Fault detection for uncertain LPV systems using probabilistic set-membership parity relation. (March 2020) - Wan, Yiming; Puig, Vicenç; Ocampo-Martinez, Carlos; Wang, Ye; Harinath, Eranda; Braatz, Richard D.
Highlights: Probabilistic set-membership parity relation approach is proposed for fault detection of uncertain linear parameter varying systems. Probabilistic information on the parametric uncertainties is exploited to reduce miss detection rate by admitting an acceptable false alarm rate. The parity relation is polynomially parameterized with respect to uncertain parameters. Gaussian mixtures are adopted to efficiently compute non-Gaussian residual distribution. Simulation comparisons with a deterministic zonotope-based method demonstrate the efficacy of the proposed approach. Abstract: This paper considers fault detection of uncertain linear parameter varying systems that have polynomial dependence on parametric uncertainties. A conventional set-membership (SM) approach is able to ensure zero false alarm rate (FAR) by using conservative threshold sets, but usually results in a high missed detection rate (MDR) due to equally treating all uncertainty realizations without distinguishing between high and low probability of occurrence. To address this limitation, a probabilistic SM parity relation approach is proposed to exploit probabilistic information on the parametric uncertainties, which results in a reduced MDR by admitting an acceptable FAR. The parity relation is first polynomially parameterized with respect to uncertain parameters. Then, Gaussian mixtures are adopted to efficiently compute uncertainty propagation from stochastic uncertainties to the residual distribution. To achieve an acceptable FAR, a non-convex confidence set of residuals – represented by a union of ellipsoids – is determined for the consistency test. The effectiveness of the proposed approach is illustrated using a continuous stirred tank reactor example including performance comparisons with a deterministic zonotope-based method.