Fault feature extraction of rolling element bearings based on wavelet packet transform and sparse representation theory

Extracting reliable features from vibration signals is a key problem in machinery fault recognition. This study proposes a novel sparse wavelet reconstruction residual (SWRR) feature for rolling element bearing diagnosis based on wavelet packet transform (WPT) and sparse representation theory. WPT has obtained huge success in machine fault diagnosis, which demonstrates its potential for extracting discriminative features. Sparse representation is an increasingly popular algorithm in signal processing and can find concise, high-level representations of signals that well matches the structure of analyzed data by using a learned dictionary. If sparse coding is conducted with a discriminative dictionary for different type signals, the pattern laying in each class will drive the generation of a unique residual. Inspired by this, sparse representation is introduced to help the feature extraction from WPT-based results in a novel manner: (1) learn a dictionary for each fault-related WPT subband; (2) solve the coefficients of each subband for different classes using the learned dictionaries and (3) calculate the reconstruction residual to form the SWRR feature. The effectiveness and advantages of the SWRR feature are confirmed by the practical fault pattern recognition of two bearing cases.