{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,8]],"date-time":"2025-11-08T22:16:34Z","timestamp":1762640194194,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2023,11,11]],"date-time":"2023-11-11T00:00:00Z","timestamp":1699660800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["61705093","K20221054"],"award-info":[{"award-number":["61705093","K20221054"]}]},{"name":"Wuxi Science and Technology Plan ProjectBasic Research","award":["61705093","K20221054"],"award-info":[{"award-number":["61705093","K20221054"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Due to the highly nonlinear, multi-stage, and time-varying characteristics of the marine lysozyme fermentation process, the global soft sensor models established using traditional single modeling methods cannot describe the dynamic characteristics of the entire fermentation process. Therefore, this study proposes a weighted ensemble learning soft sensor modeling method based on an improved seagull optimization algorithm (ISOA) and Gaussian process regression (GPR). First, an improved density peak clustering algorithm (ADPC) was used to divide the sample dataset into multiple local sample subsets. Second, an improved seagull optimization algorithm was used to optimize and transform the Gaussian process regression model, and a sub-prediction model was established. Finally, the fusion strategy was determined according to the connectivity between the test samples and local sample subsets. The proposed soft sensor model was applied to the prediction of key biochemical parameters of the marine lysozyme fermentation process. The simulation results show that the proposed soft sensor model can effectively predict the key biochemical parameters with relatively small prediction errors in the case of limited training data. According to the results, this model can be expanded to the soft sensor prediction applications in general nonlinear systems.<\/jats:p>","DOI":"10.3390\/s23229119","type":"journal-article","created":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T02:46:47Z","timestamp":1699843607000},"page":"9119","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Soft Sensor Modeling Method for the Marine Lysozyme Fermentation Process Based on ISOA-GPR Weighted Ensemble Learning"],"prefix":"10.3390","volume":"23","author":[{"given":"Na","family":"Lu","sequence":"first","affiliation":[{"name":"Key Laboratory of Agricultural Measurement and Control Technology and Equipment for Mechanical Industrial Facilities, School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Agricultural Measurement and Control Technology and Equipment for Mechanical Industrial Facilities, School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xianglin","family":"Zhu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Agricultural Measurement and Control Technology and Equipment for Mechanical Industrial Facilities, School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/j.tifs.2020.11.004","article-title":"Lysozyme and its modified forms: A critical appraisal of selected properties and potential","volume":"107","author":"Lesnierowski","year":"2021","journal-title":"Trends Food Sci. Technol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.dci.2020.103772","article-title":"Fish lysozyme gene family evolution and divergent function in early development","volume":"114","author":"Li","year":"2021","journal-title":"Dev. Comp. Immunol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"698","DOI":"10.1016\/j.foodchem.2018.09.017","article-title":"What is new in lysozyme research and its application in food industry? A review","volume":"274","author":"Wu","year":"2019","journal-title":"Food Chem."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"104654","DOI":"10.1016\/j.dci.2023.104654","article-title":"Characterization and expression patterns of lysozymes reveal potential immune functions during male pregnancy of seahorse","volume":"142","author":"Xiao","year":"2023","journal-title":"Dev. Comp. Immunol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1901","DOI":"10.3934\/mbe.2020100","article-title":"Soft sensor design based on phase partition ensemble of LSSVR models for nonlinear batch processes","volume":"17","author":"Sheng","year":"2020","journal-title":"Math. Biosci. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Wang, B., Yu, M.F., Zhu, X.L., and Zhu, L. (2020). Soft\u2014Sensing modeling based on ABC\u2014MLSSVM inversion for marine low-temperature alkaline protease MP fermentation process. BMC Biotechnol., 20.","DOI":"10.1186\/s12896-020-0603-x"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1002\/cjce.23848","article-title":"Soft sensor development based on improved just-in-time learning and relevant vector machine for batch processes","volume":"99","author":"Wang","year":"2021","journal-title":"Can. J. Chem. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"10687","DOI":"10.3934\/mbe.2022500","article-title":"Online prediction of total sugar content and optimal control of glucose feed rate during chlortetracycline fermentation based on soft sensor modeling","volume":"19","author":"Wang","year":"2022","journal-title":"Math. Biosci. