Two simple multivariate procedures for monitoring planetary gearboxes in non-stationary operating conditions

摘要

This paper deals with the diagnostics of planetary gearboxes under nonstationary operating conditions. In most diagnostics applications, energy of vibration signals (calculated directly from time series or extracted from spectral representation of signal) is used. Unfortunately energy based features are sensitive to load conditions and it makes diagnostics difficult. In this paper we used energy based 15D data vectors (namely spectral amplitudes of planetary mesh frequency and its harmonics) in order to investigate if it is possible to improve diagnostics efficiency in comparison to previous, one dimensional, approaches proposed for the same problem. Two multivariate methods, Principal Component Analysis (PCA) and Canonical Discriminant Analysis (CDA), were used as techniques for data analysis. We used these techniques in order to investigate dimensionality of the data and to visualize data in 3D and 2D spaces in order to understand data behavior and assess classification ability. As a case study the data from two planetary gearboxes used in complex mining machines (one in bad condition and the other in good condition) were analyzed. For these two machines more than 2000 15D vectors were acquired. It should be noted that due to non-stationarity of loading conditions, previous diagnostics results obtained using other techniques were moderately good (ca. 80% recognition efficiency); however there is still some need to improve diagnostics classification ability. After application of the proposed approaches it was found that the entire data could be reduced to 2 dimensions whereby data instances became visible and a good discriminant function (characterized by a misclassification rate of .0023, i.e. only 5 erroneous classifications for a total of 2183 instances) could be derived. This paper suggests a novel way for condition monitoring of planetary gearboxes based on multivariate statistics. The emphasis is put on the algebraic and geometric interpretations of the PCA. In the second approach, the CDA method has been proposed for the first time in such a context. It should be noted that existing PCA based approaches already proposed in literature also use PCA for data reduction, but they do not analyse their geometry after projection. Moreover, they considered simple laboratory data, with artificially introduced local damage; they were not applied to real case study with distributed form of wear as presented here. It should be added that just a few works may be found in the context of planetary gearbox, time varying load and multivariate statistics. So, we believe that the data processing procedure proposed here may be interesting both for scientists and engineers.