Frequency-temporal-logic-based bearing fault diagnosis and fault interpretation using Bayesian optimization with Bayesian neural networks

Abstract Rolling element bearings are widely used components in modern rotary machines, and accurate diagnosis and interpretation for faults of bearings are significant for equipment maintenance. This paper introduces a fault diagnosis method with a formal specification language, which overcomes the difficulty of understanding the decision process of fault diagnosis. The formal specification is written with a novel formal language, called frequency-temporal-logic, defining the time-frequency properties of time series signals, which not only is a classifier to diagnose the faults but also gives interpretations for the fault signals with its semantics. To find an optimal description for the fault signals, the Bayesian optimization with Bayesian neural networks has been utilized to infer the structure and parameters of the formal specification. The semantics of frequency-temporal-logic then gives the fault interpretation. Moreover, the quantitative semantics for the formal language is defined based on a novel satisfaction metric, which has a noise resistance property. Analysis of the proposed method shows that the formal description can deal with noisy signals and variable speed operations of the bearings. Finally, comparison experimental results indicate the proposed method can obtain high fault diagnosis accuracy.