Towards a reliability-aware virtual sensor framework for smart water infrastructure: An offline residual-based change-point analysis

Water utilities increasingly depend on Industrial Internet of Things (IIoT) sensors to support infrastructure planning, predictive asset maintenance, operational asset monitoring, and digital-twin applications. However, physical IIoT sensors remain vulnerable to sensor drift, calibration degradation, device failure, and communication outages, creating data observability gaps that can reduce confidence in analytics-driven operational decisions. Virtual sensors can reconstruct and predict measurements using historical and correlated sensor data streams; however, their reliability remains difficult to assess in non-stationary water and wastewater networks, where demand patterns, environmental conditions, and operational interventions change network behaviour over time. This paper proposes a reliability-aware virtual sensing framework that integrates model-based data measurement estimation and residual-based change-point analysis for the design-time and runtime reliability evaluation of virtual sensors. The empirical evaluation examines the offline change-point analysis component of the framework using water-flow and wastewater-level telemetry data. Six change-point methods are applied independently to examine whether residual changes persist or recur, thereby supporting the validation of Time-to-Hallucination (TTH). TTH is defined as a model-specific timing indicator measured from the start of a forecast or outage assessment to the first residual outside the limits calibrated from earlier residual behaviour. The key finding was that overall accuracy did not show when a virtual sensor’s performance began to deteriorate. Offline residual analysis revealed changes hidden by the full-period accuracy results. TTH identified the first time a model’s residual moved outside its calibrated limits, providing an early warning that the virtual sensor may be becoming unreliable. Residual change-point analysis provided further evidence of how the residuals changed over time for both water and wastewater datasets. Comparisons of performance before and after the first residual departure provided stronger evidence of performance changes in the wastewater than in the water dataset. Together, these methods provide useful tools for offline reliability assessment and a foundation for future validation in real-time applications.