Probabilistic robust parity relation for fault detection using polynomial chaos

Abstract

In this paper, a robust parity relation approach is proposed for fault detection of linear systems with the probabilistic time-invariant parameter uncertainties. To deal with polynomial dependence on uncertain parameters, a set of parity relations with polynomial parameterization is derived to decouple the unknown initial condition. Due to the polynomial structure having a finite degree, the generated residual vector admits an exact polynomial chaos expansion with the same degree, which enables an efficient online computation for quantifying the moments of the residual vector. The obtained moments are used to calculate a confidence set for checking the consistency between the observed system behavior and the parity relations. Compared to deterministic robust parity relation methods, the employment of probabilistic information allows a less conservative way to ensure a low false alarm rate while maintaining a high fault detection rate. In contrast to the existing polynomial chaos-based fault diagnosis literature, our proposed approach avoids truncation errors of polynomial chaos expansions, and is less computationally demanding. The proposed approach is illustrated by using a two-tank system example.