Explainable Uncertainty Quantification for Wastewater Treatment Energy Prediction via Interval Type-2 Neuro-Fuzzy System

Wastewater treatment plants consume 1-3% of global electricity, making accurate energy forecasting critical for operational optimization and sustainability. While machine learning models provide point predictions, they lack explainable uncertainty quantification essential for risk-aware decision-making in safety-critical infrastructure. This study develops an Interval Type-2 Adaptive Neuro-Fuzzy Inference System (IT2-ANFIS) that generates interpretable prediction intervals through fuzzy rule structures. Unlike black-box probabilistic methods, the proposed framework decomposes uncertainty across three levels: feature-level, footprint of uncertainty identify which variables introduce ambiguity, rule-level analysis reveals confidence in local models, and instance-level intervals quantify overall prediction uncertainty. Validated on Melbourne Water's Eastern Treatment Plant dataset, IT2-ANFIS achieves comparable predictive performance to first order ANFIS with substantially reduced variance across training runs, while providing explainable uncertainty estimates that link prediction confidence directly to operational conditions and input variables.

Explainable Fuzzy GNNs for Leak Detection in Water Distribution Networks

Timely leak detection in water distribution networks is critical for conserving resources and maintaining operational efficiency. Although Graph Neural Networks (GNNs) excel at capturing spatial-temporal dependencies in sensor data, their black-box nature and the limited work on graph-based explainable models for water networks hinder practical adoption. We propose an explainable GNN framework that integrates mutual information to identify critical network regions and fuzzy logic to provide clear, rule-based explanations for node classification tasks. After benchmarking several GNN architectures, we selected the generalized graph convolution network (GENConv) for its superior performance and developed a fuzzy-enhanced variant that offers intuitive explanations for classified leak locations. Our fuzzy graph neural network (FGENConv) achieved Graph F1 scores of 0.889 for detection and 0.814 for localization, slightly below the crisp GENConv 0.938 and 0.858, respectively. Yet it compensates by providing spatially localized, fuzzy rule-based explanations. By striking the right balance between precision and explainability, the proposed fuzzy network could enable hydraulic engineers to validate predicted leak locations, conserve human resources, and optimize maintenance strategies. The code is available at github.com/pasqualedem/GNNLeakDetection.