{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:31:15Z","timestamp":1761611475131,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2019,4,23]],"date-time":"2019-04-23T00:00:00Z","timestamp":1555977600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Wireless Sensor Networks (WSNs) are prone to failures and malicious attacks. Trust evaluation is becoming a new method for fault detection in WSNs. In our previous work, a comprehensive trust model based on multi-factors was introduced for fault detection. This model was validated by simulating. However, it needs to be redeployed when adjustment to network parameters is made. To address the redeployment issue, we propose a Trust-based Formal Model (TFM) that can describe the fault detection process and check faults without simulating and running a WSN. This model derives from Petri nets with the characteristics of time, weight, and threshold. Basic structures of TFM are presented with which compound structures for general purposes can be built. The transition firing and marking updating rules are both defined for further system analysis. An efficient TFM analysis algorithm is developed for structured detection models. When trust factor values, firing time, weights, and thresholds are loaded, precise assessment of the node can be obtained. Finally, we implement TFM with the Generic Modeling Environment (GME). With an example, we illustrate that TFM can efficiently describe the fault detection process and specify faults in advance for WSNs.<\/jats:p>","DOI":"10.3390\/s19081916","type":"journal-article","created":{"date-parts":[[2019,4,24]],"date-time":"2019-04-24T03:14:28Z","timestamp":1556075668000},"page":"1916","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A Trust-Based Formal Model for Fault Detection in Wireless Sensor Networks"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7899-0265","authenticated-orcid":false,"given":"Na","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Computer and Information Engineering, Shanghai Polytechnic University, Shanghai 201209, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4176-3947","authenticated-orcid":false,"given":"Jiacun","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Software Engineering, Monmouth University, West Long Branch, NJ 07764, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3820-9195","authenticated-orcid":false,"given":"Xuemin","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Engineering, Texas Southern University, Houston, TX 77004, USA"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1109\/SURV.2013.050113.00191","article-title":"A survey of intrusion detection systems in wireless sensor networks","volume":"16","author":"Butun","year":"2014","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"20558","DOI":"10.1109\/ACCESS.2018.2821445","article-title":"Big Data Challenges and Data Aggregation Strategies in Wireless Sensor Networks","volume":"6","author":"Boubiche","year":"2018","journal-title":"IEEE Access"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Munir, A., Gordon-Ross, A., and Ranka, S. (2016). Modeling and Analysis of Fault Detection and Fault Tolerance in Embedded Wireless Sensor Networks. Modeling and Optimization of Parallel and Distributed Embedded Systems, John Wiley & Sons, Ltd.","DOI":"10.1002\/9781119086383"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/j.jnca.2016.10.019","article-title":"An analysis of fault detection strategies in wireless sensor networks","volume":"78","author":"Muhammed","year":"2017","journal-title":"J. Netw. Comput. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1109\/JSEN.2017.2771226","article-title":"Fault detection in wireless sensor networks through SVM classifier","volume":"18","author":"Zidi","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/j.eswa.2015.09.040","article-title":"Fuzzy rule-based faulty node classification and management scheme for large scale wireless sensor networks","volume":"45","author":"Chanak","year":"2016","journal-title":"Expert Syst. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"7935802","DOI":"10.1155\/2018\/7935802","article-title":"Fault Detection Modelling and Analysis in a Wireless Sensor Network","volume":"2018","author":"Jia","year":"2018","journal-title":"J. Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1145","DOI":"10.1007\/s11276-016-1207-1","article-title":"rDFD: Reactive distributed fault detection in wireless sensor networks","volume":"23","author":"Sharma","year":"2017","journal-title":"Wirel. Netw."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4349795","DOI":"10.1155\/2018\/4349795","article-title":"Distributed Fault Detection for Wireless Sensor Networks Based on Support Vector Regression","volume":"2018","author":"Cheng","year":"2018","journal-title":"Wirel. Commun. Mob. Comput."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s11277-015-2734-2","article-title":"Centralized IDS Based on Misuse Detection for Cluster-Based Wireless Sensors Networks","volume":"85","author":"Hidoussi","year":"2015","journal-title":"Wirel. Pers. Commun."},{"key":"ref_11","first-page":"371","article-title":"Review of Trust Models in Wireless Sensor Networks","volume":"8","author":"Rani","year":"2014","journal-title":"Int. J. Comput. Inf. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wang, J., Jiang, S., and Fapojuwo, A.O. (2017). A Protocol Layer Trust-Based Intrusion Detection Scheme for Wireless Sensor Networks. Sensors, 17.","DOI":"10.3390\/s17061227"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Chen, Z., Tian, L., and Lin, C. (2017). Trust Model of Wireless Sensor Networks and Its Application in Data Fusion. Sensors, 17.","DOI":"10.3390\/s17040703"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1016\/j.proeng.2012.01.063","article-title":"Research on Trust Model of Sensor Nodes in WSNs","volume":"29","author":"Gu","year":"2012","journal-title":"Procedia Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2332","DOI":"10.3390\/s100302332","article-title":"An Adaptive Fault-Tolerant Event Detection Scheme for Wireless Sensor Networks","volume":"10","author":"Yim","year":"2010","journal-title":"Sensors"},{"key":"ref_16","first-page":"257","article-title":"A Comprehensive Trust Model Based on Multi-factors for