基于组合NARX神经网络的非平稳含噪混沌时间序列在线预测

Online prediction of non-stationary chaotic time series with noise based on combinational NARX neural network

针对混沌时间序列演化复杂,数据非平稳特征及噪声严重影响混沌时间序列短期预测精度的问题,提出了基于前向差分、改进小波包去噪和外因输入的非线性自回归网络(FD-IWPD-NARX)的非平稳含噪混沌时间序列(NNCTS)在线组合预测方法。在滚动时域框架下,采用前向差分平稳窗口内时间序列数据,改进小波包去噪阈值函数改善数据去噪效果,最后通过串并行闭环NARX神经网络对平稳去噪的混沌时间序列进行训练和测试。结果表明,前向差分和提出的改进小波包去噪可以有效提升NARX神经网络的预测性能;与不分窗NARX神经网络、循环神经网络(RNN)和标准长短期记忆网络(LSTM)相比,FD-IWPD-NARX网络可基于少量数据完成模型训练,在预测精度方面具有优势,且每窗模型的训练平均时长缩短至0.12 s,具有在线应用潜力。

In response to the complex evolution of chaotic time series,as well as the serious impact of non-stationary features and noise on the short-term prediction accuracy of chaotic time series,an online combination prediction method of Non-stationary Noisy Chaotic Time Series(NNCTS) is proposed based on Forward Difference,Improved Wavelet Packet Denoising,and Nonlinear Auto-Regressive with eXogeneous inputs network(FD-IWPD-NARX).In the framework of moving horizons,the forward difference is used to the stabilize time series data in each window.The wavelet packet denoising threshold function is improved to enhance the data denoising effect.The stabilized denoised chaotic time series is then trained and tested using a series parallel closed-loop NARX neural network.The results show that the forward difference and the proposed improved wavelet packet denoising can effectively improve the predictive performance of the NARX neural network.Compared with the windowless NARX neural network,Recurrent Neural Network(RNN),and standard Long and Short-Term Memory network(LSTM),the FD-IWPD-NARX network proposed can complete model training based on a smaller amount of data,having advantages in prediction accuracy.The average model training time in each window is shortened to 0.12 s,which has the potential for online application.