摘要:外强迫随时间的变化对于非平稳系统的影响十分重要，如何从该系统中重构或提取外强迫信息则成为研究其中动力学特征的关键所在。本文基于慢特征分析方法（Slow Feature Analysis，SFA）以连续系统（改变的Lorenz系统）为参考模型，分别讨论在周期型强迫、减弱的周期型强迫、指数衰减型强迫、伴随指数衰减的周期型强迫等条件下，SFA方法对模型中不同强迫信号的提取能力。结果显示，SFA方法能够提取作用于连续系统中的外强迫信息，其提取效果与外强迫的强度、噪声以及嵌入维数m有关：对于越弱的外强迫或者存在越强的噪声干扰，提取效果越差，提取信号中将出现虚假的高频波动；嵌入维数m的增大能在一定程度上提高外强迫信号的提取效果。试验还表明，作用在单一变量上的外强迫会将其驱动信息嵌入于系统中，因此，可以通过SFA分析方法从其他变量中提取其外强迫信号。
关键词:慢特征分析方法/
驱动力/
非平稳系统/
连续系统
Abstract:The influence of gradual external forcing changes on non-stationary system is significant, and the manner by which external forcing features are reconstructed from non-stationary system has become the key to study the dynamic characteristics of the system. In this study, a continuous system (the modified Lorenz system) is used as the reference model, based on the slow feature analysis (SFA). We discuss the ability of SFA in extracting different forcing signals in the model under conditions of periodic forcing, weakened periodic forcing, exponential decay forcing, and periodic forcing with exponential decay. Results show that the SFA method can extract external forcing information acting on the continuous system and its extraction effect is correlated to the intensity of the external forcing, noise, and embedding dimension m: The weaker the external forcing or the stronger the noise interference, the worse the extraction effect. Hence, the false high-frequency fluctuation appears in the extracted signal. The increase in embedding dimension m can improve the extraction effect of the external forcing signal to a certain extent. The results also shows that the external forcing acting on a single variable embeds its driving information in the system and SFA can extract the external forcing signal from other variables.
Key words:Slow feature analysis/
Driving force/
Non-stationary system/
Continuous system
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http://www.iapjournals.ac.cn/qhhj/article/exportPdf?id=20200204
