{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T16:50:10Z","timestamp":1776099010682,"version":"3.50.1"},"reference-count":41,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100013280","name":"Major Basic Research Project of the Natural Science Foundation of the Jiangsu Higher Education Institutions","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100013280","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010023","name":"Natural Science Research of Jiangsu Higher Education Institutions of China","doi-asserted-by":"publisher","award":["25KJB470004"],"award-info":[{"award-number":["25KJB470004"]}],"id":[{"id":"10.13039\/501100010023","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Engineering Applications of Artificial Intelligence"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1016\/j.engappai.2026.114377","type":"journal-article","created":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T04:02:15Z","timestamp":1773374535000},"page":"114377","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Multirate ensemble probabilistic sparse identification of nonlinear dynamics for industrial process monitoring"],"prefix":"10.1016","volume":"173","author":[{"given":"Zixuan","family":"Lin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7054-2698","authenticated-orcid":false,"given":"Wei","family":"Fan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haiquan","family":"Yu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cong","family":"Yu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiao","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Biwen","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.engappai.2026.114377_b1","series-title":"International Conference on Machine Learning","first-page":"1247","article-title":"Deep canonical correlation analysis","author":"Andrew","year":"2013"},{"key":"10.1016\/j.engappai.2026.114377_b2","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.jprocont.2021.10.006","article-title":"OASIS-P: Operable adaptive sparse identification of systems for fault prognosis of chemical processes","volume":"107","author":"Bhadriraju","year":"2021","journal-title":"J. Process Control"},{"issue":"15","key":"10.1016\/j.engappai.2026.114377_b3","doi-asserted-by":"crossref","first-page":"3932","DOI":"10.1073\/pnas.1517384113","article-title":"Discovering governing equations from data by sparse identification of nonlinear dynamical systems","volume":"113","author":"Brunton","year":"2016","journal-title":"Proc. Natl. Acad. Sci."},{"issue":"3","key":"10.1016\/j.engappai.2026.114377_b4","doi-asserted-by":"crossref","first-page":"2085","DOI":"10.1109\/TPWRS.2022.3189602","article-title":"An online data-driven method to locate forced oscillation sources from power plants based on sparse identification of nonlinear dynamics (SINDy)","volume":"38","author":"Cai","year":"2022","journal-title":"IEEE Trans. Power Syst."},{"issue":"5","key":"10.1016\/j.engappai.2026.114377_b5","doi-asserted-by":"crossref","first-page":"2710","DOI":"10.1109\/TII.2019.2893125","article-title":"A distributed canonical correlation analysis-based fault detection method for plant-wide process monitoring","volume":"15","author":"Chen","year":"2019","journal-title":"IEEE Trans. Ind. Informatics"},{"key":"10.1016\/j.engappai.2026.114377_b6","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.isatra.2021.01.039","article-title":"Robust adaptive boosted canonical correlation analysis for quality-relevant process monitoring of wastewater treatment","volume":"117","author":"Cheng","year":"2021","journal-title":"ISA Trans."},{"issue":"4","key":"10.1016\/j.engappai.2026.114377_b7","doi-asserted-by":"crossref","first-page":"1708","DOI":"10.1109\/TASE.2019.2896205","article-title":"Multirate dynamic process monitoring based on multirate linear Gaussian state-space model","volume":"16","author":"Cong","year":"2019","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"issue":"7","key":"10.1016\/j.engappai.2026.114377_b8","doi-asserted-by":"crossref","first-page":"4749","DOI":"10.1109\/TII.2021.3105487","article-title":"Multi-rate layered operational optimal control for large-scale industrial processes","volume":"18","author":"Dai","year":"2021","journal-title":"IEEE Trans. Ind. Informatics"},{"key":"10.1016\/j.engappai.2026.114377_b9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jprocont.2017.05.002","article-title":"A novel dynamic PCA algorithm for dynamic data modeling and process monitoring","volume":"67","author":"Dong","year":"2018","journal-title":"J. Process Control"},{"key":"10.1016\/j.engappai.2026.114377_b10","doi-asserted-by":"crossref","DOI":"10.1016\/j.conengprac.2025.106551","article-title":"Concurrent quality and process monitoring with a probabilistic sparse nonlinear dynamic method","volume":"165","author":"Fan","year":"2025","journal-title":"Control Eng. Pract."},{"key":"10.1016\/j.engappai.2026.114377_b11","doi-asserted-by":"crossref","DOI":"10.1016\/j.jtice.2023.105238","article-title":"PSINDy: Probabilistic sparse identification of nonlinear dynamics for temporal process modeling and fault detection","volume":"153","author":"Fan","year":"2023","journal-title":"J. Taiwan Inst. Chem. Eng."