Kinematic Frequencies of Rotating Equipment Identified with Sparse Coding and Dictionary Learning

Abstract

The detection of faults and operational abnormalities in rotating machine elements like rolling element bearings and gears requires information about kinematic properties, such as ball-pass and gear mesh frequencies. Typically, condition-monitoring experts obtain such information from the manufacturers for diagnostics purposes. However, the reliability of such information can be compromised during installation and maintenance, for example, if components are replaced and do not match the documented specifications. Thus, methods enabling verification and online extraction of such kinematic properties are needed to improve diagnostic reliability. Unsupervised machine learning methods, like sparse coding with dictionary learning, enable automatic modeling and characterization of repeating signal structures in the time domain, which are naturally generated by rotating equipment. Sparse coding with dictionary learning represents a vibration signal as a linear superposition of noise and atomic waveforms. The activation rate of the atomic waveforms typically possesses a cyclic nature in rotating environments, similar to how bearing kinematic frequencies correlate with faults in a rolling element bearing. However, there is no explicit relationship between the activation rates of the atoms and the bearing kinematic frequencies. This motivates this investigation of the possibility to extract bearing kinematic frequencies from sparse representations. Former work describes the use of dictionary learning for the detection of anomalies in rolling element bearings. In this paper, we describe how a similar unsupervised machine learning method can be used to extract kinematic frequencies of bearings and gears, for example for anomaly detection purposes and comparisons with an expected signature. We study the activation rates and changes of atoms learned from vibration signals in two case studies. The first case is based on data from a well-known controlled experiment with faults seeded in the bearings. The second case is based on a public dataset recorded from the high-speed shaft of a wind turbine with a bearing failure. Furthermore, we compare the activation rates and weights of the atoms to the bearing kinematic frequencies and harmonics. Sparse coding with dictionary learning offers a possibility for self-learning of the kinematic frequencies of a bearing, which can be useful for the further improvement of automated anomaly detection methods in condition monitoring.