Adjoint-based numerical method using standard engineering software for the optimal placement of chlorine sensors in drinking water networks

To obtain representative water quality simulations, unknown model parameters have to be updated by combining information from the water quality model and the sensor outputs. An adjoint-based numerical method has been developed to determine the optimal placement of chlorine sensors in drinking water networks at a low computational cost. From a practical engineering perspective, the proposed optimal placement corresponds to the set of sensors that minimizes the area in which the unknown model parameters cannot be identified. The numerical strategy is implemented in the hydraulic software EPANET. Using the adjoint framework, we develop and apply an adaptive strategy in a French drinking water network that provides the optimal placement from 1 sensor to 6 sensors. We show that the highest reduction of the non-identifiable area is obtained at the first stages of the adaptive strategy. After 4 sensors, a plateau is reached.