Sensor fault detection and isolation via networked estimation: rank-deficient dynamical systems

This paper considers model-based fault detection of large-scale (possibly rank-deficient) dynamic systems. Assuming only global (and not local) observability over a sensor network, we introduce a single time-scale networked estimator/observer. Sensors take local outputs/measurements of system states with partial observability and share their information (including estimation and/or output) over a communication network, and gain distributed observability. We define the conditions on the network structure ensuring distributed observability and stabilising the error dynamics. However, system outputs are prone to faults and uncertainties, which affect the state estimation of all sensors as a consequence of communicating (possibly) faulty data. From the cyber-physical-systems (CPS) perspective, such faults add bias to the data transferred from the physical layer (dynamic system) to the cyber layer (sensor network). In this work, we propose a localised fault detection and isolation (FDI) mechanism at sensors to secure distributed estimation. This protocol enables every sensor to locally identify the possible fault at the sensor measurement, and, via local detection and isolation, to prevent the spread of biased/faulty information over the network. This distributed isolation and localisation of fault follows from our partial observability assumption instead of full observability at every sensor. Then, other sensors can estimate/track the system by using observationally-equivalent output information to recover for possible loss of observability. In particular, we study rank-deficient systems as they are known to demand more information-sharing, and thus, are more vulnerable to the spread of possible faults over the network. One challenge is the detection of faults in the presence of system/output noise without making (simplifying and unrealistic) upper-bound assumptions on the noise support. We resolve this by adopting probabilistic threshold designs on the residuals. Further, we show that additive faults at rank-deficiency-related outputs affect the residuals at all sensors, a consequence that mandates more constraints on the (distributed) FDI strategy. We address this problem by constrained LMI design of the feedback gain matrix. Finally, we design q-redundant distributed estimators, resilient to isolation/removal of up to q number of faulty sensors, and further, we consider thresholding residual history over a sliding time-window, known as the stateful FDI.