{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T17:11:02Z","timestamp":1784135462524,"version":"3.55.0"},"reference-count":41,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,7,29]],"date-time":"2022-07-29T00:00:00Z","timestamp":1659052800000},"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":["61773044"],"award-info":[{"award-number":["61773044"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["WDZC2019601A301"],"award-info":[{"award-number":["WDZC2019601A301"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["6142004210102"],"award-info":[{"award-number":["6142004210102"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62073009"],"award-info":[{"award-number":["62073009"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Key Laboratory of Science and Technology on Reliability and Environmental Engineering","award":["61773044"],"award-info":[{"award-number":["61773044"]}]},{"name":"National Key Laboratory of Science and Technology on Reliability and Environmental Engineering","award":["WDZC2019601A301"],"award-info":[{"award-number":["WDZC2019601A301"]}]},{"name":"National Key Laboratory of Science and Technology on Reliability and Environmental Engineering","award":["6142004210102"],"award-info":[{"award-number":["6142004210102"]}]},{"name":"National Key Laboratory of Science and Technology on Reliability and Environmental Engineering","award":["62073009"],"award-info":[{"award-number":["62073009"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61773044"],"award-info":[{"award-number":["61773044"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["WDZC2019601A301"],"award-info":[{"award-number":["WDZC2019601A301"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["6142004210102"],"award-info":[{"award-number":["6142004210102"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62073009"],"award-info":[{"award-number":["62073009"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Resilience, the ability of a system to withstand disruptions and quickly return to a normal state, is essential for a low-Earth-orbit satellite communication system (LEO-SCS), as its large number of satellites, may encounter various disturbances. As a developing system with asymmetrical and insufficient data, it is with both aleatory and epistemic uncertainties, which renders existing resilience measures inapplicable. This paper utilizes uncertainty theory to define belief instantaneous availability, based on which a new resilience measure for the LEO-SCS is proposed. As the resilience is mainly determined by the dynamic and uncertain characteristics of an LEO-SCS, an uncertain satellite network evolution model is developed to describe its operating patterns, and an evaluation method is proposed to estimate its resilience. To illustrate our proposed uncertain theory-based resilience evaluation method, an LEO-SCS case with 48 satellites is studied, and its resilience values under different backup strategies are compared to assist in system design decisions.<\/jats:p>","DOI":"10.3390\/sym14081568","type":"journal-article","created":{"date-parts":[[2022,8,1]],"date-time":"2022-08-01T23:49:27Z","timestamp":1659397767000},"page":"1568","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Uncertainty Theory-Based Resilience Analysis for LEO Satellite Communication Systems"],"prefix":"10.3390","volume":"14","author":[{"given":"Ji","family":"Ma","sequence":"first","affiliation":[{"name":"School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4488-6574","authenticated-orcid":false,"given":"Rui","family":"Kang","sequence":"additional","affiliation":[{"name":"School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China"},{"name":"Science and Technology on Reliability and Environmental Engineering Laboratory, Beijing 100191, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruiying","family":"Li","sequence":"additional","affiliation":[{"name":"School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China"},{"name":"Science and Technology on Reliability and Environmental Engineering Laboratory, Beijing 100191, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qingyuan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China"},{"name":"Science and Technology on Reliability and Environmental Engineering Laboratory, Beijing 100191, China"},{"name":"School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liang","family":"Liu","sequence":"additional","affiliation":[{"name":"Institute of Telecommunication and Navigation Satellites, China Academy of Space Technology, Beijing 100094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xuewang","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Telecommunication and Navigation Satellites, China Academy of Space Technology, Beijing 100094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Schrogl, K.U. (2019). Handbook of Space Security: Policies, Applications and Programs, Springer.","DOI":"10.1007\/978-3-030-23210-8"},{"key":"ref_2","unstructured":"DOD (2011). FACT SHEET: Resilience of Space Capabilities, Department of Defence. Technical Report."