Regularized Decoupling Transformer-Based Variable Selection and Soft Sensor Modeling for Fermentation Processes

Soft sensor modeling of fermentation processes is crucial to enhance yield and quality. However, the nonlinear and dynamic characteristics of these processes, coupled with variable redundancy, often degrade model performance. A variable selection and soft sensor modeling scheme based on regularized decoupling Transformer (RDTF) is proposed in this study to address these issues. First, a network framework comprising an embedding network, positional encoding, and a multilayer Transformer (TF) encoder is employed to extract dynamic nonlinear features. Second, a decoupling layer with mean and variance networks ensures that the latent variables are representative and can independently reflect the information from the original process variables. Third, a regression model is established between these latent variables and quality indicators. Regularization technology, namely, a gradient penalty term in the loss function, allows the model to select the most critical process variables for predicting quality indicators, addressing feature redundancy and collinearity, and improving the model’s performance and robustness. Last, the effectiveness of the proposed RDTF is verified through a simulated penicillin fermentation process case and real penicillin and erythromycin production cases. Across multiple real fermentation cases, the model achieves $R^{2}$ values exceeding 0.95 and consistently outperforms existing models in terms of accuracy and stability. These results highlight RDTF’s potential for industrial applications.