Multivariate statistical methods for detection of spur gear faults

Abstract

In this study, multivariate statistical techniques are experimented for a spur gear system and a methodology is proposed. The approach is based on the analysis of multidimensional gear vibration data without any feature extradiction and data transformation. The scheme is performed using the vibration signals acquired from a lab-scale single stage gearbox in three dimensions of x, y and z directions. As a groundwork, multi-normality assumptions are established using homogeneity, autocorrelation, and univariate normality tests. The bi-dimensional frequency histograms are also plotted to show bi-normality for experimental gear data. Then, mean vectors and covariance matrices of conditions of good, worn, 1-tooth broken from wheel gear and 1-tooth broken from each pinion and wheel gear are estimated. To compare gear conditions statistically, multivariate analysis of variance is proposed and applied. Moreover, the single metric of Mahalanobis distances are calculated to classify unknown test samples, utilizing the maximum likelihood estimates. The numerical results indicate that multivariate statistical analysis techniques can be applied in early detection of spur gear faults, in which univariate tests fail.

A DPCA-based online fault indicator for gear faults using three-direction vibration signals

“…The most commonly used feature extraction methods include empirical mode decomposition (EMD) [2][3][4], singular value decomposition (SVD) [5,6], wavelet transforms [7][8][9], variational mode decomposition (VMD) [10][11][12] and so on. After fault features extracted, BP neural network [13], support vector machine (SVM) [12], -nearest neighbor algorithm ( -NN) [14] and so on are used to identify the types of faults. Although many methods have adaptive properties, such as EMD, VMD, -NN, their greatest weakness is that their computational burden is too heavy to be suitable for online application.…”

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