时间序列预测是一类非常重要的问题,但基本上局限于参数不可变问题的研究,而对实际问题中经常出现的更重要的参数可变系统的预测,由于构成几乎所有已有预测技术基础的Taken嵌入定理不再成立,所以这方面的研究成果极少.使用一种将(多)小波变换与反向传播神经网络相结合的新型网络结构--(多)小波神经网络,尝试对参数可变时间序列的预测.因为(多)小波神经网络的误差函数是一个凸函数,这在一定程度上可以避免经典神经网络容易陷入局部极小、收敛速度慢等问题.对著名的Ikeda参数可变系统的实验表明,多小波神经网络的预测性能较单小波神经网络要好,而单小波神经网络的性能较BP网要好.因此,该方法不失为时间可变系统预测的一种好的推荐.%Time series prediction is a very important problem in many applications and the current prediction techniques are nearly all based on the Takens' embedding theorem. Many realistic systems are parameter-varying systems, and the embedding theorems are invalid, predicting the behavior of parameter-varying systems is more difficult. This paper proposes the novel prediction techniques for parameter-varying systems reconstruction, which are based on wavelet neural network (WNN) and multiwavelets neural network (MWNN). These techniques absorb the advantages of high resolution of wavelet and learning of neural networks. The significant improvement is that the error's functions of both networks are convex, and the problem of poor convergence and undesired local minimum can be solved remarkably. Ikeda time series generated by the parameter-varying systems is adopted to check the prediction performance of the proposed models. The numerical experiments show that the three proposed models are feasible, MWNN has the top performance, and WNN could lead the better results than NN in the prediction of the parameter-varying systems.
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