Bayesian Failure Localization Identifies Inconsistencies between Water Distribution Network Models and Real-World Conditions

Accurately calibrated models of water distribution networks (WDNs) are crucial in predicting system behavior. However, besides imperfect calibration, more fundamental inconsistencies between WDN models and real WDNs may come from unforeseen factors between model and reality, such as topology errors from missing or excess pipe connections in the network plan, valves in unexpected settings, misspecified pipe diameters by design, incrustation or pipe aging, and leakages. Testing WDN models for inconsistencies and localizing their error sources for model improvement is crucial. Bayesian model evidence (BME) is a statistically motivated quantity that can be used to test models even in the face of uncertain parameters and uncertain data. Yet, BME cannot identify and localize inconsistencies within the network. Therefore, the current paper introduces a novel criterion called local model evidence (LME), which identifies and localizes model-to-data mismatches at specific nodes within a WDN model using Bayesian analysis principles. Based on Bayesian principles, it determines whether any given model-to-data mismatch at a WDN node is plausibly explainable by combining parameter uncertainty and measurement errors or points toward an inconsistency. We first tested the introduced LME criterion for identifying pipe failures on a widely used EPANET benchmark WDN model and then applied it to a real-life WDN. Both the test and application cases successfully demonstrated LME’s capability to identify pipe failures. In the fully controlled benchmark case, LME detected partially closed valves, while in the real-life WDN, it identified aging pipes and dimension errors. Overall, we found the LME-based Bayesian framework essential for pinpointing inconsistencies between the WDN model and real-world conditions during the precalibration stage of modeling.