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

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

许美玲^{1, 2,},
王依雯^1,

1.
大连理工大学电子信息与电气工程学部大连 116023
2.
东北大学智能工业数据解析与优化教育部重点实验室沈阳 110004

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. 本文通信作者. 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研究生. 主要研究方向为时间序列预测. E-mail: wangyiwen0802@163.com

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出版历程
- 收稿日期: 2018-08-15
- 网络出版日期: 2019-12-28
- 刊出日期: 2021-07-27

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

XU Mei-Ling^{1, 2
,},
WANG Yi-Wen^1
,

1.
Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116023
2.
Key Laboratory of Data Analytics and Optimization for Smart Industry (Northeastern University), Ministry of Education, Shenyang 110004

Funds: Supported by National Natural Science Foundation of China(61702077), Fundamental Research Funds for the Central Universities (DUT16RC(3)123)

More Information

Author Bio:
XU Mei-Ling　Lecturer at the Key Laboratory of Data Analytics and Optimization for Smart Industry (Northeastern University), Ministry of Education. Postdoctor at the Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology. Her research interest covers neural networks and multivariate time series prediction. Corresponding author of this paper

WANG Yi-Wen　Master student at the Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology. Her main research interest is time series prediction

摘要

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.
- 时间序列 /
- 预测模型 /
- 差分进化 /
- 回声状态网络
Abstract:
For the echo state network, it is difficult to select the suitable reservoir parameters for different time series. In this paper, we propose a new prediction model which uses an improved differential evolution algorithm to optimize the parameters of the echo state network. The scale factor and crossover probability of differential evolution algorithms are adaptively adjusted. In addition, offspring generation strategy is also adaptively adjusted. To verify the effectiveness of the proposed method, experiments were conducted on Lorenz time series, and monthly average temperature - rainfall time series of Dalian. Experimental results show that the model can improve forecast accuracy and has good generalization ability and practicability.
- Time series /
- predictive model /
- differential evolution /
- echo state network

HTML全文

图 1 ESN结构示意图

Fig. 1 Structure of ESN

下载: 全尺寸图片幻灯片

图 2 IDE-ESN算法流程图

Fig. 2 Flow chart for IDE-ESN

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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	RMSE	SMAPE	NRMSE
AF-ESN	2.0850E-06	1.8571E-07	2.7992E-07
PSO-ESN	1.0139E-06	1.0211E-07	1.3613E-07
ELM	1.8422E-03	6.6638E-04	2.1061E-04
TLBO-ESN	7.7210E-07	1.6737E-07	1.0528E-07
IDE-ESN	3.2156E-07	9.8008E-08	4.3089E-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-ESN	PSO-ESN	TLBO-ESN	IDE-ESN
时间	1405.4289 s	47.6972 s	168.3124 s	102.8856 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	RMSE	SMAPE	NRMSE
AF-ESN	1.8042	0.2902	0.1820
PSO-ESN	1.6511	0.2956	0.1666
ELM	5.4235	0.6704	0.5520
TLBO-ESN	1.6726	0.2088	0.1708
IDE-ESN	1.4215	0.2741	0.1440

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-ESN	PSO-ESN	TLBO-ESN	IDE-ESN
时间	347.1955 s	10.5115 s	31.1971 s	15.1921 s

下载: 导出CSV

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