Provably correct design of observations for fault detection with privacy preservation

During the operation of complex cyber-physical systems, detection of faults needs to be performed using limited state information for practicality and privacy concerns. While a well-designed observation can distinguish a faulty behavior from the normal behavior, it can also represent the action of hiding some of the state information or discrete mode transitions. In this paper, we present a framework for constructing the observation maps in the form of metric temporal logic (MTL) formulae that can be formally proven to detect fault in a switched system while preserving certain privacy conditions. We simulate finitely many nominal trajectories and use the robustness tubes around the simulated trajectories to cover the infinite trajectories that constitute the system behavior. Thus the inferred MTL formulae from the simulated trajectories can be used for classifying the system behaviors in a provably correct fashion. We implement our approach on the simulation model of a smart building testbed to detect the open window fault while preserving the privacy of the room occupancy.