Real-Time Missing Data Estimation in Water Networks

Estimating missing data (e.g., pressure) in geographically distributed nodes is one of the fundamental challenges in a water distribution network (WDN). The Model-Based Kalman Filter is a simple solution that can estimate missing data in systems with a linear Gaussian state model. However, in large WDN, the state model is non-linear, and accurate system dynamics are unknown. Thus, we investigate the use of Data-Driven Kalman Filter (DDKF), in which the Recurrent Neural Network (RNN) updates the Kalman Gain. This data-driven approach has the potential to reduce approximation errors caused by the state model’s nonlinearity. As a result, this work demonstrates the application of a DDKF in a WDN. In addition, we demonstrate numerically that the DDKF can overcome approximation errors caused by flow equations and can estimate missing data in a WDN.