A Model-Based Fault Detection and Prognostics Scheme for Takagi–Sugeno Fuzzy Systems

In this paper, a novel model-based fault detection (FD) and prediction scheme is developed for a class of Takagi-Sugeno (T-S) fuzzy systems. Unlike other FD schemes, in the proposed design, an FD observer with online fault learning capability is utilized to generate a residual which is obtained by comparing the system output with respect to the observer output. A fault is declared active if the generated residual exceeds an a priori chosen threshold. Subsequently, the fault magnitude is estimated online by using a suitable parameter update law. Upon detection, the online estimate of the fault magnitude is used in a mathematical equation to determine time-to-failure (TTF) or remaining useful life. TTF is determined by projecting the estimated fault magnitude at the current time instant against a failure threshold. Note that the previously reported FD schemes could neither estimate the magnitude of a growing fault in real time nor were they able to predict the remaining useful life of the fuzzy system. In this paper, the stability of the proposed FD and prognostics scheme is verified using the Lyapunov theory. Finally, two different simulation case studies are considered to verify the theoretical conjectures presented in this paper.