system

    图  4  Henon混沌系统测试样本的预测误差

    Fig.  4  Prediction error in the testing process of the Henon chaotic system

    图  5  动态系统训练样本RMSE

    Fig.  5  RMSE values in the training process of the dynamic system

    图  6  动态系统样本拟合效果

    Fig.  6  Sample fitting effect of dynamic system

    图  7  动态系统测试样本的预测误差

    Fig.  7  Prediction error in the testing process of dynamic system

    图  8  Mackey-Glass时间序列训练样本RMSE

    Fig.  8  RMSE values in the training process of Mackey-Glass time series

    图  9  Mackey-Glass时间序列拟合效果

    Fig.  9  Sample fitting effect of Mackey-Glass time series

    图  10  Mackey-Glass时间序列测试样本的预测误差

    Fig.  10  Prediction error in the testing process of Mackey-Glass time series

    图  11  非线性系统训练样本RMSE

    Fig.  11  RMSE values in the training process of nonlinear systems

    图  12  非线性系统拟合效果

    Fig.  12  Sample fitting effect of nonlinear system

    图  13  非线性系统测试样本的预测误差

    Fig.  13  Prediction error in the testing process of nonlinear system

    图  14  出水氨氮训练样本RMSE

    Fig.  14  RMSE values in the training process of effluent NH$_4$-N

    图  15  出水氨氮拟合效果

    Fig.  15  Sample fitting effect of effluent NH$_4$-N

    图  16  出水氨氮测试样本的预测误差

    Fig.  16  Prediction error in the testing process of effluent NH$_4$-N

    表  1  不同网络对Henon混沌时间序列的预测结果

    Table  1  Prediction results of Henon chaotic time series with different networks

    网络 规则数 训练RMSE 测试RMSE
    WTFMC-RFNN 3 0.0030 0.0057
    IRSFNN(Ful) [26] 3 0.0160 0.0140
    IRSFNN(TSK) [26] 4 0.0170 0.0150
    RSEFNN-LF [27] 9 0.0320 0.0230
    TRFN-S [28] 6 0.0280 0.0270
    WRFNN [29] 7 0.1910 0.1880
    RFNN 3 0.0088 0.0136
    下载: 导出CSV

    表  2  不同网络对动态系统的预测结果

    Table  2  Prediction results of dynamic network with different networks

    网络 规则数 训练RMSE 测试RMSE
    WTFMC-RFNN 4 0.0021 0.011
    IRSFNN(Ful) [26] 3 0.011 0.031
    IRSFNN(TSK) [26] 3 0.015 0.036
    RSEFNN-LF [27] 4 0.020 0.040
    TRFN-S [28] 3 0.032 0.047
    WRFNN [29] 5 0.064 0.098
    RSONFIN [30] 4 0.025 0.078
    HO-RNFS [31] 3 0.054 0.082
    RFNN 4 0.0047 0.025
    下载: 导出CSV

    表  3  不同网络对Mackey-Glass时间序列的预测结果

    Table  3  Prediction results of Mackey-Glass time series with different networks

    网络 规则数 训练RMSE 测试RMSE
    WTFMC-RFNN 6 0.0070 0.0079
    TRFN-S [28] 5 0.0124
    D-FNN [32] 10 0.0082
    LRFNN-SVR [12] 3 0.0407 0.0550
    FLNFN-CCPSO [33] 0.0083 0.0084
    FAOS-PFNN [34] 11 0.0073 0.0127
    RFNN 6 0.0098 0.0171
    下载: 导出CSV

    表  4  不同网络对非线性系统的预测结果

    Table  4  Prediction results of nonlinear system identification with different networks

    网络 规则数 训练RMSE 测试RMSE
    WTFMC-RFNN 6 0.0023 0.0048
    IRSFNN(TSK) 8 0.0065 0.0131
    RSEFNN-LF 7 0.0077 0.0125
    TRFN-S 6 0.0048 0.0104
    WRFNN 10 0.0059 0.0146
    HO-RNFS 6 0.0051 0.0097
    FAOS-PFNN [34] 5 0.0252
    DFNN [35] 6 0.0283
    GDFNN [36] 8 0.0108
    RFNN 6 0.0087 0.0167
    下载: 导出CSV

    表  5  不同网络对出水氨氮的预测结果

    Table  5  Prediction results of effluent NH$_4$-N with different networks with different networks

    网络 规则数 训练RMSE 测试RMSE
    WTFMC-RFNN 12 0.0041 0.0351
    IRSFNN (TSK) 16 0.0052 0.0468
    RSEFNN-LF 12 0.0048 0.0404
    TRFN-S 14 0.0045 0.0394
    WRFNN 15 0.0053 0.0529
    HO-RNFS 15 0.0047 0.0458
    RFNN 12 0.0041 0.0437
    下载: 导出CSV
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  • 收稿日期:  2018-12-22
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