Optimal Bayesian estimation and control scheme for gear shaft fault detection

Fault detection and diagnosis of gear transmission systems have attracted a lot of attention in recent years, but there are very few papers dealing with the early detection of shaft cracks. In this paper, a new methodology for predicting failures of a gear shaft system is presented. The time synchronous averaging (TSA) method is applied to the gear shaft vibration data, and the wavelet transform technique is then used to obtain quantitative indicators of gear shaft deterioration. System deterioration is modeled as a hidden, 3‐state continuous‐time homogeneous Markov process. States 0 and 1, which are not observable, represent healthy and unhealthy system conditions, respectively. Only the failure state 2 is assumed to be observable. The computed quantities, which are stochastically related to the system state, are chosen as the observation process in the hidden Markov modeling framework. The objective is to develop a method for optimally predicting impending system failures, which maximizes the long‐run expected average system availability per unit time. Model parameters are estimated using the EM algorithm and an optimal Bayesian fault prediction scheme is proposed. The entire procedure is illustrated using real gear shaft vibration data.