{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T16:25:04Z","timestamp":1774283104568,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2017,12,4]],"date-time":"2017-12-04T00:00:00Z","timestamp":1512345600000},"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":["61433001"],"award-info":[{"award-number":["61433001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Transfer entropy (TE) is a model-free approach based on information theory to capture causality between variables, which has been used for the modeling and monitoring of, and fault diagnosis in, complex industrial processes. It is able to detect the causality between variables without assuming any underlying model, but it is computationally burdensome. To overcome this limitation, a hybrid method of TE and the modified conditional mutual information (CMI) approach is proposed by using generated multi-valued alarm series. In order to obtain a process topology, TE can generate a causal map of all sub-processes and modified CMI can be used to distinguish the direct connectivity from the above-mentioned causal map by using multi-valued alarm series. The effectiveness and accuracy rate of the proposed method are validated by simulated and real industrial cases (the Tennessee-Eastman process) to capture process topology by using multi-valued alarm series.<\/jats:p>","DOI":"10.3390\/e19120663","type":"journal-article","created":{"date-parts":[[2017,12,4]],"date-time":"2017-12-04T11:16:38Z","timestamp":1512386198000},"page":"663","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Capturing Causality for Fault Diagnosis Based on Multi-Valued Alarm Series Using Transfer Entropy"],"prefix":"10.3390","volume":"19","author":[{"given":"Jianjun","family":"Su","sequence":"first","affiliation":[{"name":"Shandong Electric Power Research Institute for State Grid Corporation of China, Jinan 250003, China"}]},{"given":"Dezheng","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Urban Rail Transit and Logistics, Beijing Union University, Beijing 100101, China"}]},{"given":"Yinong","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Urban Rail Transit and Logistics, Beijing Union University, Beijing 100101, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0254-9000","authenticated-orcid":false,"given":"Fan","family":"Yang","sequence":"additional","affiliation":[{"name":"Tsinghua Laboratory for Information Science and Technology and Department of Automation, Tsinghua University, Beijing 100084, China"}]},{"given":"Yan","family":"Zhao","sequence":"additional","affiliation":[{"name":"Shandong Electric Power Research Institute for State Grid Corporation of China, Jinan 250003, China"}]},{"given":"Xiangkun","family":"Pang","sequence":"additional","affiliation":[{"name":"Shandong Electric Power Research Institute for State Grid Corporation of China, Jinan 250003, China"}]}],"member":"1968","published-online":{"date-parts":[[2017,12,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Yang, F., Duan, P., Shah, S.L., and Chen, T.W. (2014). Capturing Causality from Process Data. Capturing Connectivity and Causality in Complex Industrial Processes, Springer.","DOI":"10.1007\/978-3-319-05380-6"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Khandekar, S., and Muralidhar, K. (2014). Springerbriefs in applied sciences and technology. Dropwise Condensation on Inclined Textured Surfaces, Springer.","DOI":"10.1007\/978-1-4614-8447-9"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"97","DOI":"10.2307\/3060550","article-title":"Climates of south asia","volume":"164","author":"Pant","year":"1998","journal-title":"Geogr. J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1140\/epjst\/e2009-01098-2","article-title":"Complex networks in climate dynamics","volume":"174","author":"Donges","year":"2009","journal-title":"Eur. Phys. J. Spec. Top."},{"key":"ref_5","first-page":"1639","article-title":"Testing for linear and nonlinear granger causality in the stock price-volume relation","volume":"49","author":"Hiemstra","year":"1994","journal-title":"J. Financ."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"154101","DOI":"10.1103\/PhysRevLett.106.154101","article-title":"Predicting catastrophes in nonlinear dynamical systems by compressive sensing","volume":"106","author":"Wang","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Hlavackova-Schindler, K., Palus, M., Vejmelka, M., and Bhattacharya, J. (2007). Causality detection based on information. Phys. Rep., 441.","DOI":"10.1016\/j.physrep.2006.12.004"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Duggento, A., Bianciardi, M., Passamonti, L., Wald, L.L., Guerrisi, M., Barbieri, R., and Toschi, N. (2016). Globally conditioned granger causality in brain-brain and brain-heart interactions: A combined heart rate variability\/ultra-high-field (7 t) functional magnetic resonance imaging study. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci., 374.","DOI":"10.1098\/rsta.2015.0185"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1016\/j.nucengdes.2015.11.016","article-title":"A fault diagnosis method based on signed directed graph and matrix for nuclear power plants","volume":"297","author":"Liu","year":"2016","journal-title":"Nucl. Eng. Des."