{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T14:54:02Z","timestamp":1784645642844,"version":"3.55.0"},"reference-count":34,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,3,12]],"date-time":"2020-03-12T00:00:00Z","timestamp":1583971200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100005187","name":"U.S. Nuclear Regulatory Commission","doi-asserted-by":"publisher","award":["31310018M0043"],"award-info":[{"award-number":["31310018M0043"]}],"id":[{"id":"10.13039\/100005187","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Dynamic Bayesian networks (DBNs) represent complex time-dependent causal relationships through the use of conditional probabilities and directed acyclic graph models. DBNs enable the forward and backward inference of system states, diagnosing current system health, and forecasting future system prognosis within the same modeling framework. As a result, there has been growing interest in using DBNs for reliability engineering problems and applications in risk assessment. However, there are open questions about how they can be used to support diagnostics and prognostic health monitoring of a complex engineering system (CES), e.g., power plants, processing facilities and maritime vessels. These systems\u2019 tightly integrated human, hardware, and software components and dynamic operational environments have previously been difficult to model. As part of the growing literature advancing the understanding of how DBNs can be used to improve the risk assessments and health monitoring of CESs, this paper shows the prognostic and diagnostic inference capabilities that are possible to encapsulate within a single DBN model. Using simulated accident sequence data from a model sodium fast nuclear reactor as a case study, a DBN is designed, quantified, and verified based on evidence associated with a transient overpower. The results indicate that a joint prognostic and diagnostic model that is responsive to new system evidence can be generated from operating data to represent CES health. Such a model can therefore serve as another training tool for CES operators to better prepare for accident scenarios.<\/jats:p>","DOI":"10.3390\/a13030064","type":"journal-article","created":{"date-parts":[[2020,3,12]],"date-time":"2020-03-12T12:22:51Z","timestamp":1584015771000},"page":"64","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["A Dynamic Bayesian Network Structure for Joint Diagnostics and Prognostics of Complex Engineering Systems"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0135-5324","authenticated-orcid":false,"given":"Austin D.","family":"Lewis","sequence":"first","affiliation":[{"name":"Systems Risk and Reliability Analysis Lab (SyRRA), Center for Risk and Reliability, University of Maryland, College Park, MD 20742, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Katrina M.","family":"Groth","sequence":"additional","affiliation":[{"name":"Systems Risk and Reliability Analysis Lab (SyRRA), Center for Risk and Reliability, University of Maryland, College Park, MD 20742, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,12]]},"reference":[{"key":"ref_1","first-page":"193","article-title":"Building and using dynamic risk-informed diagnosis procedures for complex system accidents","volume":"3","author":"Groth","year":"2020","journal-title":"Proc. Inst. Mech. Eng. O-J. Ris."},{"key":"ref_2","first-page":"1","article-title":"A Review on Prognostics Methods for Engineering Systems","volume":"99","author":"Guo","year":"2019","journal-title":"IEEE Trans. Reliab."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1483","DOI":"10.1016\/j.ymssp.2005.09.012","article-title":"A review on machinery diagnostics and prognostics implementing condition-based maintenance","volume":"20","author":"Jardine","year":"2006","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1016\/j.ress.2006.12.004","article-title":"Formalisation of a new prognosis model for supporting proactive maintenance implementation on industrial system","volume":"93","author":"Muller","year":"2008","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.ress.2005.03.006","article-title":"Complex system reliability modelling with dynamic object oriented Bayesian networks (DOOBN)","volume":"91","author":"Weber","year":"2006","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_6","first-page":"391","article-title":"Advances in PHM application frameworks: Processing methods, prognosis models, decision making","volume":"33","author":"Crespo","year":"2013","journal-title":"Chem. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"106598","DOI":"10.1016\/j.ress.2019.106598","article-title":"A systematic methodology for Prognostic and Health Management system architecture definition","volume":"193","author":"Li","year":"2020","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.ress.2009.08.001","article-title":"A data-driven fuzzy approach for predicting the remaining useful life in dynamic failure scenarios of a nuclear system","volume":"95","author":"Zio","year":"2010","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1111\/j.1467-8640.1989.tb00324.x","article-title":"A model for reasoning about persistence and causation","volume":"5","author":"Dean","year":"1989","journal-title":"Comput. Intell."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1016\/j.engappai.2019.09.002","article-title":"Data-driven approach augmented in simulation for robust fault prognosis","volume":"86","author":"Djeziri","year":"2019","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1037","DOI":"10.1007\/s10845-014-0933-4","article-title":"Data-driven prognostic method based on Bayesian approaches for direct remaining useful life prediction","volume":"27","author":"Mosallam","year":"2016","journal-title":"J. Intell. Manuf."