Modified Varying Index Coefficient Autoregression Model for Representation of the Nonstationary Vibration From a Planetary Gearbox

Abstract

Planetary gearbox fault detection is important in terms of life-threatening failure prevention and maintenance optimization. This paper focuses on the representation of the planetary gearbox baseline vibration signals via time series models. Faults can be detected by examining any changes in model residuals or parameters. Varying index coefficient autoregression (VICAR) model is a good option for accurately modeling complex nonlinear data-generating-processes. Applying VICAR to represent nonstationary baseline vibrations from a planetary gearbox under variable rotating speed conditions, the covariate vector can be expanded to include the rotating speed. However, we found that lagged predictors dominate the smooth functions in the expanded VICAR. The inclusion of rotating speed becomes in vain. To cope with this problem, we propose a modified VICAR model that effectively makes use of the rotating speed while retaining the highly flexible nonlinearity modeling capacity of the VICAR model. The modification lies in separating the lagged predictor and rotating speed via independent smooth functions. Parameter estimation and variable selection methods were developed accordingly. An experimental study was conducted which reveals the superiority of the modified VICAR model in comparison with autoencoders, expanded VICAR, and linear parameter varying autoregression models.