Optimizing wastewater treatment sampling strategies through Markov Chain Monte Carlo Bayesian inference in Activated Sludge Model No. 3
Activated sludge models provide mechanistic frameworks for understanding biological wastewater treatment processes, but their practical implementation remains constrained by challenges in parameter estimation and uncertainty quantification under realistic monitoring conditions. This thesis develops a comprehensive Bayesian inference framework for Activated Sludge Model No. 3 that integrates sensitivity screening, identifiability diagnostics, and Markov chain Monte Carlo estimation to deliver robust parameter estimates and predictive uncertainty bounds across diverse monitoring designs. The methodology combines normalised sensitivity analysis to identify negligible parameters, profile likelihood analysis to distinguish estimable from non-estimable parameters, and principal component analysis to represent correlation structures among weakly identifiable parameters through latent variables. The No-U-Turn sampler implements full Bayesian inference, integrating literature-informed priors with synthetic observational data to characterise posterior distributions for 36 kinetic and stoichiometric parameters. Five monitoring regimes spanning intensive 14-day campaigns with four daily measurements to sparse year-long programmes with weekly sampling were systematically evaluated, controlling measurement noise and system configuration. Three inference configurations were compared across all monitoring regimes: structured workflow employing sensitivity screening, identifiability classification, and dimensionality reduction; progressively simplified configurations removing screening steps; and direct estimation of all parameters from literature-informed priors without preprocessing. Diagnostic statistics including convergence measures, effective sample sizes, and divergence rates quantified sampling performance, while posterior predictive checks assessed forecast accuracy for effluent compounds including chemical oxygen demand, nitrogen species, alkalinity, and suspended solids. The results revealed unexpected findings with substantial practical implications. Structured preprocessing degraded rather than improved inference quality when informative priors were available, with direct estimation across all parameters achieving superior convergence and predictive accuracy despite operating in larger parameter spaces. The mechanism appears to be that fixing parameters introduces rigidity forcing compensatory adjustments producing sharp posterior curvature, while dimensionality reduction through principal component analysis imposes linear correlation structures mismatched to true posterior geometry. Literature-informed priors achieve protective regularisation without sacrificing flexibility for joint parameter adjustment. However, this advantage depends critically on reliable prior information. Replacing literature-centred priors with uninformed uniform distributions produced catastrophic failures including 58 percent divergence rates and operationally useless predictions despite year-long high-frequency data, demonstrating that observed compounds cannot uniquely identify all parameters through data likelihood alone. Monitoring design effectiveness depends on alignment between sampling structure and compound timescales. Short intensive campaigns excel for rapidly responding compounds with dynamics unfolding over hours to days, achieving mean absolute errors below one milligram per litre for organic carbon and ammonium despite limited temporal windows. However, these designs fail catastrophically for slow transformations like Total Kjeldahl Nitrogen where cycling occurs over weeks to months, exhibiting systematic biases exceeding six milligrams per litre. Conversely, sparse year-long monitoring captures seasonal dynamics essential for nitrogen processes while sacrificing short-term resolution. The research establishes that successful mechanistic model calibration necessarily integrates observational evidence with external process knowledge, provides quantitative tools for evaluating monitoring design trade-offs before implementation, and challenges conventional wisdom regarding preprocessing workflows developed primarily for optimisation-based rather than probabilistic inference contexts.
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