Uncertainty Estimation in Predicting Oxygenation by Plunging Jet Aerators Using Probabilistic Machine Learning and Conformal Prediction

Surinder Deswal¹, Mahesh Pal²

^1,2Department of Civil Engineering, National Institute of Technology Kurukshetra, Kurukshetra, India.

Abstract

Estimation of oxygen transfer capacity of plunging jet aerators in wastewater treatment, whether by analytical or machine learning (ML) approaches, is susceptible to inherent uncertainties due to variability in input parameters. Accurately estimating and integrating these uncertainties is crucial for enhancing oxygenation predictions, enabling designers to select the optimal configuration of plunging jet aerators for maximum efficiency. This study introduces an innovative approach that utilises the integration of probabilistic ML and conformal prediction (CP) based uncertainty estimation to model plunging jets for wastewater treatment. Three CP-based approaches — splitCP, CV+, and conformal quantile regression (CQR) — are integrated with seven ML algorithms, namely Gradient Boosting (GB), Extreme Gradient Boosting (XGBoost), Light Gradient Boosting Machines (LightGBM), Gaussian Process Boosting (GPBoost), Categorical Boosting (CatBoost), Natural Gradient Boosting (NGBoost) and Probabilistic Gradient Boosting (PGBM). This integration aimed to create a statistically and probabilistically robust model for predicting ‘volumetric oxygen transfer coefficient at standard conditions’ [K_L a₍₂₀₎] of the plunging jet oxygenation system.
The study utilised a dataset comprising of 88 laboratory experiments. The performance of the CP-based ML models was evaluated using – mean predicted interval width and effective coverage criteria for conformal prediction; whereas, sharpness, CRPS and NLL for probabilistic prediction. The results suggest the potential of GB, NGBoost and GPBoost ML algorithms with the CV+ based CP approach due to a superior balance between a smaller mean interval width and higher effective coverage. However, considering the outcome of probabilistic prediction criteria in conjunction with the CP estimates, the GB algorithm with CV+ based CP approach offers the best overall model for uncertainty estimation, as confidence intervals or risk quantification play a crucial role in designing and optimising plunging jet aeration systems.

Keywords: Plunging jet aerators, machine learning (ML), uncertainty, conformal prediction (CP), probabilistic prediction, Gradient Boosting (GB), XGBoost, LightGBM, GPBoost, CatBoost, NGBoost, PGBM, AutoSampler

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