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Development of an Algorithm for Identifying Changes in System Dynamics from Time Series

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Document pages: 10 pages

Abstract: The development of an algorithm with related mathematical concepts andsupporting hypothesis for detecting changes in system dynamics from time seriesalong with empirical analysis and theoretical justification is presented. Forthe method, changes in the second largest eigenvalue of Markov Chain (SLEM) ormixing rate, is observed as an indicator of the changes in system dynamics. TheMarkov chain is created from empirical transition probabilities of a timeseries. The method is developed for the application of detecting hemorrhagefrom arterial blood pressure in anesthetized swine. The rationale of the changein the SLEM is investigated empirically with an artificial blood pressure modeland, by studying correlations with other measures such as smoothness of timeseries, and density of the transition probability matrix of the Markov chain.The mathematical analysis shows that the change in the SLEM is a consequence ofthe change in the transition probabilities between different states andreflects information about the system dynamics.

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