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基于改进差分进化和回声状态网络的时间序列预测研究

许美玲 王依雯

许美玲, 王依雯. 基于改进差分进化和回声状态网络的时间序列预测研究. 自动化学报, 2019, 45(x): 1−9 doi: 10.16383/j.aas.c180549
引用本文: 许美玲, 王依雯. 基于改进差分进化和回声状态网络的时间序列预测研究. 自动化学报, 2019, 45(x): 1−9 doi: 10.16383/j.aas.c180549
Xu Mei-Ling, Wang Yi-Wen. Time series prediction based on improved differential evolution and echo state network. Acta Automatica Sinica, 2019, 45(x): 1−9 doi: 10.16383/j.aas.c180549
Citation: Xu Mei-Ling, Wang Yi-Wen. Time series prediction based on improved differential evolution and echo state network. Acta Automatica Sinica, 2019, 45(x): 1−9 doi: 10.16383/j.aas.c180549

基于改进差分进化和回声状态网络的时间序列预测研究

doi: 10.16383/j.aas.c180549
基金项目: 国家自然科学基金(61702077), 中央高校基本科研业务费(DUT16RC(3)123)资助
详细信息
    作者简介:

    许美玲:东北大学智能工业数据解析与优化教育部重点实验室讲师, 大连理工大学电子信息与电气工程学部博士后. 主要研究方向为神经网络和多元时间序列预测. E-mail: xuml@dlut.edu.cn

    王依雯:大连理工大学电子信息与电气工程学部硕士生. 主要研究方向为时间序列预测. E-mail: wangyiwen0802@163.com

Time Series Prediction Based on Improved Differential Evolution and Echo State Network

Funds: Supported by National Natural Science Foundation of China(61702077), Fundamental Research Funds for the Central Universities (DUT16RC(3)123)
  • 摘要: 针对回声状态网络无法根据不同的时间序列有效地选择储备池参数的问题, 本文提出一种新型预测模型, 利用改进的差分进化算法来优化回声状态网络. 其中差分进化算法的缩放因子F、交叉概率CR和变异策略自适应调整, 以提高算法的寻优性能. 为验证本文方法的有效性, 对Lorenz时间序列、大连月平均气温 − 降雨量数据集进行仿真实验. 由实验结果可知, 本文提出的模型可以提高时间序列的预测精度, 且具有良好的泛化能力及实际应用价值.
  • 图  1  ESN结构示意图

    Fig.  1  Structure of ESN

    图  2  IDE-ESN算法流程图

    Fig.  2  Flow chart for IDE-ESN

    图  3  Lorenz-x(t)序列: IDE-ESN的预测曲线及误差曲线

    Fig.  3  Lorenz-x(t) series: prediction and error curves obtained by IDE-ESN

    图  4  Lorenz-x(t)序列: 不同模型的适应度曲线

    Fig.  4  Lorenz-x(t) series: the curves of Fitness for different models

    图  5  大连月平均气温: IDE-ESN的预测曲线及误差曲线

    Fig.  5  Dalian monthly average temperature series: prediction and error curves obtained by IDE-ESN

    图  6  大连月平均气温: 不同模型的适应度曲线

    Fig.  6  Dalian monthly average temperature series: the curves of Fitness for differential models

    表  1  Lorenz-x(t)序列: IDE-ESN模型参数

    Table  1  Lorenz-x(t) series: parameters in IDE-ESN

    储备池参数取值
    储备池规模50
    稀疏度0.0210
    谱半径0.9589
    输入变化因子0.0600
    下载: 导出CSV

    表  2  Lorenz-x(t) 序列: 测试集仿真结果

    Table  2  Lorenz-x(t) time series: prediction results on the test dataset

    模型RMSENRMSESMAPE
    AF-ESN2.0850e-061.8571e-072.7992e-07
    PSO-ESN1.0139e-061.0211e-071.3613e-07
    ELM1.8422e-036.6638e-042.1061e-04
    TLBO-ESN7.7210e-071.6737e-071.0528e-07
    IDE-ESN3.2156e-079.8008e-084.3089e-08
    下载: 导出CSV

    表  3  Lorenz-x(t) 序列: 不同模型的运行时间

    Table  3  Lorenz-x(t) series: run time of different models

    模型AF-ESNPSO-ESNTLBO-ESNIDE-ESN
    时间1405.4289 s47.6972 s168.3124 s102.8856 s
    下载: 导出CSV

    表  4  大连月平均气温: IDE-ESN模型参数

    Table  4  Dalian monthly average temperature-rainfall series: parameters in IDE-ESN

    储备池参数取值
    储备池规模47
    稀疏度0.0206
    谱半径0.9802
    输入变化因子0.0459
    下载: 导出CSV

    表  5  大连月平均气温: 测试集仿真结果

    Table  5  Dalian monthly average temperature series: prediction results for the test dataset

    模型RMSENRMSESMAPE
    AF-ESN1.80420.29020.1820
    PSO-ESN1.65110.29560.1666
    ELM5.42350.67040.5520
    TLBO-ESN1.67260.20880.1708
    IDE-ESN1.42150.27410.1440
    下载: 导出CSV

    表  6  大连月平均气温: 不同模型的运行时间

    Table  6  Dalian monthly average temperature series: run time of different models

    模型AF-ESNPSO-ESNTLBO-ESNIDE-ESN
    时间347.1955 s10.5115 s31.1971 s15.1921 s
    下载: 导出CSV
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