{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T11:25:32Z","timestamp":1762341932068,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2022,9,22]],"date-time":"2022-09-22T00:00:00Z","timestamp":1663804800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62033014","2021zzts0700"],"award-info":[{"award-number":["62033014","2021zzts0700"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Application Projects of Integrated Standardization and New Paradigm for Intelligent Manufacturing from the Ministry of Industry and Information Technology of China","award":["62033014","2021zzts0700"],"award-info":[{"award-number":["62033014","2021zzts0700"]}]},{"name":"the Fundamental Research Funds for the Central Universities of Central South University","award":["62033014","2021zzts0700"],"award-info":[{"award-number":["62033014","2021zzts0700"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In industrial processes, the composition of raw material and the production environment are complex and changeable, which makes the production process have multiple steady states. In this situation, it is difficult for the traditional single-mode monitoring methods to accurately detect the process abnormalities. To this end, a multimode monitoring method based on the factor dynamic autoregressive hidden variable model (FDALM) for industrial processes is proposed in this paper. First, an improved affine propagation clustering algorithm to learn the model modal factors is adopted, and the FDALM is constructed by combining multiple high-order hidden state Markov chains through the factor modeling technology. Secondly, a fusion algorithm based on Bayesian filtering, smoothing, and expectation-maximization is adopted to identify model parameters. The Lagrange multiplier formula is additionally constructed to update the factor coefficients by using the factor constraints in the solving. Moreover, the online Bayesian inference is adopted to fuse the information of different factor modes and obtain the fault posterior probability, which can improve the overall monitoring effect of the model. Finally, the proposed method is applied in the sintering process of ternary cathode material. The results show that the fault detection rate and false alarm rate of this method are improved obviously compared with the traditional methods.<\/jats:p>","DOI":"10.3390\/s22197203","type":"journal-article","created":{"date-parts":[[2022,9,22]],"date-time":"2022-09-22T23:07:55Z","timestamp":1663888075000},"page":"7203","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Monitoring Method Based on FDALM and Its Application in the Sintering Process of Ternary Cathode Material"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8384-2948","authenticated-orcid":false,"given":"Ning","family":"Chen","sequence":"first","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}]},{"given":"Fuhai","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7844-6780","authenticated-orcid":false,"given":"Jiayao","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}]},{"given":"Kai","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}]},{"given":"Chunhua","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}]},{"given":"Weihua","family":"Gui","sequence":"additional","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/S0098-1354(02)00161-8","article-title":"A review of process fault detection and diagnosis Part II: Quantitative model and search strategies","volume":"27","author":"Venkatasubramanian","year":"2003","journal-title":"Comput. 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