基于改进回声状态网络的混沌时间序列多步预测
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摘要
本文主要通过对传统回声状态网络(ESN)的结构和学习机理的研究,探讨了回声状态网络对混沌时间序列的预测方法。因为混沌时间序列对初始条件的极端敏感性,回声状态网络在混沌时间序列的预测研究中多用于不含噪声的理想条件,而在实际生活中普遍存在的噪声与样本序列共存的情况,使得回声状态网络在实际工程应用中可用性不强,预测结果难以达到满意。
针对这一不足,本文选用小波分析与回声状态网络结合,提出一种改进型回声状态网络,使小波变换与ESN网络实现松散型和紧致型结合。在对混沌时间序列进行预测前,首先使ESN网络与小波变换基于松散型结合,对含有噪声的混沌时间序列,利用小波变换对ESN输入数据做去噪的预处理,使得相空间重构时能够更好的使其确定相空间混沌吸引子的真实运动轨迹,重构合理的相空间结构,计算输入误差更具有合理性；然后使ESN网络与小波函数基于紧致型结合,替换原网络中S型神经元,利用回声状态网络新型的学习机理,建立一种直接的多步预测方法,实现对含噪混沌时间序列的5步、10步以至于50步的预测。
仿真实验结果表明,把消噪后的预测样本分别输入传统回声状态网络与使用S型神经元的回声状态网络相比较,改进后的回声状态网络在对含有噪声的实验数据的多步预测中,网络的泛化能力和预测精度都有较大程度提升。
In this paper,the traditional echo state network(ESN) through the structure and learning mechanism of the study,on the echo state network prediction method of chaotic time series. Because of chaotic time series extreme sensitivity to initial conditions, make the echo state network in chaotic time series prediction of noise are used for non-ideal conditions, but in real life, noise and the sample sequence common coexistence of the situation in which echo state networks in the practical application availability is not strong, difficult to achieve satisfactory predictions.
According to the shortages, this paper selects this wavelet analysis combined with echo state networks, propose a modified echo state network to transform loose with the ESN network and the combination of compact type. In chaotic time series prediction to first make ESN network and wavelet transform based on a loose combination of the noisy chaotic time series using wavelet transform denoising ESN to do pretreatment, makes the phase space reconstruction can better determine the phase space of make the chaotic attractor real trajectories of phase space reconstruction, reasonable structure, the calculation error is more reasonable input, Then make ESN network based on wavelet function with tight, replace original type of neuron network, with the new state of echo mechanism of learning network, establish a direct multi-step forecast method, the realization of noise chaotic time series of 5 steps,10 steps that 50 step.
Simulation results show that the denoising after samples separately predict with traditional echo state network input use of S-type neurons in the state, improved network compared to the echo state network containing noise experimental data of multi-step forecast, network generalization ability and forecasting precision are large and degree of ascension.
针对这一不足,本文选用小波分析与回声状态网络结合,提出一种改进型回声状态网络,使小波变换与ESN网络实现松散型和紧致型结合。在对混沌时间序列进行预测前,首先使ESN网络与小波变换基于松散型结合,对含有噪声的混沌时间序列,利用小波变换对ESN输入数据做去噪的预处理,使得相空间重构时能够更好的使其确定相空间混沌吸引子的真实运动轨迹,重构合理的相空间结构,计算输入误差更具有合理性；然后使ESN网络与小波函数基于紧致型结合,替换原网络中S型神经元,利用回声状态网络新型的学习机理,建立一种直接的多步预测方法,实现对含噪混沌时间序列的5步、10步以至于50步的预测。
仿真实验结果表明,把消噪后的预测样本分别输入传统回声状态网络与使用S型神经元的回声状态网络相比较,改进后的回声状态网络在对含有噪声的实验数据的多步预测中,网络的泛化能力和预测精度都有较大程度提升。
In this paper,the traditional echo state network(ESN) through the structure and learning mechanism of the study,on the echo state network prediction method of chaotic time series. Because of chaotic time series extreme sensitivity to initial conditions, make the echo state network in chaotic time series prediction of noise are used for non-ideal conditions, but in real life, noise and the sample sequence common coexistence of the situation in which echo state networks in the practical application availability is not strong, difficult to achieve satisfactory predictions.
