Model-reduced fault detection for multi-rate sensor fusion with unknown inputs

In multi-sensor fusion, it is hard to guarantee that all sensors work at the single sampling rate, especially in the distributive and/or heterogeneous case, and fault detection (FD) in multi-rate sensor fusion may face the existence of unknown inputs (UIs) in complex environment. Meanwhile, model reduction often refers to propose a possible lower-dimensional model to replace the original model without adding significant error in practical applications. By the fact that FD in dynamic systems should only focus on the fault-related controllability and observability characteristics, it is a good idea to obtain the fault-related controllable and observable subsystem via system decomposition (i.e., model reduction) for FD. Such a kind of model reduction not only guarantee the FD performance, but also reduce the system dimensions. To this end, we propose the model-reduced fault detection (MRFD) problem for multi-rate sensor fusion subject to UIs and faults imposed on the actuator and sensors. Our aim is to design a fast and computation-effective FD scheme based on the reduced model. We use the singular decomposition for UI decoupling, and then obtain the fault-related subsystem via controllability and observability decomposition. And then the multi-rate observer (MRO) with causality constraints is designed. Different from the traditional observer used for FD, the proposed MRO outputs the fault-related partial state estimate as soon as any a sensor measurement is received, resulting in fast and computation-effective FD. Furthermore, conditions for the existence of a stable MRO, fault-to-state controllability, and fault detectability are explored. A simulation example for simplified longitudinal flight control system and method comparison with the existing multi-rate FD algorithms show the effectiveness of the proposed MRFD method.