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 3g VS m−3d−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 R2 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 KI,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.
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BibTeX
@misc{hellmann2026global,
title = {{Global Parameter Identification and Uncertainty Quantification of reduced-order ADM1 using Maximum Likelihood Estimation and Bayesian Inference}},
author = {Simon Hellmann and Leander Lerch and Terrance Wilms and Moritz Reumschüssel and Alberto Meola and Félix Delory and Steffi Knorn and Stefan Streif and Sören Weinrich},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19098},
eprint = {2610.19098},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19098},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Global Parameter Identification and Uncertainty Quantification of reduced-order ADM1 using Maximum Likelihood Estimation and Bayesian Inference
AU - Simon Hellmann
AU - Leander Lerch
AU - Terrance Wilms
AU - Moritz Reumschüssel
AU - Alberto Meola
AU - Félix Delory
AU - Steffi Knorn
AU - Stefan Streif
AU - Sören Weinrich
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.19098
UR - https://arxiv.org/abs/2610.19098
AB - 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 3g VS m^−3d^−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_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.
ER -