Performance Index for Optimizing Sensor Fault Detection of a Class of Nonlinear Systems
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This paper develops a performance index that can be used to find the optimal design parameters of the observer-based residual generator and adaptive threshold of a fault detection scheme for a class of nonlinear systems. The performance of the fault detection scheme is analyzed with respect to the fault detectability of incipient sensor faults, which depends on the dynamic behavior of the residual and the adaptive threshold generator. The proposed performance index is based on the distance between two limit sets that are guaranteed to include the residual under fault-free and faulty conditions. The novelty of this distance metric stems from the parametrization of the limit sets in relation to (i) the design parameters of both the residual generator and adaptive threshold, (ii) the bounds on the system disturbances and measurement noise, and (iii) the fault function and evolution rate. An optimization problem is formulated for finding the design parameters of the fault detection scheme such that the set of guaranteed strongly detectable faults is maximized, where this set is defined based on the distance between the separated fault-free and faulty limit set.