Worst-Case False Alarm Analysis of Fault Detection Systems

Model-based fault detection methods can be used to reduce the size, weight, and cost of safety-critical aerospace systems. However, the implementation of these methods is based on models. Therefore, disturbance and model uncertainty must be considered in order to certify the fault detection system. This paper considers the worst-case false alarm probability over a class of stochastic disturbances and model uncertainty. This is one analysis needed to assess the overall system reliability. The single step, worst-case false alarm probability is shown to be equivalent to a robust H2 analysis problem. Hence known results from the robust H2 literature can be used to upper bound this worst-case probability. Next, bounds are derived for the worst-case false alarm probability over multiple time steps. The multi-step analysis is important because reliability requirements for aerospace systems are typically specified over a time window, e.g. per hour. The bounds derived for the multi-step analysis account for the time correlations introduced by the system dynamics and fault detection filters. Finally, a numerical example is presented to demonstrate the proposed technique.