Study on Chaotic Time Series Data Analysis Method and Its Application

混沌时间序列数据分析方法及其应用研究

• 批准号: 12680440
• 负责人: OHI Fumio
• 金额: $ 1.02万
• 依托单位: Nagoya Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12680440/
• 关键词: chaos; time series analysis; fractal dimension; information theory; queuing theory

This research concerns about chaos / fractal method for characterization of complex systems, especially about chaotic analyzing method for time series data.In this study we have showed from the theoretical and applicable point of views that the cos analysis method, which was proposed by F. Ohi in 1999 as a chaotic method for analyzing time series data, is effective for detecting abnormal motion of some machines in advance. Applying the method to the pressure data of an extruder, we have showed that we can practically use the method for detecting the strangeness of the machine. We also have theoretically analyzed the method itself and showed that the method gives us the value -1/2, by using Ergodic Theorem, when time series data is absolutely random. This result shows that the method can be applied to decide whether the data is random or not. These results are published in the following paper; Fumio Ohi, Tatsuya Suzuki and Kazuomi Sugimoto, On A Chaotic Method Classifying Time Series Da … More ta, Transaction of the Japan Society for Industrial and Applied Mathematics, Vol. 12, No. 1, pp. 67- 78, 2002It is well known that cellular automata are typically used as models of complex systems. In this work we, furthermore, explained the periodic property of cellular automata with rule number 180 by using the properties of time-space pattern of the rule number 90. This result was published in the following paper: Fumio Ohi and Yoshikazu Takamatsu (2001), Time-Space Pattern and Periodic Property of Elementary Cellular Automata - Sierpinski Gasket and Partially Sierpinski Gasket, Japan Journal of Industrial and Applied Mathematics, Vol. 18, No. 1, pp. 59 - 73.For the chaos / fractal characterization of complex systems, we have tried to explain the channel capacity and ambiguity of ambiguity sets in the information theory by using Hausdorff dimension. Obtained results were opened in the Annual Conference of the Japan Society for Industrial and Applied Mathematics and are also under submission to Japan Journal of Industrial and Applied Mathematics. For queuing system, one of the most complicated systems, we have built up a model and evaluate the tail of the waiting time distribution by using Large Deviation Theory, of which results are opened at an international symposium. Less

本文研究了复杂系统的混沌/分形表征方法，特别是时间序列数据的混沌分析方法，从理论和应用的角度证明了F. Ohi等提出的混沌时间序列分析方法，对于提前检测某些机械的异常运动是有效的。将该方法应用于挤出机的压力数据，结果表明，该方法可用于机器奇异性的检测。本文还对该方法进行了理论分析，证明了当时间序列数据是绝对随机的时，利用遍历定理，该方法给出的值为-1/2。这一结果表明，该方法可以用来判断数据是否是随机的。这些结果发表在以下论文中; Fumio Ohi，Tatsuya Suzuki和Kazuomi Sugimoto，On A Chaotic Method Classifying Time Series Da ...更多信息 ta，《日本工业与应用数学学会学报》，第12卷，第1期，pp. 67-78，2002众所周知，元胞自动机通常用作复杂系统的模型。本文还利用规则数90的时空模式的性质解释了规则数180的元胞自动机的周期性。这一结果发表在以下论文中：Fumio Ohi和Yoshikazu Takamatsu（2001），基本元胞自动机的时空模式和周期性质- Sierpinski Gasket和部分Sierpinski Gasket，日本工业和应用数学杂志，第18卷，第1期，第11页。59 - 73.对于复杂系统的混沌/分形特征，我们试图用Hausdorff维数来解释信息论中模糊集的信道容量和模糊度。所获得的结果在日本工业和应用数学学会年会上公开，并提交给日本工业和应用数学杂志。对于排队系统这一最复杂的系统之一，我们建立了一个模型，并利用大偏差理论计算了等待时间分布的尾部，其结果已在一次国际研讨会上公开。少

项目成果

Fumio Ohi and Yoshikazu Takamatsu: "Time-Space Pattern and Periodic Property of Elementary Cellular Automata-Sierpinski Gasket and Partially Sierpinski Gasket-"Japan Journal of Industrial and Applied Mathematics. Vol.18 No.1. 59-73 (2001)

Fumio Ohi和Yoshikazu Takamatsu：“基本元胞自动机的时空模式和周期性质-谢尔宾斯基垫片和部分谢尔宾斯基垫片-”日本工业和应用数学杂志。

鈴木 達也: "定常無記憶通信路に対する通信路容量の次元論的説明"日本応用数理学会2001年度年会講演予稿集. 62-63 (2001)

Tatsuya Suzuki：“固定无记忆通道的通道容量的维度解释”日本应用数学学会 2001 年年会记录 62-63 (2001)。

Fumio, Ohi: "Time-Space Pattern and Periodic Property of Elementary Cellular Automata - Sierpinaki Gasket and Partially Sierpinski Gasket"Japan Journal of Industrial and Applied Mathematics. Vol.18,No.1. 59-73 (2001)

Fumio, Ohi：“基本元胞自动机的时空模式和周期特性 - Sierpinaki 垫片和部分 Sierpinski 垫片”日本工业与应用数学杂志。

Fumio, Ohi: "Chaotic Analysis Method for Time Series Data"Fall National Conference of ORSJ. 238-239 (2001)

Fumio, Ohi：“时间序列数据的混沌分析方法”ORSJ 秋季全国会议。

Wei, Feng: "Large deviation analysis of a polling system with Markov-modulated arrival processes and Bernoulli service schedule"Proceeding of 10th International. Symposium on Applied Stochastic Model and Data Analysis. Vol.1. 424-429 (2001)

魏峰：“马尔可夫调制到达过程和伯努利服务时间表的轮询系统的大偏差分析”第十届国际会议论文集。