Sequential detection of transient changes in stochastic - dynamical systems
Journal de la Société Française de Statistique
Société Française de Statistique
This paper deals with the problem of detecting transient changes in stochastic-dynamical systems. A statistical observation model which depends on unknown system states (often regarded as the nuisance parameter) is developed. The negative impact of nuisance parameter is then eliminated from the observation model by utilizing the invariant statistics. The Variable Threshold Window Limited CUmulative SUM (VTWL CUSUM) test, previously developed for independent observations, is adapted to the novel observation model. Taking into account the transient change detection criterion, minimizing the worst-case probability of missed detection subject to an acceptable level of the worst-case probability of false alarm within a given time period, the thresholds of the VTWL CUSUM test are optimized. It is shown that the optimized VTWL CUSUM algorithm is equivalent to the Finite Moving Average (FMA) detection rule. A numerical method for estimating the probability of false alarm and missed detection is proposed. The theoretical results are applied to the problem of cyber/physical attack (stealing water from a reservoir) detection on a simple Supervisory Control and Data Acquisition (SCADA) water distribution system.