Experimental application of a method for hidden parameter tracking in a slowly changing, chaotic system

Joseph Paul Cusumano, D. Chelidze, A. Chatterjee

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Abstract

Results are presented of an experimental application of a method for tracking hidden parameters in slowly changing chaotic systems. The method exploits the time scale separation between fast dynamic variables and a slow drifting parameter. Locally linear tracking models are constructed using data from the reference system sampled on a fast time scale, employing delay coordinate embedding. These reference models are used to track parameter drift. The method is successfully applied to a forced oscillator with a two-well potential. The effect of the choice of prediction time interval is studied. It is also observed that a simple correction for estimated modeling error gives a more sensitive tracking metric. For purposes of comparison with such model-based tracking methods, a heuristic method is also presented for detecting parameter changes using the autocorrelation function of the recorded time series. The relative merits of heuristic versus model-based techniques are discussed. Directions for future work are suggested.

Original languageEnglish (US)
Pages (from-to)45-54
Number of pages10
JournalAmerican Society of Mechanical Engineers, Tribology Division, TRIB
Volume7
StatePublished - Dec 1 1997

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Chaotic systems
Heuristic methods
Autocorrelation
Time series

All Science Journal Classification (ASJC) codes

  • Engineering(all)

Cite this

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AB - Results are presented of an experimental application of a method for tracking hidden parameters in slowly changing chaotic systems. The method exploits the time scale separation between fast dynamic variables and a slow drifting parameter. Locally linear tracking models are constructed using data from the reference system sampled on a fast time scale, employing delay coordinate embedding. These reference models are used to track parameter drift. The method is successfully applied to a forced oscillator with a two-well potential. The effect of the choice of prediction time interval is studied. It is also observed that a simple correction for estimated modeling error gives a more sensitive tracking metric. For purposes of comparison with such model-based tracking methods, a heuristic method is also presented for detecting parameter changes using the autocorrelation function of the recorded time series. The relative merits of heuristic versus model-based techniques are discussed. Directions for future work are suggested.

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