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IMA Journal of Management Mathematics Advance Access originally published online on February 21, 2007
IMA Journal of Management Mathematics 2008 19(1):39-50; doi:10.1093/imaman/dpm002
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© The authors 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Gearbox failure diagnosis based on vector autoregressive modelling of vibration data and dynamic principal component analysis

Bing Liu{dagger} and V. Makis{ddagger}

Mechanical and Industrial Engineering Department, University of Toronto, Toronto, Ontario, Canada M5S 3G8

{dagger} Email: mgt.liu{at}utoronto.ca

{ddagger} Email: makis{at}mie.utoronto.ca

Received on 4 August 2006. Accepted on 14 December 2006.

An effective gearbox failure diagnosis helps prevent catastrophic gearbox failure and can contribute to significant economic benefits. This paper proposes a gear failure diagnosis method based on vector autoregressive modelling of high-frequency vibration data, dimensionality reduction applying dynamic principal component analysis (PCA) and condition monitoring using a multivariate control chart. After extracting useful information from the vibration data obtained from distinct directions via dynamic PCA, a failure diagnosis scheme is implemented and tested using real gearbox vibration data. It is shown that the failure diagnosis scheme can indicate the gear teeth failure pattern when the gear is damaged, which has not been demonstrated in the previous studies. For a comparison, PCA is applied to the same data set. The results show that the advantages of dynamic PCA over PCA for failure diagnosis using vibration data consist not only in indicating more accurately the occurrence of incipient fault and the actual gear condition, but also in a much lower false alarm rate.

Keywords: dimensionality reduction; dynamic PCA; fault detection; Q control chart; vector autoregressive modelling; vibration data analysis


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