Real-Time Biomass Estimation in High-Density Yeast Fermentations Using Soft Sensor Modeling

Accurate biomass monitoring remains a bottleneck in industrial fermentation, where conventional offline methods, gravimetric dry cell weight (DCW) and spectrophotometric optical density at 600 nm (OD₆₀₀), are incompatible with real-time process control. Online optical probes operating at 860 nm (OD₈₆₀) provide continuous, non-invasive monitoring, but their signals become increasingly nonlinear due to multiple light scattering, limiting direct interpretation without mathematical transformation. This study develops and validates interpretable soft sensor regression models that convert nonlinear OD₈₆₀ signals into DCW and OD₆₀₀ across three industrially relevant yeast species, Pichia pastoris, Kluyveromyces marxianus, and Yarrowia lipolytica. Fed-batch datasets from 19 independent batches were used to evaluate 14 candidate models, including nonlinear and spline-based functions. Model performance was assessed by the nested leave-one-batch-out cross-validation (LOBO-CV) to prevent information leakage from batch-correlated data. Model selection followed a parsimony criterion, retaining the simplest model within 5% of the minimum cross-validated RMSE. For DCW prediction, selected models achieved cross-validated coefficients of determination (R²) of 0.85-0.91 across species; OD₆₀₀ predictions were less accurate (R² _CV = 0.49-0.90), reflecting dilution-driven noise amplification inherent to high-density spectrophotometric measurements. A dual-model strategy is presented, pairing software-optimized implementations with simplified piecewise-linear equations suitable for calculator-based deployment in industrial environments.