Robust detection of gearbox deterioration using compromised autoregressive modeling and Kolmogorov–Smirnov test statistic—Part I: Compromised autoregressive modeling with the aid of hypothesis tests and simulation analysis

A novel technique for detection of gearbox deterioration is proposed in Part I of this study. The proposed technique makes use of a time-varying autoregressive (AR) model and establishes a compromised AR model based on healthy gear motion residual (GMR) signals under varying load conditions and employs the Kolmogorov–Smirnov (K–S) goodness-of-fit (GOF) test statistic as a measure of gear condition. The order of the time-varying AR model is selected using a novel model order selection technique with the aid of hypothesis tests. The principal criterion for the selection of AR model order requires that the normality of the AR model residuals of the non-stationary healthy GMR signals under varying load conditions can be guaranteed. In the case where such orders are available, the one that results in the statistically least variance of the gear condition indicator, i.e. the K–S test statistic, is selected with the aid of the Bartlett's test. In the case where, under all considered orders, the normality condition cannot be met for all non-stationary healthy GMR signals, the order that results in the least violation against the normality condition can be identified with the aid of the Satterthwaite's t′-test. The coefficients of the time-varying AR model are estimated by means of a noise-adaptive Kalman filter. Validation of the proposed technique is carried out by using two sets of simulated entire lifetime gear vibration signals, i.e. clean and contaminated signals, to simulate the cases of sufficient and insufficient removal of background noise, respectively. The simulated tests demonstrate that the proposed technique possesses appealing effectiveness in identifying the optimum AR model order for robust gear condition detection under varying load conditions. The optimum performance of this technique is further confirmed by examining alternative orders.