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4811","DOI":"10.1021\/ie0206453","article-title":"A systematic framework for the development and analysis of signed digraphs for chemical processes. 2. Control loops and flowsheet analysis","volume":"42","author":"Maurya","year":"2003","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1016\/j.jprocont.2007.11.007","article-title":"A practical method for identifying the propagation path of plant-wide disturbances","volume":"18","author":"Bauer","year":"2008","journal-title":"J. Process Control"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1534\/genetics.115.176107","article-title":"Fine mapping causal variants with an approximate bayesian method using marginal test statistics","volume":"200","author":"Chen","year":"2015","journal-title":"Genetics"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/j.jeconom.2015.07.007","article-title":"Testing for granger causality with mixed frequency data","volume":"192","author":"Ghysels","year":"2016","journal-title":"J. Econom."},{"key":"ref_14","unstructured":"Yang, F., Fan, N.J., and Ye, H. (2013). Application of PDC method in causality analysis of chemical process variables. J. Tsinghua Univ. (Sci. Technol.), 210\u2013214."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1109\/TCST.2006.883234","article-title":"Finding the direction of disturbance propagation in a chemical process using transfer entropy","volume":"15","author":"Bauer","year":"2007","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2052","DOI":"10.1109\/TCST.2012.2233476","article-title":"Direct causality detection via the transfer entropy approach","volume":"21","author":"Duan","year":"2013","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1109\/TCST.2014.2345095","article-title":"Transfer zero-entropy and its application for capturing cause and effect relationship between variables","volume":"23","author":"Duan","year":"2015","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"158101","DOI":"10.1103\/PhysRevLett.100.158101","article-title":"Symbolic transfer entropy","volume":"100","author":"Staniek","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5868","DOI":"10.3390\/e17085868","article-title":"Detection of causality between process variables based on industrial alarm data using transfer entropy","volume":"17","author":"Yu","year":"2015","journal-title":"Entropy"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1014","DOI":"10.1109\/TASE.2013.2248000","article-title":"Detection of correlated alarms based on similarity coefficients of binary data","volume":"10","author":"Yang","year":"2013","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1016\/j.isatra.2012.03.005","article-title":"Improved correlation analysis and visualization of industrial alarm data","volume":"51","author":"Yang","year":"2012","journal-title":"ISA Trans."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1103\/PhysRevLett.85.461","article-title":"Measuring information transfer","volume":"85","author":"Schreiber","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Dehnad, K. (1986). Density Estimation for Statistics and Data Analysis by Bernard Silverman, Chapman and Hall.","DOI":"10.2307\/1269475"},{"key":"ref_24","unstructured":"Cover, T. (1994, January 27\u201329). Information Theory and Statistics. Proceedings of the IEEE-IMS Workshop on Information Theory and Statistics, Alexandria, VA, USA."},{"key":"ref_25","unstructured":"Cover, T.M., and Thomas, J.A. (1601). Elements of Information Theory, Tsinghua University Press."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"046211","DOI":"10.1103\/PhysRevE.63.046211","article-title":"Synchronization as adjustment of information rates: Detection from bivariate time series","volume":"63","author":"Palus","year":"2001","journal-title":"Phys. Rev. E Stat. Nonlinear Soft Matter Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"258701","DOI":"10.1103\/PhysRevLett.108.258701","article-title":"Escaping the curse of dimensionality in estimating multivariate transfer entropy","volume":"108","author":"Runge","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_28","unstructured":"Kantz, H., and Schreiber, T. (1997). Nonlinear Time Series Analysis, Cambridge University Press."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/0098-1354(93)80018-I","article-title":"A plant-wide industrial process control problem","volume":"17","author":"Downs","year":"1993","journal-title":"Comput. Chem. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/0959-1524(96)00031-5","article-title":"Decentralized control of the tennessee eastman challenge process","volume":"6","author":"Ricker","year":"1996","journal-title":"J. Process Control"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/12\/663\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:52:36Z","timestamp":1760208756000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/12\/663"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,4]]},"references-count":30,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2017,12]]}},"alternative-id":["e19120663"],"URL":"https:\/\/doi.org\/10.3390\/e19120663","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,12,4]]}}}