},{"key":"10.1016\/j.engappai.2026.114377_b12","first-page":"16718","article-title":"Robust Bayesian regression via hard thresholding","volume":"35","author":"Fan","year":"2022","journal-title":"Adv. Neural Inf. Process. Syst."},{"issue":"6","key":"10.1016\/j.engappai.2026.114377_b13","doi-asserted-by":"crossref","first-page":"2573","DOI":"10.1109\/TCST.2022.3156296","article-title":"Dynamic probabilistic predictable feature analysis for multivariate temporal process monitoring","volume":"30","author":"Fan","year":"2022","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"10.1016\/j.engappai.2026.114377_b14","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.jprocont.2022.02.004","article-title":"Robust probabilistic predictable feature analysis and its application for dynamic process monitoring","volume":"112","author":"Fan","year":"2022","journal-title":"J. Process Control"},{"key":"10.1016\/j.engappai.2026.114377_b15","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/j.jprocont.2019.11.010","article-title":"A multi-feature extraction technique based on principal component analysis for nonlinear dynamic process monitoring","volume":"85","author":"Guo","year":"2020","journal-title":"J. Process Control"},{"key":"10.1016\/j.engappai.2026.114377_b16","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.jprocont.2021.06.003","article-title":"A multi-rate sampling data fusion method for fault diagnosis and its industrial applications","volume":"104","author":"Huang","year":"2021","journal-title":"J. Process Control"},{"issue":"1","key":"10.1016\/j.engappai.2026.114377_b17","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1109\/TIE.2015.2466557","article-title":"Performance-driven distributed PCA process monitoring based on fault-relevant variable selection and Bayesian inference","volume":"63","author":"Jiang","year":"2015","journal-title":"IEEE Trans. Ind. Electron."},{"issue":"7\u20138","key":"10.1016\/j.engappai.2026.114377_b18","doi-asserted-by":"crossref","first-page":"1103","DOI":"10.1016\/S0098-1354(01)00683-4","article-title":"A new multivariate statistical process monitoring method using principal component analysis","volume":"25","author":"Kano","year":"2001","journal-title":"Comput. Chem. Eng."},{"key":"10.1016\/j.engappai.2026.114377_b19","doi-asserted-by":"crossref","DOI":"10.1016\/j.engappai.2023.106093","article-title":"Novel aeroengine fault diagnosis method based on feature amplification","volume":"122","author":"Lin","year":"2023","journal-title":"Eng. Appl. Artif. Intell."},{"key":"10.1016\/j.engappai.2026.114377_b20","first-page":"1","article-title":"Dynamic partial-least-squares-based fault detection for nonlinear distributed parameter systems","volume":"73","author":"Luo","year":"2024","journal-title":"IEEE Trans. Instrum. Meas."},{"issue":"5","key":"10.1016\/j.engappai.2026.114377_b21","doi-asserted-by":"crossref","DOI":"10.1002\/stc.2698","article-title":"Probabilistic principal component analysis-based anomaly detection for structures with missing data","volume":"28","author":"Ma","year":"2021","journal-title":"Struct. Control. Health Monit."},{"issue":"2","key":"10.1016\/j.engappai.2026.114377_b22","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1007\/s43153-021-00125-2","article-title":"Non-linear process monitoring using kernel principal component analysis: A review of the basic and modified techniques with industrial applications","volume":"39","author":"Pani","year":"2022","journal-title":"Braz. J. Chem. Eng."},{"issue":"3","key":"10.1016\/j.engappai.2026.114377_b23","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.1214\/aoms\/1177704472","article-title":"On estimation of a probability density function and mode","volume":"33","author":"Parzen","year":"1962","journal-title":"Ann. Math. Stat."},{"key":"10.1016\/j.engappai.2026.114377_b24","doi-asserted-by":"crossref","DOI":"10.1016\/j.conengprac.2022.105182","article-title":"An analytical partial least squares method for process monitoring","volume":"124","author":"Qin","year":"2022","journal-title":"Control Eng. Pract."},{"key":"10.1016\/j.engappai.2026.114377_b25","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.automatica.2018.06.029","article-title":"Process monitoring using a generalized probabilistic linear latent variable model","volume":"96","author":"Raveendran","year":"2018","journal-title":"Automatica"},{"issue":"3","key":"10.1016\/j.engappai.2026.114377_b26","doi-asserted-by":"crossref","first-page":"2626","DOI":"10.1109\/TIE.2020.2972472","article-title":"Key-performance-indicator-related process monitoring based on improved kernel partial least squares","volume":"68","author":"Si","year":"2020","journal-title":"IEEE Trans. Ind. Electron."