Distributionally robust fault detection design and assessment for dynamical systems

Abstract

We present a novel distributionally robust optimization approach for integrated design and assessment of fault detection system. Its salient feature is the guaranteed robustness against the inexactness of probability distribution of unknown disturbances. The integrated design problem is formulated as a distributionally robust chance constrained program (DRCCP). It maximizes fault detectability subject to the constraint on the worst-case false alarm rate among a continuum of probability distributions. The moment-based and Wasserstein ambiguity sets are used as two different ways of uncertainty description, which differ manifestly from generic settings where disturbances follow either Gaussian or norm-bounded assumptions. We show that the use of two different ambiguity sets in fault detection leads to specific statistical properties. To solve DRCCPs efficiently, we develop exact reformulations and tailored solution algorithms, and in some cases the optimal solution turns out to be classical fault detection design. In addition, a distributionally robust assessment strategy is developed, which evaluates the worst-case and best-case detectability under known faults by solving tractable convex programs. The efficacy of the proposed approach is illustrated on the fault detection of a laboratory three-tank system.