Distributionally Robust Fault Detection Trade-off Design with Prior Fault Information

TL;DR

This paper introduces a novel distributionally robust fault detection framework that leverages prior fault information to improve detectability of critical faults while maintaining overall robustness against unknown distributions.

Contribution

It proposes a new robustness metric and chance constraint, along with a heuristic algorithm for fault detection under uncertain distributions, incorporating prior fault knowledge.

Findings

Effective detection of known critical faults demonstrated in case studies.

Balanced robustness between critical and all faults achieved.

Algorithm shows promising results in simulated and real-world systems.

Abstract

The robustness of fault detection algorithms against uncertainty is crucial in the real-world industrial environment. Recently, a new probabilistic design scheme called distributionally robust fault detection (DRFD) has emerged and received immense interest. Despite its robustness against unknown distributions in practice, current DRFD focuses on the overall detectability of all possible faults rather than the detectability of critical faults that are a priori known. Henceforth, a new DRFD trade-off design scheme is put forward in this work by utilizing prior fault information. The key contribution includes a novel distributional robustness metric of detecting a known fault and a new relaxed distributionally robust chance constraint that ensures robust detectability. Then, a new DRFD design problem of fault detection under unknown probability distributions is proposed, and this offers a flexible balance between the robustness of detecting known critical faults and the overall detectability against all possible faults. To address the resulting semi-infinite chance-constrained problem, we first reformulate it to a finite-dimensional problem characterized by bilinear matrix inequalities. Subsequently, a tailored heuristic solution algorithm is developed, which includes a sequential minimization procedure and an initialization strategy. Finally, case studies on a simulated three-tank system and a real-world battery cell are carried out to showcase the effectiveness of the proposed heuristic algorithm and the advantages of our DRFD method.