Incomplete Phase Space Reconstruction Method Based on Subspace Adaptive Evolution Approximation

Tai-Fu Li,Ji-Ke Ge,Wei Jia,Wei Zhou,Yu-Cheng Liu,Li-Zhong Yao

doi:10.1155/2013/983051

Abstract

The chaotic time series can be expanded to the multidimensional space by phase space reconstruction, in order to reconstruct the dynamic characteristics of the original system. It is difficult to obtain complete phase space for chaotic time series, as a result of the inconsistency of phase space reconstruction. This paper presents an idea of subspace approximation. The chaotic time series prediction based on the phase space reconstruction can be considered as the subspace approximation problem in different neighborhood at different time. The common static neural network approximation is suitable for a trained neighborhood, but it cannot ensure its generalization performance in other untrained neighborhood. The subspace approximation of neural network based on the nonlinear extended Kalman filtering (EKF) is a dynamic evolution approximation from one neighborhood to another. Therefore, in view of incomplete phase space, due to the chaos phase space reconstruction, we put forward subspace adaptive evolution approximation method based on nonlinear Kalman filtering. This method is verified by multiple sets of wind speed prediction experiments in Wulong city, and the results demonstrate that it possesses higher chaotic prediction accuracy.

Highlights

In recent years, industrial disasters and accidents occurred frequently, the meteorological and hydrological conditions were complicated and changeable, and financial markets fluctuated drastically
Time delay selection methods that are commonly used in the chaotic short-term prediction mainly include autocorrelation method [11], mutual information method [12], and singular value fraction method [13]
It is difficult to determine the threshold of the singular value, because the singular value fraction method is largely affected by noise

Summary

Introduction

Industrial disasters and accidents occurred frequently, the meteorological and hydrological conditions were complicated and changeable, and financial markets fluctuated drastically. The embedding dimension m and delay time τ, needed to be determined before the phase space reconstruction [9, 10]. The prediction model based on phase space reconstruction has been used to adopt the functional approximation method based on the neural network [18,19,20,21], which has strong nonlinear fitting capability and can approximate any complex nonlinear relationships. We can constitute a phase space by choosing a kind of phase space reconstruction method, and the space may be incomplete, not separate, and can be seen as a subspace of the ideal phase space On this basis, we put forward adaptive neural network model based on nonlinear Kalman filtering and realize the subspace approximation of dynamic evolution system.

Subspace Approximation of Phase Space Reconstruction

Neural Network Model Based on Nonlinear Kalman Filtering

Simulation Examples

Conclusion and Further Work