Time series imputation in wastewater treatment plant monitoring: a multi-plant evaluation under heterogeneous dataset structures and missingness patterns

Data-driven operation of wastewater treatment plants (WWTPs) requires reliable monitoring data, yet missing values result from sensor failures and operational interruptions. Despite numerous proposed imputation models, WWTP evaluations rely on a single facility, randomly distributed point missingness, aggregate performance without variable-level analysis, and limited statistical analysis. This study addresses these limitations through the first multi-plant evaluation of six imputation approaches (linear interpolation, KNN, MICE, CSDI, Transformer, and SAITS) across 14 WWTP datasets. Models were evaluated at 5–40% missingness under non-consecutive and 6-day block patterns using R 2 and nRMSE. Performance varied markedly across facilities and variables. Even the best-performing model yielded R 2 of 0.09–0.74, while linear interpolation remained competitive for weakly correlated effluent variables and multivariate models benefited from stronger influent correlations. Kendall's W indicated reproducible rate-dependent responses across plants, while ANOVA and OLS regression showed significant effects of both missingness pattern and rate. Performance was lower under consecutive than non-consecutive missingness at the same rate and declined with increasing rate, with model-specific sensitivity. Transformer and SAITS showed low sensitivity to missingness pattern and rate with a favorable balance between accuracy and computational efficiency. In short records, consecutive block missingness produced a counterintuitive inversion, with R 2 being lower at a 5% missingness rate than at 40%, whereas nRMSE increased consistently with the missingness rate. This discrepancy indicates that rate-based evaluation in short records with consecutive missingness depends on the selected metric. These findings distinguish dataset-driven from model-specific effects and guide the selection and evaluation of robust imputation strategies.