Wavelet energy-based visualization and classification of high-dimensional signal for bearing fault detection

This study investigates a methodology for interpretable visualizing and classifying high-dimensional data such as vibration signals in machine fault detection application. Although principal component analysis is one of the most widely used dimension reduction methods, it does not clearly explain the source of signal variations (i.e., statistical characteristics such as mean and variance), but just locate signals on low-dimensional space which maximizing data dispersion. This deficiency restricts its interpretability to specific problems of process control and thus limits their broader usefulness. To overcome this deficiency, this study exploits the multiscale energy analysis of discrete wavelet transformation, so-called wavelet scalogram, in unsupervised manner. Wavelet scalogram allows us to first obtain a very low-dimensional feature subset of our data, which is strongly correlated with the characteristics of the data without considering the classification method used, although each of these features is uncorrelated with each other. In supervised learning scheme, it can be eventually combined with silhouette statistics for the purpose of more effective visualization of the main sources of different classes and classifying signals into different classes. Finally, nonparametric multi-class classifiers such as classification and regression tree and k-nearest neighbors quantitatively evaluate the performance of our approach for machine fault classification problem in terms of the 10-fold misclassification error rate.