{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T20:15:51Z","timestamp":1760300151302,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,1,28]],"date-time":"2019-01-28T00:00:00Z","timestamp":1548633600000},"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":["61763037","21466026"],"award-info":[{"award-number":["61763037","21466026"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of the Inner Mongolia Autonomous Region of China","award":["2017MS0601"],"award-info":[{"award-number":["2017MS0601"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Multiple phases with phase to phase transitions are important characteristics of many batch processes. The linear characteristics between phases are taken into consideration in the traditional algorithms while nonlinearities are neglected, which can lead to inaccuracy and inefficiency in monitoring. The focus of this paper is nonlinear multi-phase batch processes. A similarity metric is defined based on kernel entropy component analysis (KECA). A KECA similarity-based method is proposed for phase division and fault monitoring. First, nonlinear characteristics can be extracted in feature space via performing KECA on each preprocessed time-slice data matrix. Then phase division is achieved with the similarity variation of the extracted feature information. Then, a series of KECA models and slide-KECA models are established for steady and transitions phases respectively, which can reflect the diversity of transitional characteristics objectively and preferably deal with the stage-transition monitoring problem in multistage batch processes. Next, in order to overcome the problem that the traditional contribution plot cannot be applied to the kernel mapping space, a nonlinear contribution plot diagnosis algorithm is proposed, which is easier, more intuitive and implementable compared with the traditional one. Finally, simulations are performed on penicillin fermentation and industrial application. Specifically, the proposed method detects the abnormal agitation power and the abnormal substrate supply at 47 h and 86 h, respectively. Compared with traditional methods, it has better real-time performance and higher efficiency. Results demonstrate the ability of the proposed method to detect faults accurately and effectively in practice.<\/jats:p>","DOI":"10.3390\/e21020121","type":"journal-article","created":{"date-parts":[[2019,1,29]],"date-time":"2019-01-29T11:27:52Z","timestamp":1548761272000},"page":"121","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["KECA Similarity-Based Monitoring and Diagnosis of Faults in Multi-Phase Batch Processes"],"prefix":"10.3390","volume":"21","author":[{"given":"Yongsheng","family":"Qi","sequence":"first","affiliation":[{"name":"Institute of Electric Power, Inner Mongolia University of Technology, Hohhot 010080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuebin","family":"Meng","sequence":"additional","affiliation":[{"name":"Institute of Electric Power, Inner Mongolia University of Technology, Hohhot 010080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chenxi","family":"Lu","sequence":"additional","affiliation":[{"name":"Institute of Electric Power, Inner Mongolia University of Technology, Hohhot 010080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuejin","family":"Gao","sequence":"additional","affiliation":[{"name":"College of Electronic and Control Engineering, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lin","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Electric Power, Inner Mongolia University of Technology, Hohhot 010080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"366","DOI":"10.3724\/SP.J.1004.2010.00366","article-title":"Phase-based statistical modeling, online monitoring and quality prediction for batch processes","volume":"36","author":"Zhao","year":"2010","journal-title":"Acta Autom. Sin."},{"doi-asserted-by":"crossref","unstructured":"Yan, H.L., Yang, W.D., Zhang, H., Tao, B., and Zheng, Y. (2017, January 26\u201327). Density Peaks Clustering Based Sub-phase Partition and Monitoring for Batch Process. Proceedings of the 2017 6th Data Driven Control and Learning Systems (DDCLS), Chongqing, China.","key":"ref_2","DOI":"10.1109\/DDCLS.2017.8068086"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"906","DOI":"10.1016\/j.neucom.2015.10.018","article-title":"An improved SVM integrated GS-PCA fault diagnosis approach of Tennessee Eastman process","volume":"174","author":"Gao","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_4","first-page":"1023","article-title":"Fault diagnosis for refrigeration system based on PCA-PNN","volume":"67","author":"Liang","year":"2016","journal-title":"CIESC J."},{"unstructured":"Kosanovich, K.A., Piovoso, M.J., Dahl, K.S., Macgregor, J.F., and Nomikos, P. (July, January 29). Multi-way PCA applied to an industrial batch process. Proceedings of the 1994 American Control Conference\u2014ACC \u201994, Baltimore, MD, USA.","key":"ref_5"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1002\/aic.10024","article-title":"Sub-PCA modeling and on-line monitoring strategy for batch processes","volume":"50","author":"Lu","year":"2004","journal-title":"AIChE J."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"835","DOI":"10.1021\/ie0707624","article-title":"Improved batch process monitoring and quality prediction based on multiphasestatistical analysis","volume":"47","author":"Zhao","year":"2008","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.chemolab.2013.03.017","article-title":"Step-wise sequential phase partition (SSPP) algorithm based statistical modeling and online process monitoring","volume":"125","author":"Zhao","year":"2013","journal-title":"Chemometr. Intell. Lab. Syst."},{"key":"ref_9","first-page":"1291","article-title":"Multiphase AR-PCA monitoring for batch processes based on the batch weighted soft classifying","volume":"36","author":"Hu","year":"2015","journal-title":"Chin. J. Sci. Instrum."