Grey-box modeling framework for consolidated bioprocessing systems: an endpoint-guided approach

Abstract

Consolidated bioprocessing (CBP) combines enzyme production, biomass hydrolysis, and fermentation within a single process, but its modeling remains difficult because of biological nonlinearities, feedstock heterogeneity, and limited time-resolved measurements. This paper presents an endpoint-guided grey-box framework that connects data-driven endpoint prediction, phase-structured mechanistic reconstruction, and synthetic state-estimation analysis. A literature-derived CBP ethanol dataset containing 540 runs and 90 encoded input features was preprocessed using out-of-fold residual screening, after which several nonlinear regressors were compared using both log-transformed and raw endpoint targets. Repeated cross-validation selected a raw-target XGBoost model, XGB_raw, as the final endpoint surrogate, with RMSE \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$=1.566 \pm 0.465$$\end{document}. The independent hold-out subset favored histogram-based gradient boosting models, indicating that the leading boosting-based models were closely matched. For XGB_raw, hold-out performance improved after residual screening from RMSE \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$=7.491$$\end{document}, MAE \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$=2.798$$\end{document}, and \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$R^2=0.821$$\end{document} to RMSE \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$=2.025$$\end{document}, MAE \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$=1.253$$\end{document}, and \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$R^2=0.940$$\end{document}. Feature-attribution analysis identified hemicellulose content, substrate concentration, temperature, residence time, enzyme-assisted pretreatment, pH, cellulose content, and mixing rate as important endpoint predictors. The selected endpoint surrogate was then coupled to a three-phase hybrid simulator representing enzyme production, hydrolysis, and fermentation. Endpoint-guided calibration identified biologically plausible parameterizations that reproduced the target endpoint through moderate changes in growth, enzyme production, hydrolytic capacity, and product formation. Because independent time-resolved CBP trajectories were unavailable, the simulated profiles are interpreted as endpoint-constrained reconstructions rather than validated kinetic trajectories. A synthetic unscented Kalman filter study showed accurate reconstruction of sugar and scaled-product states, with lower-fidelity recovery of enzyme dynamics. Overall, the framework provides a feasibility-oriented basis for CBP endpoint prediction, mechanistic interpretation, and preliminary soft-sensing design under sparse-data conditions.

Keywords

Consolidated bioprocessing / Grey-box modeling / Endpoint-guided hybrid modeling / Soft sensing / Unscented Kalman filter

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Funding

Universität Duisburg-Essen (3149)

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