An integrated approach for sensor placement in linear dynamic systems

This paper investigates the sensor placement in linear dynamic systems for fault detectability and isolability. A linear system is modelled by a bond graph (BG) that can be associated in a natural way with a set of linear differential-algebraic equations (DAEs). Simultaneously, possible sensor locations are modelled as junctions on the BG. Causal paths capture cause-effect relationships of a linear system and provide a means to analyze what subset of junctions contributes to fault detectability and isolability. Furthermore, this paper exploits DAEs associated with a BG and proves a necessary and sufficient condition of sensor placement to fulfill fault detectability. Based on the fault detectability condition, a necessary condition of sensor placement to achieve two-fault distinguishability is developed in the DAEs model and serves as the basis of formulating the sensor placement problem with regard to a fault set F. For efficiency, a dedicated dynamic programming (DP) algorithm is devised to attain the optimal set of junctions for fault isolability. The two-tank system is employed to illustrate the sensor placement steps in a linear system. The optimal set(s), computed by the proposed sensor placement methodology, is/are validated by deriving primary analytical redundancy relations (ARRs) of the two-tank system.