Study on Chaotic Time Series Data Analysis Method and Its Application

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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