基于VMD和GRNN的混沌时间序列预测
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摘要
随着非线性混沌动力学的发展,混沌时间序列的预测已经成为一个非常重要的研究方向。针对混沌时间序列的非线性和非平稳性的特点,提出一种变模态分解(VMD)和广义神经网络(GRNN)相结合的混沌时间序列预测方法,首先将混沌时间序列分解为多个固有模态函数(IMF)和余量(RF),然后对每个分量建立GRNN预测模型,最后将各分量的预测结果之和作为混沌时间序列的预测结果。采用Mackey-Glass混沌时间序列作为仿真实例,实验结果表明VMD-GRNN模型的预测精度相对于BP、ARMA和EMD-GRNN均有提高,证明了上述方法的有效性。
With the development of nonlinear chaotic dynamics, the prediction of chaotic time series has become a very important research direction. In view of the complexity, nonlinearity and nonstationarity of chaotic time series, a chaotic time series prediction model is proposed based on VMD and generalized neural network(GRNN). Firstly, the sequence was decomposed into several intrinsic mode functions(IMF) and residual(RF); then a GRNN prediction model for each component was established. Finally, the prediction results of each component were taken as the prediction results of nonlinear time series. The method was applied to Mackey-Glass chaotic time series prediction. The simulation results show that the VMD-GRNN models have higher predication accuracy compared with BP, ARMA and EMD-GRNN, thus illustrate the effectiveness of the method.
With the development of nonlinear chaotic dynamics, the prediction of chaotic time series has become a very important research direction. In view of the complexity, nonlinearity and nonstationarity of chaotic time series, a chaotic time series prediction model is proposed based on VMD and generalized neural network(GRNN). Firstly, the sequence was decomposed into several intrinsic mode functions(IMF) and residual(RF); then a GRNN prediction model for each component was established. Finally, the prediction results of each component were taken as the prediction results of nonlinear time series. The method was applied to Mackey-Glass chaotic time series prediction. The simulation results show that the VMD-GRNN models have higher predication accuracy compared with BP, ARMA and EMD-GRNN, thus illustrate the effectiveness of the method.
引文
[1] 张军峰,胡寿松. 基于一种新型聚类算法的RBF神经网络混沌时间序列预测[J]. 物理学报, 2007,56(2):713-719.
[2] F Takens. Detecting strange attractors in turbulence[M]. Dynamical Systems and Turbulence, Warwick 1980. Springer Berlin Heidelberg, 1981:366-381.
[3] Norden E Huang, et. al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time seri[M]. The Royal Society, 1998.
[4] R Ricci, et. al. Diagnostics of gear faults based on EMD and automatic selection of intrinsic mode functions[J]. Mechanical Systems & Signal Processing, 2011,25(3): 821-838.
[5] S Lahmiri. Long memory in international financial markets trends and short movements during 2008 financial crisis based on variational mode decomposition and detrended fluctuation analysis[J]. Physica A Statistical Mechanics & Its Applications, 2015,437:130-138.
[6] N Zhao, et al. Interference alignment with delayed channel state information and dynamic AR-model channel prediction in wireless networks[J]. Wireless Networks, 2015,21(4):1227-1242.
[7] L Zhao, et al. Using monitoring data of surface soil to predict whole crop-root zone soil water content with PSO-LSSVM, GRNN and WNN[J]. Earth Science Informatics, 2014,7(1):59-68.
[8] K Dragomiretskiy, D Zosso. Variational Mode Decomposition[J]. IEEE Transactions on Signal Processing, 2014,62(3):531-544.
[9] D F Specht. A general regression neural network.[J]. IEEE Transactions on Neural Networks, 1991,2(6):568.
[10] A Wolf, et al. Determining Lyapunov exponents from a time series[J]. Physica D Nonlinear Phenomena, 1985,16(3):285-317.
[2] F Takens. Detecting strange attractors in turbulence[M]. Dynamical Systems and Turbulence, Warwick 1980. Springer Berlin Heidelberg, 1981:366-381.
[3] Norden E Huang, et. al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time seri[M]. The Royal Society, 1998.
[4] R Ricci, et. al. Diagnostics of gear faults based on EMD and automatic selection of intrinsic mode functions[J]. Mechanical Systems & Signal Processing, 2011,25(3): 821-838.
[5] S Lahmiri. Long memory in international financial markets trends and short movements during 2008 financial crisis based on variational mode decomposition and detrended fluctuation analysis[J]. Physica A Statistical Mechanics & Its Applications, 2015,437:130-138.
[6] N Zhao, et al. Interference alignment with delayed channel state information and dynamic AR-model channel prediction in wireless networks[J]. Wireless Networks, 2015,21(4):1227-1242.
[7] L Zhao, et al. Using monitoring data of surface soil to predict whole crop-root zone soil water content with PSO-LSSVM, GRNN and WNN[J]. Earth Science Informatics, 2014,7(1):59-68.
[8] K Dragomiretskiy, D Zosso. Variational Mode Decomposition[J]. IEEE Transactions on Signal Processing, 2014,62(3):531-544.
[9] D F Specht. A general regression neural network.[J]. IEEE Transactions on Neural Networks, 1991,2(6):568.
[10] A Wolf, et al. Determining Lyapunov exponents from a time series[J]. Physica D Nonlinear Phenomena, 1985,16(3):285-317.