Study on Chaotic Time Series Data Analysis Method and Its Application

研究了复杂系统的混沌/分形方法，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说明了由F.Ohi于1999年提出的混沌时间序列数据分析方法，对于提前检测某些机器的异常运动是有效的。将该方法应用于某挤出机的压力数据，结果表明，该方法对挤出机的异物检测是可行的。我们还对该方法本身进行了理论分析，证明了当时间序列数据是绝对随机的时，该方法利用遍历定理给出了-1/2的值。结果表明，该方法可用于判断数据是否具有随机性。这些结果发表在下面的论文中：Fumio Ohi，Tatsuya Suzuki和Kazuomi Sugimoto，on a混沌方法分类时间序列Da…更多信息，日本工业和应用数学学会会刊，第12卷，第1期，第67-78页，2002众所周知，元胞自动机通常被用作复杂系统的模型。在这项工作中，我们进一步利用规则数为90的时空模式的性质解释了规则数为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垫片和部分Sierpinski垫片，日本工业与应用数学杂志，第18卷，第1期，第59-73页。对于复杂系统的混沌/分形表征，我们试图用Hausdorff维来解释信息论中的信道容量和歧义集的模糊性。所取得的成果已在日本工业和应用数学学会年会上公布，并正在提交给《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，我们建立了一个模型，并利用大偏差理论对等待时间分布的尾部进行了估计，其结果在国际研讨会上公开发表。较少

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