},{"key":"ref_3","unstructured":"Turner, J.S. (2014). A Methodology for Measuring Resilience in a Satellite-Based Communication Network. [Master\u2019s Thesis, Air University]."},{"key":"ref_4","unstructured":"Han, J., Zhang, Y.S., Tang, Y.F., and Tong, Z. (2019). A method of communication constellation resilience evaluation. IOP Conference Series: Materials Science and Engineering, IOP Publishing."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"106608","DOI":"10.1016\/j.ress.2019.106608","article-title":"Space mission resilience with inter-satellite networking","volume":"193","author":"Lowe","year":"2020","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1109\/JSYST.2009.2017396","article-title":"Methodology for assessing the resilience of networked infrastructure","volume":"3","author":"Reed","year":"2009","journal-title":"IEEE Syst. J."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.strusafe.2011.12.004","article-title":"A three-stage resilience analysis framework for urban infrastructure systems","volume":"36\u201337","author":"Ouyang","year":"2012","journal-title":"Struct. Saf."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Li, R., Dong, Q., Jin, C., and Kang, R. (2017). A new resilience measure for supply chain networks. Sustainability, 9.","DOI":"10.3390\/su9010144"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4687","DOI":"10.1109\/JSYST.2020.3036129","article-title":"Uncertainty of resilience in complex networks with nonlinear dynamics","volume":"15","author":"Moutsinas","year":"2021","journal-title":"IEEE Syst. J."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.strusafe.2008.06.020","article-title":"Aleatory or epistemic? Does it matter?","volume":"31","author":"Kiureghian","year":"2009","journal-title":"Struct. Saf."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/j.actaastro.2019.08.024","article-title":"Space systems resilience optimisation under epistemic uncertainty","volume":"165","author":"Filippi","year":"2019","journal-title":"Acta Astronaut."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1007\/PL00012898","article-title":"An assessment of the RAIM performance of a combined Galileo\/GPS navigation system using the marginally detectable errors (MDE) algorithm","volume":"5","author":"Ochieng","year":"2002","journal-title":"GPS Solut."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Dong, Q., Li, R., and Kang, R. (2022). System resilience evaluation and optimization considering epistemic uncertainty. Symmetry, 14.","DOI":"10.3390\/sym14061182"},{"key":"ref_14","unstructured":"Liu, B. (2007). Uncertainty Theory, Springer."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1007\/s00500-012-0935-0","article-title":"Uncertain random variables: A mixture of uncertainty and randomness","volume":"17","author":"Liu","year":"2012","journal-title":"Soft Comput."},{"key":"ref_16","unstructured":"Liu, B. (2010). Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, Springer."},{"key":"ref_17","unstructured":"Ebeling, C. (2010). An Introduction to Reliability and Maintainability Engineering, Waveland Press."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"15505","DOI":"10.1109\/ACCESS.2017.2733839","article-title":"A model-based reliability metric considering aleatory and epistemic uncertainty","volume":"5","author":"Zeng","year":"2017","journal-title":"IEEE Access"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Ippolito, L.J. (2017). Satellite Communications Systems Engineering: Atmospheric Effects, Satellite Link Design and System Performance, Wiley. [2nd ed.].","DOI":"10.1002\/9781119259411"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"6009","DOI":"10.1109\/TVT.2019.2910570","article-title":"Temporal netgrid model-based dynamic routing in large-scale small satellite networks","volume":"68","author":"Li","year":"2019","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1109\/90.917071","article-title":"A distributed routing algorithm for datagram traffic in LEO satellite networks","volume":"9","author":"Ekici","year":"2001","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1109\/MWC.2007.386616","article-title":"Exploring the routing strategies in next-generation satellite networks","volume":"14","author":"Alagoz","year":"2007","journal-title":"IEEE Wirel. Commun."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Williams, A., Harding, W., and Hagemeier, H. (1999, January 28\u201330). Assessment of responsive replenishment launch for constellation management. Proceedings of the Space Technology Conference and Exposition, Albuquerque, NM, USA.","DOI":"10.2514\/6.1999-4615"},{"key":"ref_24","unstructured":"Zhang, G., and Zhang, H. (2001). Satellite Mobile Communication System, Posts & Telecom Press."