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An Application Of Functional Data Analysis To Local Damage Detection

Author

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  • Leśkow Jacek

    (Cracow University of Technology, Cracow, Poland .)

  • Skupień Maria

    (Pedagogical University of Cracow, Cracow, Poland .)

Abstract

Vibration signals sampled with a high frequency constitute a basic source of information about machine behaviour. Few minutes of signal observations easily translate into several millions of data points to be processed with the purpose of the damage detection. Big dimensionality of data sets creates serious difficulties with detection of frequencies specific for a particular local damage. In view of that, traditional spectral analysis tools like spectrograms should be improved to efficiently identify the frequency bands where the impulsivity is most marked (the so-called informative frequency bands or IFB). We propose the functional approach known in modern time series analysis to overcome these difficulties. We will process data sets as collections of random functions to apply techniques of the functional data analysis. As a result, we will be able to represent massive data sets through few real-valued functions and corresponding parameters, which are the eigenfunctions and eigen-values of the covariance operator describing the signal. We will also propose a new technique based on the bootstrap resampling to choose the optimal dimension in representing big data sets that we process. Using real data generated by a gearbox and a wheel bearings we will show how these techniques work in practice.

Suggested Citation

  • Leśkow Jacek & Skupień Maria, 2019. "An Application Of Functional Data Analysis To Local Damage Detection," Statistics in Transition New Series, Polish Statistical Association, vol. 20(1), pages 131-151, March.
    • Handle: RePEc:vrs:stintr:v:20:y:2019:i:1:p:131-151:n:8
    DOI: 10.21307/stattrans-2019-008
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    References listed on IDEAS

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    1. Mas, André, 2002. "Weak convergence for the covariance operators of a Hilbertian linear process," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 117-135, May.
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