Probability Analysis of Fault Diagnosis Performance for Satellite Attitude Control Systems

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 paper are the probabilistic performance evaluation of the FD system in the context of FAR and a contribution analysis-based method of fault isolation. First, 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. Second, 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. Third, 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.