},{"doi-asserted-by":"crossref","unstructured":"Li, C.L., Wang, P., and Gao, X.J. (2016, January 27\u201329). Improved multi-stage online monitoring strategy for batch process. Proceedings of the 2016 35th Chinese Control Conference (CCC), Chengdu, China.","key":"ref_10","DOI":"10.1109\/ChiCC.2016.7554432"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4472","DOI":"10.1177\/0142331217750222","article-title":"Phase partition and identification based on a two-step method for batch process","volume":"40","author":"Guo","year":"2018","journal-title":"Trans. Inst. Meas. Control"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"6518","DOI":"10.1109\/TIE.2017.2682012","article-title":"Quality Relevant and Independent Two Block Monitoring Based on Mutual Information and KPCA","volume":"64","author":"Huang","year":"2017","journal-title":"IEEE Trans. Ind. Electromics"},{"key":"ref_13","first-page":"164","article-title":"Moving window KPCA with reduced complexity for nonlinear dynamic process monitoring","volume":"64","author":"Jaffel","year":"2016","journal-title":"ISA Instrum. Syst. Autom. Soc."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1109\/TPAMI.2009.100","article-title":"Kernel Entropy Component Analysis","volume":"32","author":"Jenssen","year":"2010","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1016\/j.neucom.2014.06.045","article-title":"Wavelet kernel entropy component analysis with application to industrial process monitoring","volume":"147","author":"Yang","year":"2015","journal-title":"Neurocomputing"},{"key":"ref_16","first-page":"1063","article-title":"Novel fault monitoring strategy for chemical process based on KECA","volume":"67","author":"Qi","year":"2016","journal-title":"CIESC J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1016\/j.measurement.2016.04.036","article-title":"Recent Progress on Decoupling Diagnosis of Hybrid Failures in Gear Transmission Systems using Vibration Sensor Signal: A Review","volume":"90","author":"Li","year":"2016","journal-title":"Measurement"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"972","DOI":"10.1016\/j.asoc.2017.10.029","article-title":"Automatic equipment fault fingerprint extraction for the fault diagnostic on the batch process data","volume":"68","author":"Rostami","year":"2018","journal-title":"Appl. Soft Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.jprocont.2016.10.003","article-title":"Fault prognosis for batch production based on percentile measure and gamma process: Application to semiconductor manufacturing","volume":"48","author":"Nguyen","year":"2016","journal-title":"J. Process Control"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"54158","DOI":"10.1109\/ACCESS.2018.2871455","article-title":"Least Squares and Contribution Plot Based Approach for Quality-Related Process Monitoring","volume":"6","author":"Wang","year":"2018","journal-title":"IEEE Access"},{"key":"ref_21","first-page":"1193","article-title":"Modified reconstruction-based contribution plots for fault isolation","volume":"36","author":"Guo","year":"2015","journal-title":"Chin. J. Sci. Instrum."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4403","DOI":"10.1021\/ie000141+","article-title":"Reconstruction-based fault identification using a combined index","volume":"40","author":"Yue","year":"2001","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_23","first-page":"23","article-title":"Algorithm based on direct signal and entropy optimization Spaceborne\/fixed BISAR imaging","volume":"34","author":"Zhang","year":"2015","journal-title":"Foreign Electron. Meas. Technol."},{"key":"ref_24","first-page":"25","article-title":"Class center and feature weighting based feature selection algorithm","volume":"38","author":"Cui","year":"2015","journal-title":"Electron. Meas. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1016\/j.ifacol.2018.09.255","article-title":"Improved batch process monitoring and diagnosis based on multiphase KECA","volume":"51","author":"Qi","year":"2018","journal-title":"IFAC-PapersOnLine"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1016\/j.jfranklin.2006.03.018","article-title":"The Cauchy-Schwarz Divergence and Parzen Windowing: Connections to Graph Theory and Mercer Kernel","volume":"343","author":"Jenssen","year":"2006","journal-title":"J. Frankl. Inst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.neucom.2008.03.017","article-title":"A New Information Theoretic Analysis of Sum-of-Squared-Error Kernel Clustering","volume":"72","author":"Jenssen","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_28","first-page":"611","article-title":"Study on PSO-based decision-tree SVM multi-class classification method","volume":"29","author":"Wang","year":"2015","journal-title":"J. Electron. Meas. Instrum."},{"unstructured":"Scholkopf, B., Platt, J., and Hofmann, T. (2006). Kernel maximum entropy data transformation and an enhanced spectral clustering algorithm. Conference of Advances in Neural Information Processing Systems, MIT Press.","key":"ref_29"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1553","DOI":"10.1016\/S0098-1354(02)00127-8","article-title":"A modular simulation package for fed-batch fermentation: Penicillin production","volume":"26","author":"Birol","year":"2002","journal-title":"Comput. Chem. Eng."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/2\/121\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:29:12Z","timestamp":1760185752000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/2\/121"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,28]]},"references-count":30,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,2]]}},"alternative-id":["e21020121"],"URL":"https:\/\/doi.org\/10.3390\/e21020121","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2019,1,28]]}}}