关键词: 非平稳系统/
非线性系统/
驱动力/
慢特征分析
English Abstract
Extracting the driving force signal from hierarchy system based on slow feature analysis
Pan Xin-Nong1,2,Wang Ge-Li1,
Yang Pei-Cai1
1.Key Laboratory of Middle Atmosphere and Global Environment Observation, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China;
2.University of Chinese Academy of Sciences, Beijing 100049, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 41575058).Received Date:08 October 2016
Accepted Date:16 January 2017
Published Online:05 April 2017
Abstract:Extracting the signals from non-stationary time series is a difficult task in many fields such as physics, economics, and atmospheric sciences. The theory of hierarchy suggests that varying driving force leads to the non-stationary behavior, so extracting and analyzing the slowly varying features can help to study non-stationary dynamical system, which has become a compelling question recently. Slow feature analysis (SFA) is an effective technique for extracting slowly varying driving forces from quickly varying non-stationary time series. The basic idea of SFA is to nonlinearly extend the reconstructive signal into a combination form with one or higher order polynomials, and to apply the principal component analysis to this extended signal and its time derivatives. The algorithm is guaranteed to seek an optimal solution from a group of functions directly and can extract a lot of uncorrelated features that are ordered by slowness. A series of studies has shown its superiority in extracting the driving force of non-stationary time series. The extracted signal is found to be highly correlated with the real driving force. Results based on ideal models show that either the slow driving force itself or a slower subcomponent can be detected by SFA. Yet despite all that, the further investigating of SFA is still needed to reduce its uncertainty. In this study, we create two types of non-stationary models by the logistic map with time-varying parameters: one includes two varying driving forces with different time periods constraining the evolution of time series in a non-stationary way; and the other is a three-layer structure encompassing two superimposed signals in which the slower signal of driving force is modulated by the lowest one. According to the ideal model and SFA, we conduct the numerical experiments to develop corresponding analysis method and discuss its application prospect in extracting driving force signals. We find that for the system of first kind, either the slowest signal or the combination of two driving forces constructed by SFA contains some uncertain information. However, we can detect the two independent driving forces from the constructed signal by wavelet analysis. For the three-hierarchy system that includes two superimposed signals of driving force, successive applications through SFA on the original time series and the constructed SFA signal will in turn detect the slower varying driving force signal and the slowest varying driving forces signal. The successful application of SFA shows its promising prospect in analyzing the external driving forces in non-stationary system and understanding relevant dynamic mechanism.
Keywords: non-stationary system/
nonlinear system/
driving force/
slow feature analysis
