Fault detection and isolation for hybrid systems using structured parity residuals

Many physical systems are hybrid which means that both continuous and discrete states influence their dynamic behavior. The time evolution of the continuous states is constrained by vector fields that change due to internal or external discrete events. This paper is concerned with FDI (fault detection and isolation) for this kind of system. Two types of faults may be considered for hybrid dynamical systems depending on the component of the model that is affected by faults that may affect the current mode behavior or may affect the trajectory of the discrete evolution. The general principle of model-based FDI algorithms is to check the consistency of the known signals (inputs and outputs) w.r.t. a model. Parity residuals are special signals that reflect that consistency. As a direct consequence, these residuals may be used to detect faults in a given mode. Moreover, under the hypothesis that all modes are discernable, on-line mode identification is also possible which leads to diagnose the faults affecting the discrete sequence. In this paper, necessary and sufficient conditions are derived to guarantee the discernability between two modes and the complete FDI methodology, using parity residuals, is described.