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延迟深度回声状态网络及其在时间序列预测中的应用

薄迎春 张欣 刘宝

薄迎春, 张欣, 刘宝. 延迟深度回声状态网络及其在时间序列预测中的应用, 2020, 46(8): 1644−1653 doi: 10.16383/j.aas.c180264
引用本文: 薄迎春, 张欣, 刘宝. 延迟深度回声状态网络及其在时间序列预测中的应用, 2020, 46(8): 1644−1653 doi: 10.16383/j.aas.c180264
Bo Ying-Chun, Zhang Xin, Liu Bao. Delayed deep echo state network and its application on time series prediction. Acta Automatica Sinica, 2020, 46(8): 1644−1653 doi: 10.16383/j.aas.c180264
Citation: Bo Ying-Chun, Zhang Xin, Liu Bao. Delayed deep echo state network and its application on time series prediction. Acta Automatica Sinica, 2020, 46(8): 1644−1653 doi: 10.16383/j.aas.c180264

延迟深度回声状态网络及其在时间序列预测中的应用

doi: 10.16383/j.aas.c180264
基金项目: 

国家自然科学基金 21606256

中央高校基本科研业务费专项资金 20CX05006A

详细信息
    作者简介:

    张欣  中国石油大学(华东)讲师. 2013年获得东北大学工学博士学位.主要研究方向为自适应动态规划理论及智能控制. E-mail: zhangxin@upc.edu.cn

    刘宝  中国石油大学(华东)教授. 2006年获得东华大学工学博士学位.主要研究方向为智能优化控制. E-mail: liubao@upc.edu.cn

    通讯作者:

    薄迎春  中国石油大学(华东)讲师. 2013年获得北京工业大学工学博士学位.主要研究方向为神经网络及智能控制.本文通信作者. E-mail: boyingchun@sina.com.cn

Delayed Deep Echo State Network and Its Application on Time Series Prediction

Funds: 

National Natural Science Foundation of China 21606256

the Fundamental Research Funds for the Central Universities 20CX05006A

More Information
    Author Bio:

    ZHANG Xin  Lecturer at China University of Petroleum (East China). She received her Ph. D. degree from Northeastern University in 2013. Her research interest covers adaptive dynamical programming theory and intelligent control

    LIU Bao  Professor at China University of Petroleum (East China). He received his Ph. D. degree from Donghua University in 2006. His main research interest is intelligent optimization control

    Corresponding author: BO Ying-Chun  Lecturer at China University of Petroleum (East China). He received his Ph. D. degree from Beijing University of Technology in 2013. His research interest covers artiflcial neural networks and intelligent control. Corresponding author of this paper
  • 摘要: 为提高回声状态网络对于时间序列预测问题的处理能力, 本文提出了一种延迟深度回声状态网络构造方法.该方法将多个子神经元池顺序连接, 每两个相邻的子神经元池之间嵌入了一个滞后环节.由于滞后环节的存在,该网络可将长时记忆任务转化为一系列短时记忆任务, 从而简化长时依赖问题的求解, 同时降低神经元池的构建难度.实验表明, 该网络具有强大的短时记忆容量, 对初始参数有较好的鲁棒性, 对时间序列预测问题的处理能力也比常规回声状态网络有显著提高.
    Recommended by Associate Editor LIU Qing-Shan
    1)  本文责任编委  刘青山
  • 图  1  回声状态网络结构

