Incomplete Phase Space Reconstruction Method Based on Subspace Adaptive Evolution Approximation

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.

Support Vector Regression Based on Grid-Search Method for Short-Term Wind Power Forecasting

“…Moreover, a bibliographical survey associated with the general application of research and developments was presented by Lei et al [12] in the fields of wind power forecasting. Li et al [13] presented ideal subspace approximation techniques based on a chaotic time series and nonlinear Kalman filtering, and the wind speed prediction experiments were used to demonstrate the high chaotic prediction accuracy. Hoai et al [14] optimized an empirical-statistical downscaling technique for prediction based on a feed-forward multilayer perceptron (MLP) neural network, and they gave the numerical simulation to demonstrate the robustness of proposed technology.…”