Clustering and imputation of daily water consumption data using visibility algorithms

Background The adoption of smart water meters enables high-resolution time-series data for informed and data-driven water management. However, the increasing volume and complexity of user-level consumption data can hinder efficient network monitoring and data management. This study proposes a visibility-based framework for characterising water consumption behaviour and supporting the optimisation of smart-meter networks.Methods The proposed approach transforms raw consumption time series into the visibility domain using the Natural Visibility Graph (NVG). Each consumption profile is represented as a geometric structure from which visibility relationships, referred to as “visibility tokens”, are extracted. These tokens characterise user behaviour and provide the basis for clustering users according to their consumption patterns. The methodology was applied to a real-world case study in Apulia, Italy, involving 3,051 users and 93% network coverage.Results The framework identified 200 representative Master Tokens, each acting as a cluster representative of a prototypical consumption behaviour. Thus, approximately 93.4% of the users can be represented through a reduced set of Master profiles, substantially decreasing the complexity of network-level data management while preserving the main characteristics of demand patterns. Internal cluster variance analysis and Pearson correlation coefficients confirmed a high degree of similarity within the identified clusters. High-coherence clusters corresponded to predictable consumption behaviours, whereas low-coherence clusters highlighted more irregular patterns potentially requiring increased monitoring frequency.Conclusions The results demonstrate the potential of visibility-based clustering for optimising smart water-meter networks. Monitoring the 200 Master profiles could enable representative demand knowledge to be maintained while reducing the need for continuous high-frequency data transmission from the remaining users. This strategy could reduce communication requirements and potentially extend the battery life of field devices, while providing a basis for adaptive monitoring strategies based on the behavioural coherence of user clusters.