WSNs","volume":"10","author":"Wang","year":"2015","journal-title":"Int. J. Comput. Commun. Control"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Fishwick, P. (2007). Petri Nets for Dynamic Event-Driven System Modeling. Handbook of Dynamic System Modeling, CRC Press. Chapter 24.","DOI":"10.1201\/9781420010855"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Wang, J. (1998). Timed Petri Nets: Theory and Application, Kluwer Academic Publishers.","DOI":"10.1007\/978-1-4615-5537-7"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Kohlhase, M., Johansson, M., Miller, B., de Moura, L., and Tompa, F. (2016). Formalization of Normal Random Variables in HOL. Intelligent Computer Mathematics, Springer International Publishing.","DOI":"10.1007\/978-3-319-42547-4"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/s00165-014-0304-0","article-title":"Formal probabilistic analysis of detection properties in wireless sensor networks","volume":"27","author":"Elleuch","year":"2015","journal-title":"Formal Aspects Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.procs.2015.08.325","article-title":"Formalizing Mobile Ad Hoc and Sensor Networks Using VDM-SL","volume":"63","author":"Riaz","year":"2015","journal-title":"Procedia Comput. Sci."},{"key":"ref_22","first-page":"24","article-title":"TEPAWSN: A Formal Analysis Tool for Wireless Sensor Networks","volume":"1","author":"Man","year":"2009","journal-title":"Int. J. Res. Rev. Comput. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Bonsangue, M.M., and Johnsen, E.B. (2007). Formal Modeling and Analysis of the OGDC Wireless Sensor Network Algorithm in Real-Time Maude. Formal Methods for Open Object-Based Distributed Systems, Springer.","DOI":"10.1007\/978-3-540-72952-5"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Wermelinger, M., and Margaria-Steffen, T. (2004). Specification and Analysis of Real-Time Systems Using Real-Time Maude. Fundamental Approaches to Software Engineering, Springer.","DOI":"10.1007\/b95935"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.entcs.2005.10.040","article-title":"PMaude: Rewrite-based Specification Language for Probabilistic Object Systems","volume":"153","author":"Agha","year":"2006","journal-title":"Electron. Notes Theor. Comput. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"156","DOI":"10.5121\/ijwmn.2010.2211","article-title":"Probabilistic verification and evaluation of Backoff procedure of the WSN ECo-MAC protocol","volume":"2","author":"Zayani","year":"2010","journal-title":"Int. J. Wirel. Mob. Netw."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/j.ifacol.2016.07.441","article-title":"Algebraic fault detection and isolation for parabolic distributed\u2013parameter systems using modulation functions","volume":"49","author":"Fischer","year":"2016","journal-title":"IFAC-PapersOnLine"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1007\/978-3-319-49806-5_23","article-title":"Formal Verification of a Cross-Layer, Trustful Space-Time Protocol for Wireless Sensor Networks","volume":"10063","author":"Silva","year":"2016","journal-title":"Lect. Notes Comput. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/s10732-014-9258-x","article-title":"Heuristic strategies for assessing wireless sensor network resiliency: An event-based formal approach","volume":"21","author":"Testa","year":"2015","journal-title":"J. Heuristics"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1109\/COMST.2002.5341329","article-title":"Formal methods for specification and analysis of communication protocols","volume":"4","author":"Babich","year":"2002","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1142\/S0218194013400135","article-title":"Resource Oriented Workflow Nets and Workflow Resource Requirement Analysis","volume":"23","author":"Wang","year":"2013","journal-title":"Int. J. Softw. Eng. Knowl. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"6837","DOI":"10.1016\/j.ifacol.2017.08.1204","article-title":"A Discussion on Fault detection for a class of Hybrid Petri Nets","volume":"50","author":"Lefebvre","year":"2017","journal-title":"IFAC-PapersOnLine"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Dimitrakos, T., Moona, R., Patel, D., and McKnight, D.H. (2012). A Provenance-Based Trust Model for Delay Tolerant Networks. Trust Management VI, Springer.","DOI":"10.1007\/978-3-642-29852-3"},{"key":"ref_34","unstructured":"Lory, P. (2003, January 1\u20135). A colored Petri net trust model. Proceedings of the 14th International Workshop on Database and Expert Systems Applications, Prague, Czech Republic."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Kapitanova, K., and Son, S.H. (2009, January 17\u201319). MEDAL: A coMpact event description and analysis language for wireless sensor networks. Proceedings of the 2009 Sixth International Conference on Networked Sensing Systems (INSS), Pittsburgh, PA, USA.","DOI":"10.1109\/INSS.2009.5409936"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1007\/978-3-030-04648-4_19","article-title":"A Formal Model for Temporal\u2014Spatial Event in Internet of Vehicles","volume":"11280","author":"Wang","year":"2018","journal-title":"Lect. Notes Comput. Sci."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1023\/B:AIRE.0000045502.10941.a9","article-title":"A Survey of Outlier Detection Methodologies","volume":"22","author":"Hodge","year":"2004","journal-title":"Artif. Intell. Rev."},{"key":"ref_38","unstructured":"Chandola, V., Banerjee, A., and Kumar, V. (2007). Outlier Detection: A Survey, University of Minnesota. Technical Report 07-017."},{"key":"ref_39","first-page":"130","article-title":"Trust Management Scheme Based on D-S Evidence Theory for Wireless Sensor Networks","volume":"2013","author":"Feng","year":"2013","journal-title":"Int. J. Distrib. Sens. Netw."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/8\/1916\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:46:29Z","timestamp":1760186789000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/8\/1916"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,23]]},"references-count":39,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2019,4]]}},"alternative-id":["s19081916"],"URL":"https:\/\/doi.org\/10.3390\/s19081916","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,4,23]]}}}