A robust method to simultaneously place sensors and calibrate parameters for urban drainage pipe system models using Bayesian decision theory

Urban drainage models (UDMs) require observation data from sensors for calibration before managing urban floods. However, there is often the case that sensors are not available when model calibration is required, and hence sensor placing and model calibration need to be simultaneously considered in many engineering practices. While many methods are available for either sensor deployment or model calibration with given observation data, there is a lack of approach to consider these two objectives simultaneously. To address this gap, this paper proposes a method that simultaneously enables sensor placement and model calibration using Bayesian decision theory. First, a graph partition strategy is used to ensure overall uniformity in sensor distribution. Subsequently, Bayesian Experimental Design is employed to identify optimal sensor locations by maximizing expected data worth, measured by the relative entropy between prior and posterior probabilities. The UDM is sequentially calibrated using an ensemble smoother algorithm with observation data collected from these strategically placed sensors. Effectiveness and robustness of the method are tested using two real-world UDMs of different scales under various rainfall and parameter scenarios. Comparisons with two empirical approaches, where sensors are evenly deployed or installed in flood hotspots, show that the proposed method provides more accurate water level and flood predictions with less uncertainties across various scenarios. The proposed method is anticipated to be promising in engineering applications as sensor placing and model calibration are often simultaneously needed especially for many new UDMs or existing UDMs without sensors.