Quantitative analysis of incipient fault detectability for time-varying stochastic systems based on weighted moving average approach

•Fault detectability is defined for stochastic systems by considering FAR and MDR.•Detectability of incipient faults is quantitatively analyzed by using statistical theory.•A novel incipient fault detection method is designed for stochastic systems. In this paper, the problem of incipient fault detection is investigated for linear time-varying (LTV) systems with stochastic noises. The fault detectability in a probabilistic sense is defined for LTV stochastic systems by considering false alarm rate (FAR) and missed detection rate (MDR) simultaneously. Necessary and sufficient conditions are derived to reveal the relationship among the fault amplitude, FAR and MDR, and the reason why incipient faults are difficult to detect is quantitatively analyzed in the model-based framework. To improve the sensibility of the residual to incipient faults, the weighted moving average approach is introduced and its parameters, the optimal weight and the smallest window length, are accurately analyzed in theory. Moreover, the concept of average fault detectability is introduced, which is conducive to providing a feasible scheme for incipient fault detection. Finally, a numerical example and an experiment are given to show the effectiveness of the derived results.