A noise adaptive approach for nodal water demand estimation in water distribution systems

Hydraulic models have emerged as a powerful tool for simulating the real behavior of water distribution systems (WDSs). In using the models for estimating nodal water demands, measurement uncertainty must be considered. A common approach is to use the covariance of measurement noises to quantify the measurement uncertainty. The noise covariance is typically assumed constant and estimated a priori. However, such an assumption is frequently misleading as actual measurement accuracies are affected by measuring instruments and environmental noises. In this study, we develop a variational Bayesian approach for real-time estimation of noise covariance and nodal water demands. The approach can adaptively adjust the noise covariance with the variation of the noise intensity, thereby efficiently avoiding model overfitting. The measurement residual decomposition reveals that this new approach is effective in determining model structural errors caused by topological structure parameterization.