Performance Tradeoffs for Networked Jump Observer-Based Fault Diagnosis

In this paper, we address the fault diagnosis problem for discrete-time multi-sensor systems over communication networks with measurement dropouts. We use the measurement outcomes to model the measurement reception scenarios. Based on this, we propose the use of a jump observer to diagnose multiple faults. We model the faults as slow time-varying signals and introduce this dynamic in the observer to estimate the faults and to generate a residual. The fault detection is assured by comparing the residual signal with a prescribed threshold. We design the jump observer, the residual and the threshold to attain disturbance attenuation, fault tracking and detection conditions and a given false alarm rate. The false alarm rate is upper bounded by means of Markov's inequality. We explore the tradeoffs between the minimum detectable faults, the false alarm rate and the response time to faults of the fault diagnoser. By imposing the disturbances and measurement noises to be Gaussian, we tighten the false alarm rate bound which improves the time needed to detect a fault. A numerical example is provided to illustrate the effectiveness of the theory developed in the paper.