Leveraging multi-level correlations for imputing monitoring data in water supply systems using graph signal sampling theory

Data missing and anomalies in monitoring equipment have become critical barriers to developing intelligent Water Supply Systems (WSS). The valid data preceding and after the missing segments can be utilized to impute missing values. However, traditional imputation methods, such as linear interpolation and prediction-based methods, have limited capacity to use data relationships or can only utilize information before the missing values. Therefore, existing methods still need to work on efficiently and conveniently achieving high-accuracy imputation. According to the continuity and periodicity of WSS data, missing values often exhibit multi-level correlations with valid data. This paper innovatively employs graph structures to analyze the multi-level correlations at different timestamps and applies graph signal sampling algorithms to extract low-frequency features for imputation. A novel Graph-based Data Imputation (GDI) method has been developed, which leverages multi-level correlations to propagate information and completes imputation tasks without requiring complex feature engineering and pre-training processes. Results indicate that GDI outperforms Holt-Winters, Support Vector Regression, and Gated Recurrent Unit in the task of imputing continuous missing data. It can still achieve $R^2>0.8$ even when the proportion of missing values reaches 80 %. These results demonstrate that GDI ensures a more streamlined and efficient imputation with high robustness and accuracy.