Distributionally robust trade‐off design of parity relation based fault detection systems

Abstract

The fault detection (FD) system design aims at optimizing the trade‐off between false alarm rate (FAR) and fault detection rate (FDR) under stochastic disturbances or uncertainties. A challenging difficulty in practice is the inexact information of stochastic disturbance distribution, that is, the actual distribution deviates from the one used in the design. To address this challenge, a distributionally robust optimization (DRO) approach that accounts for the inexact distribution information is proposed for the parity relation based FD of stochastic discrete‐time linear systems. It introduces moment‐based and entropy‐based ambiguity sets to describe the inexact disturbance distribution. Over such ambiguity sets, the FD system design for a scalar residual maximizes the worst‐case FDR with respect to a reference fault mode, while ensuring a predefined worst‐case FAR. To address the limitation of a scalar residual, the FD test of a vector residual is constructed with respect to a parameterized set of multiple fault modes. The resulting FD tests can be expressed in the same structure as the celebrated generalized likelihood ratio test (GLRT), while only the detection threshold is adjusted to compensate for distribution ambiguity. Moreover, the worst‐case FDR in the presence of any given fault is evaluated by solving another DRO problem. Using a continuous stirred tank reactor example with inexact distribution information, it is demonstrated that the proposed designs achieve desirable performance trade‐off and provide effective worst‐case FDR evaluations, while the GLRT fails to ensure the predefined FAR.

A note on diagnosis and performance degradation detection in automatic control systems towards functional safety and cyber security

“…Note that (57) is of the identical form with (54). Consequently, applying the same procedure with ( 55)- (56), matrix Φ can be identified, which then enables a reliable performance degradation detection.…”

“…Equation ( 61) is similar to (54) and can serve as a performance model. During online operations, the system performance can be assessed by an online identification of weights w i , i = 1, • • • , N, and computation of J (k) according to (60).…”

“…Although their extensions to systems with normally distributed process and measurement noises have been addressed in [16], efficient handling of model uncertainties remains to be an open issue. Recently, [53][54][55] have proposed to apply the so-called distributionally robust optimization (DRO) technique [56,57] to enhancing the robustness of fault detection systems against model uncertainties. In particular, it is advantageous that DRO technique enables handlings and solutions in a probabilistic setting.…”

Analysis of prevention measures in Shenzhen based on SIQR model during the novel coronavirus pneumonia

“…Two classes of robust FD methods are proposed in the literature based on the ways to model uncertainties: the stochastic and set-based methods. The stochastic methods consider that uncertainties are modeled by means of known stochastic distributions and then use the probability theory as the mathematical tool to implement FD [1], [2], [3], [4]. Differently, the set-based methods are deterministic approaches by considering that uncertainties are bounded by known sets, e.g., zonotopes, intervals, polytopes, ellipsoids, etc.…”