{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,6]],"date-time":"2026-09-06T05:15:56Z","timestamp":1788671756541,"version":"build-2803163510"},"reference-count":37,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2026,9,4]],"date-time":"2026-09-04T00:00:00Z","timestamp":1788480000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004735","name":"Natural Science Foundation of Hunan Province","doi-asserted-by":"crossref","award":["2025JJ70243"],"award-info":[{"award-number":["2025JJ70243"]}],"id":[{"id":"10.13039\/501100004735","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Science and Technology Plan Project of Shaoyang","award":["2024GZ1001"],"award-info":[{"award-number":["2024GZ1001"]}]},{"name":"Science and Technology Plan Project of Shaoyang","award":["2024PT4043"],"award-info":[{"award-number":["2024PT4043"]}]},{"name":"Local Science and Technology Development Fund Project of Central Guidance","award":["2024ZYC0014"],"award-info":[{"award-number":["2024ZYC0014"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Foods"],"abstract":"<jats:p>Pre-packaged fermented soybean whey-based tofu (FSW-tofu) was stored under dynamic temperature conditions (4\u201320 \u00b0C) 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 \u00b0C 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\u2013Roberts\u2013Ratkowsky 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 &gt; 0.89 and relatively low RMSE, confirming the model\u2019s 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.<\/jats:p>","DOI":"10.3390\/foods15173147","type":"journal-article","created":{"date-parts":[[2026,9,4]],"date-time":"2026-09-04T16:07:32Z","timestamp":1788538052000},"page":"3147","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Quality Variation Patterns and Predictive Modeling of Fermented Soybean Whey-Based Tofu Under Cold-Chain Conditions Using Kinetic and Machine Learning Approaches"],"prefix":"10.3390","volume":"15","author":[{"given":"Dan","family":"Zhao","sequence":"first","affiliation":[{"name":"College of Economics and Management, Shaoyang University, Shaoyang 422000, China"},{"name":"Hunan Provincial Key Laboratory of Soybean Products Processing and Safety Control, Hunan Engineering Research Center of Green Processing and Equipment of Hunan-Style Food, Shaoyang University, Shaoyang 422000, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4602-9349","authenticated-orcid":false,"given":"Zhanrui","family":"Huang","sequence":"additional","affiliation":[{"name":"Hunan Provincial Key Laboratory of Soybean Products Processing and Safety Control, Hunan Engineering Research Center of Green Processing and Equipment of Hunan-Style Food, Shaoyang University, Shaoyang 422000, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3551-1682","authenticated-orcid":false,"given":"Hao","family":"Chen","sequence":"additional","affiliation":[{"name":"Hunan Provincial Key Laboratory of Soybean Products Processing and Safety Control, Hunan Engineering Research Center of Green Processing and Equipment of Hunan-Style Food, Shaoyang University, Shaoyang 422000, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"}]},{"given":"Liangzhong","family":"Zhao","sequence":"additional","affiliation":[{"name":"Hunan Provincial Key Laboratory of Soybean Products Processing and Safety Control, Hunan Engineering Research Center of Green Processing and Equipment of Hunan-Style Food, Shaoyang University, Shaoyang 422000, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1967-0023","authenticated-orcid":false,"given":"Xiaohu","family":"Zhou","sequence":"additional","affiliation":[{"name":"Hunan Provincial Key Laboratory of Soybean Products Processing and Safety Control, Hunan Engineering Research Center of Green Processing and Equipment of Hunan-Style Food, Shaoyang University, Shaoyang 422000, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"investigation","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1372-3227","authenticated-orcid":false,"given":"Xiaojie","family":"Zhou","sequence":"additional","affiliation":[{"name":"Hunan Provincial Key Laboratory of Soybean Products Processing and Safety Control, Hunan Engineering Research Center of Green Processing and Equipment of Hunan-Style Food, Shaoyang University, Shaoyang 422000, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"validation","vocabulary":"credit"}]},{"given":"Liu","family":"Fan","sequence":"additional","affiliation":[{"name":"Yanjinpuzi Food Co., Ltd., Liuyang 410329, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"resources","vocabulary":"credit"}]},{"given":"Fengwu","family":"Li","sequence":"additional","affiliation":[{"name":"Yanjinpuzi Food Co., Ltd., Liuyang 410329, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"resources","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"113139","DOI":"10.1016\/j.lwt.2022.113139","article-title":"Evaluating the effect of different processing methods on fermented soybean whey-based tofu quality, nutrition, and flavour","volume":"158","author":"Huang","year":"2022","journal-title":"LWT"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"128880","DOI":"10.1016\/j.foodchem.2020.128880","article-title":"HS-GC-IMS with PCA to analyze volatile flavor compounds across different production stages of fermented soybean whey 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