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Medl, M., Rajamanickam, V., Striedner, G., and Newton, J. (2023). Development and Validation of an Artificial Neural-Network-Based Optical Density Soft Sensor for a High-Throughput Fermentation System. Processes, 11.","DOI":"10.3390\/pr11010297"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.isatra.2022.10.044","article-title":"An evolutionary deep learning soft sensor model based on random forest feature selection technique for penicillin fermentation process","volume":"136","author":"Hua","year":"2023","journal-title":"ISA Trans."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"11630","DOI":"10.1038\/s41598-020-68081-4","article-title":"Soft-sensor modeling for l-lysine fermentation process based on hybrid ICS-MLSSVM","volume":"10","author":"Wang","year":"2020","journal-title":"Sci. Rep."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.jbiosc.2021.04.002","article-title":"Soft-sensor development for monitoring the lysine fermentation process","volume":"132","author":"Tokuyama","year":"2021","journal-title":"J. Biosci. Bioeng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1015","DOI":"10.1002\/bit.28310","article-title":"A robust soft sensor based on artificial neural network for monitoring microbial lipid fermentation processes using Yarrowia lipolytica","volume":"120","author":"Wang","year":"2023","journal-title":"Biotechnol. Bioeng."},{"key":"ref_14","first-page":"S6019","article-title":"Research and application of biological potency soft sensor modeling method in the industrial fed-batch chlortetracycline fermentation process","volume":"22","author":"Sun","year":"2019","journal-title":"Clust. Comput. J. Netw. Softw. Tools Appl."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Shen, F.F., Zheng, J.Q., Ye, L.J., and Gu, D. (2020). Quality-Relevant Monitoring of Batch Processes Based on Stochastic Programming with Multiple Output Modes. Processes, 8.","DOI":"10.3390\/pr8020164"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Wang, Y.X., Zhou, J.Z., Wang, X.J., Yu, Q.Y., Sun, Y.K., Li, Y., Zhang, Y.G., Shen, W.Z., and Wei, X.L. (2023). Rumen Fermentation Parameters Prediction Model for Dairy Cows Using a Stacking Ensemble Learning Method. Animals, 13.","DOI":"10.3390\/ani13040678"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"73855","DOI":"10.1109\/ACCESS.2020.2988668","article-title":"LSTM Soft Sensor Development of Batch Processes with Multivariate Trajectory-Based Ensemble Just-in-Time Learning","volume":"8","author":"Shen","year":"2020","journal-title":"IEEE Access"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Zadkarami, M., Ghanavati, A.K., and Safavi, A.A. (2019, January 30\u201331). Soft Sensor Design for Distillation Columns Using Wavelets and Gaussian Process Regression. Proceedings of the 6th International Conference on Control, Instrumentation and Automation (ICCIA), Kurdistan, Iran.","DOI":"10.1109\/ICCIA49288.2019.9030850"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1172","DOI":"10.1177\/0954410020901961","article-title":"Thermal matching using Gaussian process regression","volume":"234","author":"Pearce","year":"2020","journal-title":"Proc. Inst. Mech. Eng. Part G-J. Aerosp. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"12950","DOI":"10.1109\/JSEN.2020.3003826","article-title":"Soft Sensing of Nonlinear and Multimode Processes Based on Semi-Supervised Weighted Gaussian Regression","volume":"20","author":"Shi","year":"2020","journal-title":"IEEE Sens. J."},{"key":"ref_21","first-page":"359","article-title":"Forecasting tunnel path geology using Gaussian process regression","volume":"28","author":"Mahmoodzadeh","year":"2022","journal-title":"Genmech. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"109406","DOI":"10.1016\/j.patcog.2023.109406","article-title":"Density peaks clustering algorithm based on fuzzy and weighted shared neighbor for uneven density datasets","volume":"139","author":"Zhao","year":"2023","journal-title":"Pattern Recognit."},{"key":"ref_23","first-page":"39","article-title":"Monthly Runoff Prediction Model and Its Application Based on GPR with Physically Composite Kernel","volume":"41","author":"Sun","year":"2023","journal-title":"Water Resour. Power"},{"key":"ref_24","first-page":"62","article-title":"Research on Opimal Planning of Integrated Energy System Based on Seagull Algorithm","volume":"18","author":"Yang","year":"2022","journal-title":"J. Shenyang Inst. Eng. (Nat. Sci.)"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/22\/9119\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:21:34Z","timestamp":1760131294000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/22\/9119"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,11]]},"references-count":24,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2023,11]]}},"alternative-id":["s23229119"],"URL":"https:\/\/doi.org\/10.3390\/s23229119","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2023,11,11]]}}}