A critical study of different dimensionality reduction methods for gear crack degradation assessment under different operating conditions

Gear cracks are some of the most common faults found in industrial machinery. Identification of different gear crack levels is beneficial to assessing gear crack degradation and preventing any unexpected machine breakdowns. In this paper, redundant statistical features are extracted from binary wavelet packet transform at different decomposition levels to describe different gear crack levels. Because the dimensionality of the extracted redundant statistical parameters is high to 620, it is necessary to reduce their dimensionality prior to the use of any statistical model for intelligently identifying different gear crack levels. The major idea of dimensionality reduction is that the extracted redundant statistical features in a high-dimensional space are mapped to a few significant features in a low-dimensional space, where these significant features are used to represent different gear crack levels. As of today, there are many popular linear and non-linear dimensionality reduction methods including principal component analysis, kernel principal components analysis, Isomap, Laplacian Eigenmaps and local linear embedding. Different dimensionality reduction methods have different performances in dimensionality reduction, which can be measured by prediction accuracies of some common statistical models, such as Naive Bayes classifier, linear discriminant analysis, quadratic discriminant analysis, and classification and regression tree. Gear crack level degradation data collected from a machine in a laboratory under different operating conditions including four different motor speeds and three different loads are used to investigate performances of the linear and non-linear dimensionality reduction methods. In our case study, the results show that principal component analysis has the best performance in dimensionality reduction and it results in the highest prediction accuracies in all of the aforementioned statistical models. In other words, the linear dimensionality reduction method is better than all of the non-linear dimensionality reduction methods investigated in this paper.