Quality Variation Patterns and Predictive Modeling of Fermented Soybean Whey-Based Tofu Under Cold-Chain Conditions Using Kinetic and Machine Learning Approaches

Abstract

Pre-packaged fermented soybean whey-based tofu (FSW-tofu) was stored under dynamic temperature conditions (4–20 °C) that simulated typical supermarket and e-commerce cold-chain transport modes. Changes in total viable count (TVC), psychrophilic bacterial count (PBC), hardness, springiness, chewiness, and water-holding capacity were monitored over 35 d, and a hybrid prediction model integrating mechanistic kinetics with machine learning was established. Results indicated that both temperature fluctuation amplitude and frequency significantly affected microbial proliferation and textural degradation. Under the e-commerce mode, exposure to 20 °C accelerated the TVC, reaching 5 lg CFU/g at 17 d, earlier than under the supermarket mode (27 d). However, the sustained low-temperature stress in the supermarket mode caused more profound degradation of the protein gel network, leading to more severe textural deterioration at the equivalent TVC threshold. The Baranyi–Roberts–Ratkowsky non-isothermal growth model and quality response functions served as the base framework, while random forest and gradient boosting trees were used for residual correction, yielding a coupled mechanistic-data-driven model. Independent validation yielded R2 > 0.89 and relatively low RMSE, confirming the model’s good generalization and predictive accuracy. This approach combines mechanistic interpretability with machine learning accuracy to provide a rapid assessment tool for the cold-chain quality management of FSW-tofu.