},{"issue":"9","key":"10.1016\/j.engappai.2026.114377_b27","doi-asserted-by":"crossref","first-page":"6368","DOI":"10.1109\/TII.2020.3015034","article-title":"Multisubspace orthogonal canonical correlation analysis for quality-related plant-wide process monitoring","volume":"17","author":"Song","year":"2020","journal-title":"IEEE Trans. Ind. Informatics"},{"issue":"1","key":"10.1016\/j.engappai.2026.114377_b28","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1109\/TSTE.2020.2971271","article-title":"Multi-time scale coordinated control and scheduling of inverter-based TCLs with variable wind generation","volume":"12","author":"Song","year":"2020","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"10.1016\/j.engappai.2026.114377_b29","series-title":"International Conference on Advanced Information Systems Engineering","first-page":"477","article-title":"Predictive business process monitoring with LSTM neural networks","author":"Tax","year":"2017"},{"issue":"1","key":"10.1016\/j.engappai.2026.114377_b30","first-page":"41","article-title":"A theoretical basis for the use of principal component models for monitoring multivariate processes","volume":"1","author":"Wise","year":"1990","journal-title":"Process. Control. Qual."},{"issue":"10","key":"10.1016\/j.engappai.2026.114377_b31","doi-asserted-by":"crossref","first-page":"6690","DOI":"10.1109\/TII.2021.3121770","article-title":"Deep canonical correlation analysis using sparsity-constrained optimization for nonlinear process monitoring","volume":"18","author":"Xiu","year":"2021","journal-title":"IEEE Trans. Ind. Informatics"},{"issue":"25","key":"10.1016\/j.engappai.2026.114377_b32","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.ifacol.2022.09.351","article-title":"Direct data-driven design for a sparse feedback controller based on VRFT and LASSO regression","volume":"55","author":"Yahagi","year":"2022","journal-title":"IFAC-PapersOnLine"},{"key":"10.1016\/j.engappai.2026.114377_b33","doi-asserted-by":"crossref","DOI":"10.1109\/TII.2025.3528580","article-title":"A robust probabilistic quality-relevant monitoring model with Laplace distribution","author":"Yu","year":"2025","journal-title":"IEEE Trans. Ind. Informatics"},{"key":"10.1016\/j.engappai.2026.114377_b34","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2022.110468","article-title":"A generalized probabilistic monitoring model with both random and sequential data","volume":"144","author":"Yu","year":"2022","journal-title":"Automatica"},{"key":"10.1016\/j.engappai.2026.114377_b35","doi-asserted-by":"crossref","DOI":"10.1016\/j.engappai.2025.110663","article-title":"Multimodal data imputation and fusion for trustworthy fault diagnosis of mechanical systems","volume":"150","author":"Zhang","year":"2025","journal-title":"Eng. Appl. Artif. Intell."},{"key":"10.1016\/j.engappai.2026.114377_b36","doi-asserted-by":"crossref","first-page":"1404","DOI":"10.1109\/ACCESS.2018.2886528","article-title":"A unified framework for sparse relaxed regularized regression: SR3","volume":"7","author":"Zheng","year":"2018","journal-title":"IEEE Access"},{"key":"10.1016\/j.engappai.2026.114377_b37","article-title":"Dynamic process monitoring using total multirate linear Gaussian state space model","author":"Zheng","year":"2025","journal-title":"IEEE Trans. Ind. Informatics"},{"issue":"5","key":"10.1016\/j.engappai.2026.114377_b38","doi-asserted-by":"crossref","first-page":"3305","DOI":"10.1109\/TPAMI.2023.3342828","article-title":"Semi-supervised learning for multi-label cardiovascular diseases prediction: A multi-dataset study","volume":"46","author":"Zhou","year":"2023","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"4","key":"10.1016\/j.engappai.2026.114377_b39","doi-asserted-by":"crossref","DOI":"10.1007\/s11432-018-9624-8","article-title":"Multi-rate principal component regression model for soft sensor application in industrial processes","volume":"63","author":"Zhou","year":"2020","journal-title":"Sci. China Inf. Sci."},{"issue":"7","key":"10.1016\/j.engappai.2026.114377_b40","doi-asserted-by":"crossref","first-page":"4076","DOI":"10.1109\/TII.2018.2889750","article-title":"Multirate factor analysis models for fault detection in multirate processes","volume":"15","author":"Zhou","year":"2018","journal-title":"IEEE Trans. Ind. Informatics"},{"key":"10.1016\/j.engappai.2026.114377_b41","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1016\/j.ast.2018.12.038","article-title":"Scaled sequential threshold least-squares (S2TLS) algorithm for sparse regression modeling and flight load prediction","volume":"85","author":"Zhu","year":"2019","journal-title":"Aerosp. Sci. Technol."}],"container-title":["Engineering Applications of Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0952197626006585?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0952197626006585?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T15:50:35Z","timestamp":1776095435000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0952197626006585"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6]]},"references-count":41,"alternative-id":["S0952197626006585"],"URL":"https:\/\/doi.org\/10.1016\/j.engappai.2026.114377","relation":{},"ISSN":["0952-1976"],"issn-type":[{"value":"0952-1976","type":"print"}],"subject":[],"published":{"date-parts":[[2026,6]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Multirate ensemble probabilistic sparse identification of nonlinear dynamics for industrial process monitoring","name":"articletitle","label":"Article Title"},{"value":"Engineering Applications of Artificial Intelligence","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.engappai.2026.114377","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"114377"}}