An Optimal Data-Driven Approach to Distribution Independent Fault Detection

In this article, an optimal data-driven approach is proposed to deal with the problem of distribution independent fault detection (FD) for stochastic linear discrete-time systems. For this purpose, an observer-based residual generator is first constructed using process input and output data. Without exact probability distributions for noises and faults, the so-called confidence sets are constituted in terms of mean and covariance matrix to characterize residual in fault-free and faulty cases. On this basis, a stochastic optimization FD problem is formulated, which allows an integrated design of residual evaluation function and threshold toward maximizing fault detection rate (FDR) for an acceptable false alarm rate (FAR) in the worst-case setting. Furthermore, a data-driven formulation of the underlying FD problem is studied, wherein the estimation uncertainties caused by the deviation of empirical mean and covariance matrix from their real values are concerned. The robustness of the FD system is investigated in the probabilistic context. Confidence levels of the obtained FAR and FDR are achieved quantitatively. The main advantages of the proposed FD approach lie in its independence of probability distributions for noises and faults, the robustness to the estimation uncertainties and the quantitative probabilistic evaluation to the confidence levels of FAR and FDR. A case study on a three-tank system illustrates the effectiveness of the demonstrated approach.