In this paper, we focus our study on analysis of fault diagnosis performance for satellite attitude control systems subject to $l_{2}$ -norm bounded process disturbances and measurement noises, which concerns with fault detectability and fault isolability. For an observer-based fault detection (FD), a major concern is to answer if the choice of a threshold satisfies an acceptable trade-off between fault detection rate (FDR) and false alarm rate (FAR). The smaller a threshold is, the better is the FDR, but the poorer is the FAR. In addition to this, knowledge of fault isolability is useful for answering how difficult it is to isolate a fault from another one. The main contributions of this work are the probabilistic performance evaluation of the FD system in the context of FAR and a contribution analysis based method of fault isolation. Firstly, an extended $H_{i}/H_{\infty}$ optimization based FD scheme is applied to the satellite attitude control systems and a recursive algorithm is presented to the implementation of online FD. Secondly, regarding the uncertain statistical characteristics of the unknown inputs, randomized algorithms are developed to verify the achievable FAR for a prescribed given threshold. Especially, without knowing the $l_{2}$ -norm boundedness of the unknown inputs, a probabilistic estimation of worst case threshold is also obtained to guarantee an acceptable level of FAR. Thirdly, a contribution analysis based method of fault isolation is proposed for satellite attitude control systems. Finally, the effectiveness of the proposed algorithms is verified through a satellite attitude control system.

In this paper, a novel robust fault detection (FD) approach called parity space vector machine (PSVM) is proposed for linear discrete-time systems. Aiming to achieve a tradeoff between false alarm rate (FAR) and FD rate (FDR) simultaneously, we focus our study on an integrated design of parity space-based FD in the context of residual generation and residual evaluation. Without a prior knowledge of the distribution of the unknown inputs, we propose to construct a PSVM model and formulate the underlying FD problem as a distribution-free Bayes optimal classifier, where the FAR and FDR indicate the worst-case classification accuracies of future residuals for the fault free case and faulty case. Then a bank of parity space vectors and corresponding thresholds can be designed integratedly by applying the techniques of the minimum error minimax probability machine and, at the same time, an optimal tradeoff between FAR and FDR is achieved. Finally, the effectiveness of the proposed approach is demonstrated on a longitudinal control system of unmanned aerial vehicle and further comparison with a traditional parity space-based FD is also addressed.

This article is concerned with the development of a new event-triggered parity space fault detection (FD) scheme. A linear discrete-time system model with varying sampling periods is presented for handling the problem of event-triggered FD and a new parity relation is established. Based on this, an event-triggered residual generator is constructed and the generated residual is completely decoupled from event-triggered transmission error. The design of the parity matrix is formulated into an optimization problem and an optimal solution of the parity matrix is obtained by using singular value decomposition. The issue of residual evaluation is also considered in the event-triggering implementation. The novelties of this article are twofold. First, a new event-triggered parity relation is obtained and the parity space-based residual signal achieves complete decoupling with the event-triggered transmission error. Second, the calculation of the parity matrix is independent of event parameters. So the design of the parity space-based residual generator and event generator can be carried out independently. Finally, a simulation example is considered to demonstrate the effectiveness of the proposed method.

In this paper, an optimal data-driven approach is proposed to deal with the problem of distribution independent fault detection (FD) for stochastic linear discrete-time systems. For this purpose, an observer-based residual generator is first constructed using process input and output data. Without exact probability distribution for noises and faults, the so-called confidence sets are constituted in terms of mean and covariance matrix to characterize residual in fault-free and faulty cases. On this basis, a stochastic optimization FD problem is formulated, which allows an integrated design of residual evaluation function and threshold towards maximizing fault detection rate (FDR) for an acceptable false alarm rate (FAR) in the worst-case setting. Furthermore, a data-driven formulation of the underlying FD problem is studied by constructing the confidence sets in terms of empirical estimates of mean and covariance matrix. Concerning the estimation uncertainties caused by the deviation of empirical mean and covariance matrix from their real values, the robustness of the proposed FD approach is investigated in the probabilistic context. Confidence levels of the obtained FAR and FDR are achieved quantitatively. Besides, algorithms are developed for the realization of the proposed FD system. A case study on a three-tank system illustrates the effectiveness of the demonstrated approach.

This article addresses the quantitative fault diagnosability evaluation for dynamic systems without distribution knowledge. The system dynamics in different cases are first characterized by mean vectors and covariance matrices. Then, fault detectability and isolability are defined based on the constructed characteristics. On this basis, the Mahalanobis distance (MD) is employed to propose a fault diagnosability analysis measure. Furthermore, model-based and data-driven algorithms for fault diagnosability evaluation are given according to the MD-based measure. In addition, the reliabilities of the evaluation results are considered by taking advantage of ambiguity sets of mean vectors and covariance matrices of the system dynamics. Finally, two examples are employed to verify the effectiveness of the proposed algorithms.

In this article, an integrated design diagram for a stable kernel representation (SKR)-based data-driven fault detection (FD) system and performance criteria is proposed for stochastic dynamic systems in the probabilistic sense. A new distributionally robust FD system is developed using input and output data in the absence of a system model and perfect probability distributions for noises and random faults. To be specific, an SKR-based data-driven primary residual generator is first constructed. By introducing the so-called mean-covariance based ambiguity sets, families of probability distributions of the primary residual in fault-free and the concerned multiple faulty cases are characterized. The FD system design is then formulated as a distributionally robust optimization problem in the sense of minimizing the missed detection rate (MDR) with a predefined upper bound of false alarm rate (FAR). With the aid of worst-case conditional value-at-risk, a matrix-valued distribution independent solution to the targeting FD problem is derived without posing specific distribution assumptions. The developed FD system is, thus, robust against the distributional uncertainties of noises and random faults. Simultaneously, a tighter upper bound of MDR for an identical FAR criterion is achieved in comparison with the vector-valued distributionally robust FD method. An experimental study on a laboratory setup of a three-tank system shows the applicability of the proposed method.