Interpretable online updated weights: Optimized square envelope spectrum for machine condition monitoring and fault diagnosis

Abstract

Bearings are key components of rotating machines, and their condition monitoring and fault diagnosis have received much attention from academia and industry in recent years. Existing fault diagnosis methods can be generally classified into signal processing-based fault characteristic frequency (FCF) identification methods and machine learning-based model classification methods. Though the former owns clear physical meaning, its integration with monitoring data for automatically optimizing square envelope spectrum for identification of FCF is not fully explored. As for the latter, lacking explicit interpretability of learned model weights limits its wide applications. In this paper, to address these critical issues, the integration of online monitoring data with cyclostationarity of fault transients is sufficiently studied and utilized to construct a fault cyclostationarity-based convex optimization model. The maximum logarithmic likelihood estimation is then used to solve the convex optimization model. Moreover, an online weight updating algorithm is developed to relieve the requirement of historical data and to make the weight updating of the proposed optimization model adaptive to online monitoring data. Subsequently, interpretable online updated weights as an optimized square envelope spectrum (OSES) are proposed to enhance the identification of FCF and its harmonics in the OSES. And a three-dimensional (3D) OSES and a detector with an alarming threshold are designed to eliminate the need for label information and further to simultaneously achieve incipient fault time detection, fault type diagnosis, and online fault evolution monitoring. A practical-project bearing dataset and two experimental bearing run-to-failure datasets are used to validate the effectiveness and superiority of interpretable online updated weights as the OSES and 3D OSES. Results demonstrate that the integration of fault characteristics with machine learning theory (e.g., convex optimization) is a new promising physics-informed perspective to monitor and diagnose machine faults.