    Fig.  1  Schematic diagram of ESN

    图  2  延迟深度回声状态网络结构

    Fig.  2  Schematic diagram of DDESN

    图  3  DDESN的遗忘曲线及$MC$随滞后时间变化

    Fig.  3  Forgetting curves and curves of $MC$ with $D$ in DDESN

    图  4  DDESN的记忆时间变化

    Fig.  4  Change of memory duration of DDESN

    图  5  NRMSE随$D$的变化

    Fig.  5  Change in NRMSE with $D$

    图  6  滞后时间优化过程及预测效果

    Fig.  6  Optimization process of delay time and result of prediction

    图  7  DDESN对不同时间序列问题的预测效果

    Fig.  7  Prediction results of DDESN for different problems

    图  8  $\rho$($\theta$)随$\theta$变化曲线

    Fig.  8  Changes in $\rho$($\theta$) with $\theta$

    图  9  神经元池输出信号相关度比较

    Fig.  9  Correlation comparison between reservoir signals

    表  1  ESN及DDESN参数设置

    Table  1  Parameters settings for ESN and DDESN

    Model $n$ $N^i$ $D^i$ $\rho^i$ $MC_{\max}$
    ESN 1 100 0 0.95 31.08
    DDESN$_2$ 2 50 0 $\sim$ 100 0.95 54.02
    DDESN$_5$ 5 20 0 $\sim$ 50 0.95 62.07
    下载: 导出CSV

    表  2  参数设置

    Table  2  Parameter settings

    Task $n_{\max}$ $n_\mathrm{opt}$ $D_{\max}$ $N^i$ $D_\mathrm{opt}$
    NARMA 20 2 100 30 [27]
    MSO$_2$ 20 6 100 10 [8, 9, 8, 9, 8]
    MSO$_5$ 20 6 100 20 [9, 9, 10, 9, 10]
    MSO$_8$ 20 6 100 25 [12, 13, 11, 12, 12]
    MSO$_{12}$ 20 5 100 40 [16, 17, 15, 16]
    Mackey-Glass 20 15 100 25 各层滞后时间均为6
    下载: 导出CSV

    表  3  Mackey-Glass预测性能

    Table  3  Prediction performance for Mackey-Glass

    Task ESN D & S ESN DDESN
    $\mathrm{NRMSE}_{84}$ 0.140 0.031 5$.81\times10^{-3}$
    NRMSE120 0.220 0.049 0.010
    下载: 导出CSV

    表  4  不同ESN模型的性能比较(MSO任务)

    Table  4  Performance comparison of different ESN models (MSO tasks)

    Task DDESN Balanced ESN[19] Evolutionary[27] D & S ESN[22] Evolino[28]
    MSO$_2$ $3.95\times10^{-8}$ $2.51\times10^{-12}$ $3.92\times10^{-8}$ $3.02\times10^{-9}$ $4.15\times10^{-3}$
    MSO$_5$ $6.84\times10^{-7}$ $1.06\times10^{-6}$ $2.54\times10^{-2}$ $8.21\times10^{-5}$ $0.166$
    MSO$_8$ $6.89\times10^{-6}$ $2.73\times10^{-4}$ $4.96\times10^{-3}$ $-$ $-$
    MSO$_{12}$ $1.50\times10^{-4}$ $-$ $-$ $-$ $-$
    下载: 导出CSV

    表  5  DDESN的鲁棒性测试结果

    Table  5  Robustness testing results of DDESN

    Task NARMA MSO$_{2}$ MSO$_{5}$ MSO$_{8}$ MSO$_{12}$ M-G$_{30}$
    最大NRMSE 0.2369 $7.03\times 10^{-5}$ $4.44\times 10^{-3}$ $6.33\times 10^{-2}$ $3.10\times 10^{-3}$ 0.0874
    最小NRMSE 0.1968 $3.95\times 10^{-8}$ $6.84\times 10^{-7}$ $5.17\times 10^{-6}$ $1.50\times 10^{-4}$ 0.0058
    平均NRMSE 0.2151 $1.06\times 10^{-6}$ $1.42\times 10^{-4}$ $7.17\times 10^{-4}$ $6.44\times 10^{-4}$ 0.0224
    NRMSE标准差 0.0089 $7.03\times 10^{-6}$ $7.17\times 10^{-4}$ $6.31\times 10^{-3}$ $4.41\times 10^{-4}$ 0.0130
    下载: 导出CSV
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出版历程
  • 收稿日期:  2018-04-28
  • 录用日期:  2018-08-02
  • 刊出日期:  2020-08-26

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