Sparse LPV-ARMA model for non-stationary vibration representation and its application on gearbox tooth crack detection under variable speed conditions

Time series models are effective in extracting periodic and trend properties from time series like gearbox vibration signals. However, gearboxes often operate under variable speed conditions which makes the vibration signal non-stationary. This paper proposes a sparse linear parametervarying autoregressive moving average (Spa LPV-ARMA) model for non-stationary vibration representation. Gearbox fault detection under variable speed conditions can be achieved by examining model residuals. The proposed model combines the advantages of sparse time series modeling with ARMA modeling, and therefore can capture unforeseen random fluctuations and unexpected events in the data. Simulation and experimental studies are conducted to validate the performance of the proposed Spa LPV-ARMA model. Comprehensive comparisons with classical indicators, order spectra, envelope order spectra, ARIMA model, and Spa LPV-AR model are made. The results have shown that the Spa LPV-ARMA model performs best in both modeling and fault detection accuracy.