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Li, J., and Li, Y. (2016, January 14\u201317). Modeling Ka-band satellite communication system with MPSK. Proceedings of the 2nd IEEE International Conference on Computer and Communications, Chengdu, China.","DOI":"10.1109\/CompComm.2016.7925009"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1109\/JSYST.2020.2980760","article-title":"End-to-end reliability of satellite communication network systems","volume":"15","author":"Jung","year":"2021","journal-title":"IEEE Syst. J."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1109\/MNET.001.1900550","article-title":"Enhancing the resilience of low earth orbit remote sensing satellite networks","volume":"34","author":"Yang","year":"2020","journal-title":"IEEE Netw."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1563","DOI":"10.1049\/iet-com.2009.0460","article-title":"Routing metrics for store and forward satellite constellations","volume":"4","author":"Franck","year":"2010","journal-title":"IET Commun."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4447","DOI":"10.1109\/TVT.2009.2019281","article-title":"Multicast QoS core-based tree routing protocol and genetic algorithm over an HAP-satellite architecture","volume":"58","author":"Rango","year":"2009","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Liang, J., Xiao, N., and Zhang, J. (2011). Constellation design and performance simulation of LEO satellite communication system. Communications in Computer and Information Science, Springer.","DOI":"10.1007\/978-3-642-23220-6_27"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1657","DOI":"10.1007\/s11276-009-0220-z","article-title":"A sustainable heuristic QoS routing algorithm for pervasive multi-layered satellite wireless networks","volume":"16","author":"Long","year":"2009","journal-title":"Wirel. Netw."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"675","DOI":"10.2514\/2.3267","article-title":"Systems engineering trades for the IRIDIUM constellation","volume":"34","author":"Garrison","year":"1997","journal-title":"J. Spacecr. Rocket."},{"key":"ref_33","unstructured":"Li, J. (June, January 28). The method of health management on satellite constellation network. Proceedings of the 15th International Conference on Space Operations, Marseilles, France."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1109\/LCOMM.2013.011113.122635","article-title":"Virtual topology for LEO satellite networks based on earth-fixed footprint mode","volume":"17","author":"Lu","year":"2013","journal-title":"IEEE Commun. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1636","DOI":"10.1109\/49.634801","article-title":"A dynamic routing concept for ATM-based satellite personal communication networks","volume":"15","author":"Werner","year":"1997","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2591","DOI":"10.1016\/j.camwa.2011.07.058","article-title":"Shortest path problem with uncertain arc lengths","volume":"62","author":"Gao","year":"2011","journal-title":"Comput. Math. Appl."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2351","DOI":"10.1049\/iet-cta.2010.0278","article-title":"State estimation with delayed measurements incorporating time-delay uncertainty","volume":"6","author":"Choi","year":"2012","journal-title":"IET Control Theory Appl."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Naka, H., Deng, M., and Noge, Y. (September, January 30). Particle filter based remote control for processeswith communication delays. Proceedings of the 2018 International Conference on Advanced Mechatronic Systems, Zhengzhou, China.","DOI":"10.1109\/ICAMechS.2018.8507022"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1002\/dac.823","article-title":"Priority-based adaptive routing in NGEO satellite networks","volume":"20","author":"Jamalipour","year":"2007","journal-title":"Int. J. Commun. Syst."},{"key":"ref_40","unstructured":"(2021, November 06). List of Countries by Number of Internet Users. Available online: https:\/\/en.wikipedia.org\/wiki\/List_of_countries_by_number_of_Internet_users."},{"key":"ref_41","unstructured":"(2021, November 06). The World Factbook, Available online: https:\/\/www.cia.gov\/the-world-factbook\/."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/8\/1568\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:59:19Z","timestamp":1760140759000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/8\/1568"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,29]]},"references-count":41,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["sym14081568"],"URL":"https:\/\/doi.org\/10.3390\/sym14081568","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,29]]}}}