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为提高混沌时间序列的预测精度, 提出一种基于混合神经网络和注意力机制的预测模型(Att-CNN-LSTM), 首先对混沌时间序列进行相空间重构和数据归一化, 然后利用卷积神经网络(CNN)对时间序列的重构相空间进行空间特征提取, 再将CNN提取的特征和原时间序列组合, 用长短期记忆网络(LSTM)根据空间特征提取时间特征, 最后通过注意力机制捕获时间序列的关键时空特征, 给出最终预测结果. 将该模型对Logistic, Lorenz和太阳黑子混沌时间序列进行预测实验, 并与未引入注意力机制的CNN-LSTM模型、单一的CNN和LSTM网络模型、以及传统的机器学习算法最小二乘支持向量机(LSSVM)的预测性能进行比较. 实验结果显示本文提出的预测模型预测误差低于其他模型, 预测精度更高.Chaotic time series forecasting has been widely used in various domains, and the accurate predicting of the chaotic time series plays a critical role in many public events. Recently, various deep learning algorithms have been used to forecast chaotic time series and achieved good prediction performance. In order to improve the prediction accuracy of chaotic time series, a prediction model (Att-CNN-LSTM) is proposed based on hybrid neural network and attention mechanism. In this paper, the convolutional neural network (CNN) and long short-term memory (LSTM) are used to form a hybrid neural network. In addition, a attention model with softmaxactivation function is designed to extract the key features. Firstly, phase space reconstruction and data normalization are performed on a chaotic time series, then convolutional neural network (CNN) is used to extract the spatial features of the reconstructed phase space, then the features extracted by CNN are combined with the original chaotic time series, and in the long short-term memory network (LSTM) the combined vector is used to extract the temporal features. And then attention mechanism captures the key spatial-temporal features of chaotic time series. Finally, the prediction results are computed by using spatial-temporal features. To verify the prediction performance of the proposed hybrid model, it is used to predict the Logistic, Lorenz and sunspot chaotic time series. Four kinds of error criteria and model running times are used to evaluate the performance of predictive model. The proposed model is compared with hybrid CNN-LSTM model, the single CNN and LSTM network model and least squares support vector machine(LSSVM), and the experimental results show that the proposed hybrid model has a higher prediction accuracy.
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Keywords:
- chaotic time series/
- convolutional neural network/
- long short-term memory network/
- attention mechanism
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RMSE MAE MAPE RMSPE Att-CNN-LSTM 0.003503 0.002935 0.5305 0.6767 CNN-LSTM 0.006856 0.005444 1.1064 1.7795 LSTM 0.006169 0.005316 1.1595 1.6887 CNN 0.004670 0.003849 0.8802 1.4019 LSSVM 0.009158 0.004307 1.3623 3.8604 
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模型 Att-CNN-LSTM CNN-LSTM CNN LSTM LSSVM 训练时间 /s 312.7 302 59.5 48.8 215.4 预测时间 /s 0.53 0.49 0.25 0.21 0.47 下载:
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RMSE MAE MAPE RMSPE Att-CNN-LSTM 0.0679 0.0521 1.2182 2.1102 CNN-LSTM 0.2445 0.1229 3.8849 14.7893 LSTM 0.5152 0.3901 13.6767 43.7676 CNN 0.5356 0.3811 11.0032 33.5251 LSSVM 0.5101 0.3652 9.3543 35.5644 下载:
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模型 Att-CNN-LSTM CNN-LSTM CNN LSTM LSSVM 训练时间 /s 184.6 193.9 84.28 51.21 202.4 预测时间 /s 0.47 0.55 0.20 0.23 0.45 下载:
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RMSE MAE MAPE RMSPE Att-CNN-LSTM 20.1829 17.1827 32.8167 42.3529 CNN-LSTM 30.5652 21.4093 67.4343 56.7217 LSTM 24.9137 18.2815 49.5862 62.6939 CNN 24.8534 18.4677 65.3480 44.1892 LSSVM 27.3271 19.4373 43.0987 56.6781 下载:
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模型 Att-CNN-LSTM CNN-LSTM CNN LSTM LSSVM 训练时间 /s 309.2 291.3 76.5 53.3 237.9 预测时间 /s 0.39 0.43 0.15 0.25 0.59 下载:
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