Integrated approach for optimal sensor placement and state estimation: A case study on water distribution networks

The objective of the design and operation of any water distribution network (WDN) includes meeting the desired demand at sufficient pressure at all nodes. However, this requires situational awareness; in other words, the knowledge of system state variables such as pressure and flow throughout the network. In this work, a hybrid approach is developed for sensor placement (SP) and state estimation (SE) that exploits the underlying correlation structure in the data, along with the principles governing the flow through circular pipes. The problem of SP in WDN is addressed since measuring the state variables throughout the network is not practical. The problem of SE that maps to a matrix completion problem under certain physical and logical constraints is solved later. The completed matrix represents the state of WDN at any given time. Benchmark networks used in literature were used to evaluate the proposed approach. The mean absolute percentage error (MAPE) of less than 5% was obtained while estimating the head available at nodes. The knowledge of the states in the entire network could help operate the network adaptively.