According to the shortages, this paper selects this wavelet analysis combined with echo state networks, propose a modified echo state network to transform loose with the ESN network and the combination of compact type. In chaotic time series prediction to first make ESN network and wavelet transform based on a loose combination of the noisy chaotic time series using wavelet transform denoising ESN to do pretreatment, makes the phase space reconstruction can better determine the phase space of make the chaotic attractor real trajectories of phase space reconstruction, reasonable structure, the calculation error is more reasonable input, Then make ESN network based on wavelet function with tight, replace original type of neuron network, with the new state of echo mechanism of learning network, establish a direct multi-step forecast method, the realization of noise chaotic time series of 5 steps,10 steps that 50 step.
Simulation results show that the denoising after samples separately predict with traditional echo state network input use of S-type neurons in the state, improved network compared to the echo state network containing noise experimental data of multi-step forecast, network generalization ability and forecasting precision are large and degree of ascension.
引文
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[7]宋勇,李贻斌,李彩虹.基于回声状态网络的混沌时间序列多步预测[OL].中国科技论文在线,2006.
[8]王瑟.基于改进的回声状态神经网络的非线性预测[D].南京工业大学,2006.
[9]王玉昆,张勇.基于主元分析的转炉终点ESN静态预测模型[J].辽宁科技大学学报.2009,32(4)：26-30.
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[12]陈予恕.非线性振动系统的分叉和混沌理论[M].北京,高等教育出版社,1993.
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[19]顾圣士,王志谦,程极太.太阳黑子数时间序列的分形研究及预测[J].应用数学和力学,1999,20(1)：79-84
[20]Chen L, Aihara K. Global searching ability of chaotic neural networks. IEEE Transactions On Circuits and Systems I:Fundamental Theory andApplications,1999,46(8):974-993.
[21]吴祥兴,陈忠等.混沌学导论[M].上海,上海科学技术文献出版社,1996
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[24]简相超,郑君里一种正交多项式混沌全局建模方法[J].电子学报,2002,30(1)：76-78.
[25]Farmer J D, Sidorowich J J. Predicting chaotic time series[J]. Phys. Rev. Lett.,1987.
[26]李翔.从复杂到有序：神经网络智能控制理论新进展[M].上海,上海交通大学出版社,2006.
[27]邹月娴,韩春林,肖先赐.神经网络用于通信信号分类识别研究[J].电子科技大学学报,1995,24(4),350-354.
[28]葛哲学,孙志强.神经网络理论与MATLAB实现[M].北京,电子工业出版社,2007.9.
[29]王明进,程乾生.]Kohonen自组织网络在混沌时间序列预测中的应用[J].系统工程理论与实践,1997,7：12-17.
[30]张春慨,邵惠鹤.基于神经网络模型的混沌优化及其应用[J].化工自动化及仪表,2000,27(2)：19-22.
[31]Lapedes A, and Farber R. How neural nets work [C]. In Advances in Neural Information Processing Systems,1987,442-456.
[32]Haykin S, Principe J. Making sense of a complex world[J]. IEEE Signal Processing Magazine, 1998,15(3):66-81.
[33]Casdagli M. Nonlinear prediction of chaotic time series [J]. Physica D, Nonlinear Phenomena,1989,35(3):335-356.
[34]Hopfield J J. Neural networks and physical systems with emergent collective computational abilities [J]. Proc. Natl. Acad. Sci.,1982,79 (8):2554-2558.
[35]张兴会,刘玲,陈增强,袁著祉.应用Elman神经网络的混沌时间序列预测[J].华东理工大学学报,2002,28增刊：30-33.
[36]Min Han, ZhiWei Shi and Wei Wang. Modeling dynamic system by recurrent neural networks with state variables [A]. Proc. Of International Symposium on Neural Networks, Springer, 2004,200-205.
[37]Jaeger H. Tutorial on training recurrent neural networks, covering BPTT,RTRL,EKF and "echo state network"approach. GMD Report 159,German National Research Center for Information Technology,2002
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