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Time series analysis for abnormality test and modeling of corrplex system and a study for the derived model from a view point of the theory of stochastic processes

随机过程理论视角下复杂系统异常测试与建模的时间序列分析及推导模型研究

基本信息

批准号：
14340030
负责人：
OKABE Yasunori
金额：
$ 5.82万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2004
项目状态：
已结题

项目摘要

We have obtained a formula for calculating a nonlinear filter between two discrete time stochastic processes, by using the theory of KM_2O-Langevin equations. Then we have applied it to a concrete non-linear system consisting of signal process and observation process, and given a solution for the non-linear filtering problem by obtaing an algorithm for calculating the non-linear fiter, which had been unsolved since Kalman-Bucy's work.By definning the abnormality of time series as the degree of breakdown of stationarity of time series, we have proposed Test(ABN) for catching certain signs of the abnormality of time series, by using Test(S) for testing the stationarity of time series and the generating system of polynomial type for the nonlinear information spaces associated with the discrete time stochastic processes.By applying Test(ABN) and Test(D) for testing the determinacy of time series to the time series of earthquakes, aurora and brain waves, we have discovered a new qualitative property, to be called separation property, on the region possessing stationarity after the arrival of S-wave for the deep low frequency earthquakes, the occurrence of aurora, and on the total region possessing stationarity of ECoG. This separation property do not appear for the usual earthquakes and EEG.By treating the continuous time stationary process X whose gloval time evolution is governed by [α, β, γ]-Langevin equation, we have derived both the continuous time KM_2O-Langevin equation describing the local time evolution the stochastic process X and the system of equations characterizing the coefficients appearing in the above equation.

利用KM_2O-朗之万方程理论，我们得到了两个离散时间随机过程之间的非线性滤波器的计算公式。然后将其应用于一个由信号处理和观测过程组成的具体非线性系统，给出了自Kalman-Bucy工作以来一直没有解决的非线性滤波问题的求解算法。通过将时间序列的异常定义为时间序列的平稳性的破坏程度，我们提出了捕捉时间序列异常的某些迹象的检验(ABN)。通过用检验(S)检验时间序列的平稳性和与离散时间随机过程相关的非线性信息空间的多项式型生成系统，将检验(ABN)和检验(D)应用于地震、极光和脑波时间序列的时间序列确定性检验，发现了深部低频地震、极光发生的S波到达后具有平稳性的区域和具有ECoG平稳性的全部区域的一个新的定性性质，称为分离性。这种分离性对于通常的地震和EEG是不出现的。通过处理球面时间演化受[α，β，γ]-朗之万方程支配的连续时间平稳过程X，我们导出了描述局部时间演化的连续时间KM_2O-朗之万方程和描述上述方程中出现的系数的方程组。