Global Parameter Identification and Uncertainty Quantification of reduced-order ADM1 using Maximum Likelihood Estimation and Bayesian Inference

Abstract

Anaerobic digestion (AD) models can be challenging to calibrate against real data due to limited practical identifiability, data scarcity, and model complexity. Weighted least squares objective functions and gradient-based solvers using finite differences are often used in literature, but result in suboptimal parameter estimates and large uncertainty bands. This paper identifies the parameters of a reduced-order ADM1 by comparing the frameworks of maximum likelihood estimation (MLE) and Bayesian inference (BI), and quantifies uncertainties of parameters and outputs. Multirate experimental data are taken from a lab-scale AD reactor fed with agricultural substrates and operated at organic loading rates of 3$\,$g VS $\mathrm{m^{-3}d^{-1}}$. Global optima are found via global and gradient-based local search algorithms using forward sensitivities. Enhanced scatter search provides the best global search results. These are refined by the Gauss-Newton algorithm as the best local search, which delivers $R^2$ values of 0.95 for acetic acid and 0.77 for biogas production. BI yields substantially narrower uncertainty bands than MLE and avoids the need for a global search by incorporating prior knowledge about parameter distributions. The search space is captured efficiently by log10 scaling of parameters. Algorithmic details on its implications are provided. Despite a high-resolution lab-scale dataset, the ADM1-specific inhibition parameter $K_\mathrm{I,nh3}$ is practically not identifiable with MLE, and shows a low output sensitivity, whereas a parameter for the effective ion concentration shows superb practical identifiabilty at high confidence with both MLE and BI. The present work lays a scalable base for calibration of nonlinear AD models by providing reliable simulations. It thus advances model-based monitoring and control applications of multirate processes such as agricultural AD plants.