},{"key":"ref_12","first-page":"195","article-title":"Bayesian networks for reliability analysis of complex systems","volume":"Volume 1484","author":"Coelho","year":"1998","journal-title":"Progress in Artificial Intelligence\u2013IBERAMIA 98"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/j.ress.2004.06.004","article-title":"A discrete-time Bayesian network reliability modeling and analysis framework","volume":"87","author":"Boudali","year":"2005","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_14","unstructured":"Weber, P., and Jouffe, L. (2003, January 9\u201311). Reliability modelling with dynamic bayesian networks. Proceedings of the 5th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes 2003, Wahsington, DC, USA."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2227","DOI":"10.1109\/TII.2017.2695583","article-title":"Bayesian networks in fault diagnosis","volume":"13","author":"Cai","year":"2017","journal-title":"IEEE Trans. Industr. Inform."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.ress.2018.05.017","article-title":"Dynamic availability assessment of safety critical systems using a dynamic Bayesian network","volume":"178","author":"Amin","year":"2018","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.ress.2014.10.021","article-title":"A dynamic Bayesian network based approach to safety decision support in tunnel construction","volume":"134","author":"Wu","year":"2015","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.ress.2018.07.002","article-title":"An integrated approach for system functional reliability assessment using Dynamic Bayesian Network and Hidden Markov Model","volume":"180","author":"Rebello","year":"2018","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_19","unstructured":"Medjaher, K., Moya, J.Y., and Zerhouni, N. (2009, January 10\u201312). Failure prognostic by using dynamic Bayesian Networks. Proceedings of the 2nd IFAC Workshop on Dependable Control of Discrete Systems, Bari, Italy."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1016\/j.nucengdes.2015.05.010","article-title":"Pilot study of dynamic Bayesian networks approach for fault diagnostics and accident progression prediction in HTR-PM","volume":"291","author":"Zhao","year":"2015","journal-title":"Nucl. Eng. Des."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1716","DOI":"10.1016\/j.ress.2006.09.012","article-title":"Risk-based reconfiguration of safety monitoring system using dynamic Bayesian network","volume":"92","author":"Kohda","year":"2007","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.ress.2015.02.007","article-title":"Application of dynamic Bayesian network to risk analysis of domino effects in chemical infrastructures","volume":"138","author":"Khakzad","year":"2015","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1016\/j.ress.2017.06.004","article-title":"Application of dynamic Bayesian network to performance assessment of fire protection systems during domino effects","volume":"167","author":"Khakzad","year":"2017","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.anucene.2018.01.001","article-title":"Dynamic event tree analysis with the SAS4A\/SASSYS-1 safety analysis code","volume":"115","author":"Jankovsky","year":"2018","journal-title":"Ann. Nucl. Energ."},{"key":"ref_25","unstructured":"Lewis, A., and Groth, K. (2019, January 22\u201326). A review of methods for discretizing continuous-time accident sequences. Proceedings of the 29th European Safety and Reliability Conference (ESREL 2019), Hannover, Germany."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.renene.2017.05.020","article-title":"Hybrid method for remaining useful life prediction in wind turbine systems","volume":"116","author":"Djeziri","year":"2018","journal-title":"Renew. Energ."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Garramiola, F., Poza, J., Madina, P., Del Olmo, J., and Almandoz, G. (2018). A Review in Fault Diagnosis and Health Assessment for Railway Traction Drives. Appl. Sci., 8.","DOI":"10.3390\/app8122475"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Cai, B., Shao, X., Liu, Y., Kong, X., Wang, H., Xu, H., and Ge, W. (2019). Remaining useful life estimation of structure systems under the influence of multiple causes: Subsea pipelines as a case study. IEEE Trans. Ind. Electron., in press.","DOI":"10.1109\/TIE.2019.2931491"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1016\/j.ress.2015.01.017","article-title":"A dynamic discretization method for reliability inference in Dynamic Bayesian Networks","volume":"138","author":"Zhu","year":"2015","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_30","unstructured":"Yang, Y., and Webb, G.I. (2002, January 18\u201322). A comparative study of discretization methods for naive-bayes classifiers. Proceedings of the Pacific Rim Knowledge Acquisition Workshop (PKAW\u201902), Tokyo, Japan."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/j.ress.2017.08.017","article-title":"Efficient approximate inference in Bayesian networks with continuous variables","volume":"169","author":"Li","year":"2018","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1016\/j.ress.2017.04.014","article-title":"Generalized Continuous Time Bayesian Networks as a modelling and analysis formalism for dependable systems","volume":"167","author":"Portinale","year":"2017","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.ress.2018.05.016","article-title":"Monitoring and learning algorithms for dynamic hybrid Bayesian network in on-line system health management applications","volume":"178","author":"Iamsumang","year":"2018","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_34","unstructured":"Hackford, N. (2020, January 20). PRISM Preliminary Safety Information Document, Available online: https:\/\/www.nrc.gov\/docs\/ML0828\/ML082880369.pdf."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/13\/3\/64\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:06:15Z","timestamp":1760173575000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/13\/3\/64"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,12]]},"references-count":34,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,3]]}},"alternative-id":["a13030064"],"URL":"https:\/\/doi.org\/10.3390\/a13030064","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,12]]}}}