Cross-attention fusion of Raman and NIR spectra for glucose soft sensing in fed-batch fermentation

Timely and accurate glucose monitoring is essential for maintaining stable substrate supply during fed-batch fermentation, whereas conventional offline assays are difficult to integrate into high-frequency process monitoring. In this study, a Raman-NIR multimodal soft-sensing framework based on a dual-stream cross-attention Transformer (DS-CAT) was developed for glucose prediction in fermentation broth. A total of 142 synchronized Raman-NIR records were preprocessed using Savitzky-Golay first-derivative transformation and standard normal variate normalization. The two spectral modalities were encoded independently and fused through asymmetric cross-attention to integrate broadband NIR information with localized Raman fingerprint features. Model performance was evaluated on the test set, together with leakage-controlled five-fold internal validation within the development set. On the test set, DS-CAT achieved R² = 0.991, RMSE = 1.09 g L^-1, and MAE = 0.89 g L^-1, outperforming PLSR, GBRT, CNN, and TCN under the same evaluation protocol. Five-fold validation yielded R² = 0.988 ± 0.009 and RMSE = 1.09 ± 0.55 g L^-1, providing an additional assessment of model performance across development-set partitions. Prediction-based perturbation further revealed strong dependence on Raman information, while Raman-block sensitivity analysis identified 1122-1335 cm^-1 as the interval showing the strongest prediction sensitivity. These results demonstrate the potential of Raman-NIR multimodal fusion for accurate online-compatible glucose soft sensing in fed-batch fermentation.