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

Qusai Khaled, Bahjat Mallak, Uzay Kaymak, Laura Genga

TL;DR

The paper addresses the challenge of predicting wastewater treatment energy consumption while delivering explainable uncertainty estimates. It introduces an Interval Type-2 Adaptive Neuro-Fuzzy Inference System (IT2-ANFIS) that outputs interval predictions and decomposes uncertainty across feature-, rule-, and instance-level components, with type reduction controlled by a learnable factor $q$. On Melbourne Water's Eastern Treatment Plant data, IT2-ANFIS matches first-order ANFIS performance but with substantially reduced run-to-run variance and provides interpretable uncertainty linked to input conditions and operational regimes. The approach supports risk-aware decision-making by enabling sensor prioritization and targeted data collection based on the learned uncertainty footprints, contributing to safer and more efficient WWTP operation.

Abstract

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

TL;DR

The paper addresses the challenge of predicting wastewater treatment energy consumption while delivering explainable uncertainty estimates. It introduces an Interval Type-2 Adaptive Neuro-Fuzzy Inference System (IT2-ANFIS) that outputs interval predictions and decomposes uncertainty across feature-, rule-, and instance-level components, with type reduction controlled by a learnable factor . On Melbourne Water's Eastern Treatment Plant data, IT2-ANFIS matches first-order ANFIS performance but with substantially reduced run-to-run variance and provides interpretable uncertainty linked to input conditions and operational regimes. The approach supports risk-aware decision-making by enabling sensor prioritization and targeted data collection based on the learned uncertainty footprints, contributing to safer and more efficient WWTP operation.

Abstract

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.
Paper Structure (14 sections, 11 equations, 4 figures, 2 tables)

This paper contains 14 sections, 11 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Model Architecture and Training Methodology
  4. Random grid initialization
  5. Membership Functions and Firing Strengths
  6. Type Reduction and Output Computation
  7. Optimization Strategy
  8. Experimental settings
  9. Results and Discussion
  10. Model selection and rule-complexity analysis
  11. Explainability and Uncertainty Quantification
  12. Implications of Explainable UQ
  13. Conclusion
  14. Disclosure of Interests.

Figures (4)

  • Figure 1: IT2-ANFIS Training Framework with Uncertainty Quantification
  • Figure 2: Simplified schematic of the wastewater treatment process at Melbourne Water's Eastern Treatment Plant.
  • Figure 3: Test performance of ANFIS and IT2-ANFIS across 5–50 rules. (a) Full range; (b) zoomed view of the 0–10 rule region. Each configuration is trained 10 times; solid lines show mean MSE, shaded regions show min–max. IT2-ANFIS attains reduced variance, with optimal performance at 7–10 rules.
  • Figure 4: Interval Type-2 Gaussian membership functions learned by the model, with uncertainties depicted at three levels, feature, rule and instance level. (a) highlights three learned rules for average wind speed. (b) presents the complete rule base for all features F1-13.