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利用慢特征分析法提取层次结构系统中的外强迫

潘昕浓 王革丽 杨培才

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利用慢特征分析法提取层次结构系统中的外强迫

潘昕浓, 王革丽, 杨培才

Extracting the driving force signal from hierarchy system based on slow feature analysis

Pan Xin-Nong, Wang Ge-Li, Yang Pei-Cai
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  • 在大量真实的动力系统中,外部驱动力总是随时间发生变化,正是这种变化导致了非平稳行为的产生. 因此,从此类系统的观测数据中提取和分析外强迫(也称驱动力)信号引起了人们越来越多的关注. 慢特征分析法(slow feature analysis,SFA)是从非平稳时间序列中提取外强迫信息的一种有效算法. 在其基础上利用变参数的Logistic映射产生的非平稳时间序列,通过数值试验进一步讨论了该方法的应用前景,并发展了一些相应的分析技术. 试验结果表明,对于模型中包含两个时变驱动力参数的系统,经过一次SFA处理之后,可以进一步利用子波分析技术检索出外强迫信号中的两个参数;对于模型中有两个叠加驱动力层次的三层动力系统,可先通过一次SFA处理,提取出次慢层外强迫信号,对该信号进行二次SFA处理,可提取出最慢层外强迫信号.
    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.
      通信作者: 王革丽, wgl@mail.iap.ac.cn
    • 基金项目: 国家自然科学基金(批准号:41575058)资助的课题.
      Corresponding author: Wang Ge-Li, wgl@mail.iap.ac.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 41575058).
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    Tsonis A A 1996 Nature 382 700

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    Wang S W, Zhu J H 2000 Quart. J. Appl. Meteor. 11 1 (in Chinese) [王绍武, 朱锦红 2000 应用气象学报 11 1]

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    Wang H J, Zhou G Q, Lin Z H 2002 Climatic Environ. Res. 7 220 (in Chinese) [王会军, 周广庆, 林朝晖 2002 气候与环境研究 7 220]

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    Wang G L, Yang P C, Zhou X J 2016 Theor. Appl. Climatol. 124 985

    [12]

    Chen X X, Wang G L, Jin L J 2015 China Environ. Sci. 35 694 (in Chinese) [陈潇潇, 王革丽, 金莲姬 2015 中国环境科学 35 694]

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    Krner O 2002 J. Geophs. Res. 107 ACL1-1

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    Davis A, Marshak A, Wiscombe W, Cahalan R 1996 J. Atmos. Sci. 53 1538

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    Yang P C, Bian J C, Wang G L, Zhou X J 2003 Chin. Sci. Bull. 48 1470 (in Chinese) [杨培才, 卞建春, 王革丽, 周秀骥 2003 科学通报 48 1470]

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出版历程
  • 收稿日期:  2016-10-08
  • 修回日期:  2017-01-16
  • 刊出日期:  2017-04-05

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