Semi-supervised soft sensor method for fermentation processes based on physical monotonicity and variational autoencoders

Abstract

Data-driven models have shown broad application prospects in soft sensor modeling. However, numerous challenges persist. On the one hand, data-driven soft sensor methods have high requirements on data quality. On the other hand, models relying on limited experimental data often lack physical interpretability. To tackle these challenges, a semi-supervised soft sensor method (PMVAER) for fermentation processes based on physical monotonicity and variational autoencoders (VAEs) is introduced. First, physical monotonicity constraint is incorporated into the loss function of VAEs for regression to ensure that the model's predictions adhere to physical feasibility. Next, considering the disparate sampling frequencies for process and quality variables, this approach is extended to learn from unlabeled data, creating a semi-supervised soft sensor model. The proposed model is validated on simulation and real cases of penicillin fermentation. Comparisons with five other methods verify that the proposed method exhibits exceptional predictive accuracy along with enhanced generalization ability.