{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T14:25:22Z","timestamp":1769696722683,"version":"3.49.0"},"reference-count":32,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,4,24]],"date-time":"2022-04-24T00:00:00Z","timestamp":1650758400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guizhou Education Department under Grant Qianjiaohe","award":["No.KY[2021]012"],"award-info":[{"award-number":["No.KY[2021]012"]}]},{"name":"Science and Technology Fund of Guizhou Province under Grant Qiankehe","award":["No.[2020]1Y266"],"award-info":[{"award-number":["No.[2020]1Y266"]}]},{"name":"Industrial Project of Guizhou province under Grant Qiankehe","award":["No.[2019]2152"],"award-info":[{"award-number":["No.[2019]2152"]}]},{"name":"Plan of Guizhou province Qiankehe-plant under Grant","award":["No.[2017]5788"],"award-info":[{"award-number":["No.[2017]5788"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The original virtual force algorithm (VFA) is proposed for the two-dimensional node coverage and localization of wireless sensor networks (WSN). This work proposes a novel three-dimensional improved virtual force coverage (3D-IVFC) algorithm for the 3D coverage of nodes in WSN. Firstly, the node coverage theory is analyzed, which is about node coverage in three-dimensional space. Secondly, an improved three-dimensional space virtual force coverage method is proposed with an adaptive virtual force parameter control strategy. Finally, simulation experiments are utilized to verify the performance of the 3D-IVFC approach. Experimental results show that during random initialization, the average coverage rate of the improved 3D space coverage algorithm was increased by 0.76% and the deployment time was reduced by 0.1712 s; during center initialization, the average coverage rate of the improved 3D space coverage algorithm was increased by 0.65% and the coverage time increased slightly. Moreover, the proposed method is also used to solve the three-dimensional surface node coverage of the WSN.<\/jats:p>","DOI":"10.3390\/axioms11050199","type":"journal-article","created":{"date-parts":[[2022,4,24]],"date-time":"2022-04-24T22:22:41Z","timestamp":1650838961000},"page":"199","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["An Adaptive Three-Dimensional Improved Virtual Force Coverage Algorithm for Nodes in WSN"],"prefix":"10.3390","volume":"11","author":[{"given":"Mengjian","family":"Zhang","sequence":"first","affiliation":[{"name":"Electrical Engineering College, Guizhou University, Guiyang 550025, China"},{"name":"School of Computer Science and Engineering, South China University of Technology, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6407-1276","authenticated-orcid":false,"given":"Jing","family":"Yang","sequence":"additional","affiliation":[{"name":"Electrical Engineering College, Guizhou University, Guiyang 550025, China"},{"name":"Guizhou Provincial Key Laboratory of Internet + Intelligent Manufacturing, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Qin","sequence":"additional","affiliation":[{"name":"Electrical Engineering College, Guizhou University, Guiyang 550025, China"},{"name":"Guizhou Provincial Key Laboratory of Internet + Intelligent Manufacturing, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/S1389-1286(01)00302-4","article-title":"Wireless sensor networks: A survey","volume":"38","author":"Akyildiz","year":"2002","journal-title":"Comput. Netw."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/j.jnca.2015.09.008","article-title":"Applications of wireless sensor networks for urban areas: A survey","volume":"60","author":"Rashid","year":"2016","journal-title":"J. Netw. Comput. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/j.adhoc.2005.01.004","article-title":"Underwater acoustic sensor networks: Research challenges","volume":"3","author":"Akyildiz","year":"2005","journal-title":"Ad Hoc Netw."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1016\/j.adhoc.2006.04.003","article-title":"Wireless underground sensor networks: Research challenges","volume":"4","author":"Akyildiz","year":"2006","journal-title":"Ad Hoc Netw."},{"key":"ref_5","unstructured":"Huang, C.F., Tseng, Y., and Lo, L.C. (December, January 29). The coverage problem in three-dimensional wireless sensor networks. Proceedings of the IEEE Global Telecommunications Conference, Globecom\u201904, Dallas, TX, USA."},{"key":"ref_6","unstructured":"Watfa, M.K., and Commuri, S. (2006, January 23\u201325). The 3-dimensional wireless sensor network coverage problem. Proceedings of the IEEE International Conference on Networking, Sensing and Control, Ft. Lauderdale, FL, USA."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Zhao, M., Lei, J., Lei, J., Wu, M.Y., Liu, Y., and Shu, W. (2009, January 19\u201325). Surface coverage in wireless sensor networks. Proceedings of the IEEE INFOCOM, Rio de Janeiro, Brazil.","DOI":"10.1109\/INFCOM.2009.5061912"},{"key":"ref_8","first-page":"114","article-title":"Efficient deployment approach of wireless sensor networks on 3D terrains","volume":"13","author":"Zafer","year":"2021","journal-title":"Int. J. Data Min. Model. Manag."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Bai, X., Zhang, C., Xuan, D., and Jia, W. (2009, January 19\u201325). Full-coverage and k-connectivity (k=14,6) three dimensional networks. Proceedings of the IEEE INFOCOM, Rio de Janeiro, Brazil.","DOI":"10.1109\/INFCOM.2009.5061943"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5624","DOI":"10.1109\/JSEN.2020.2970435","article-title":"Energy-efficient barrier coverage with probabilistic sensors in wireless sensor networks","volume":"20","author":"Si","year":"2020","journal-title":"IEEE Sens. J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1508","DOI":"10.1109\/TMC.2020.3024939","article-title":"Toward a realistic approach for the deployment of 3D Wireless Sensor Networks","volume":"21","author":"Saad","year":"2022","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1109\/TC.2009.166","article-title":"A study of k-coverage and measures of connectivity in 3D wireless sensor networks","volume":"59","author":"Ammari","year":"2010","journal-title":"IEEE Trans. Comput."},{"key":"ref_13","first-page":"1447","article-title":"Research on deployment, coverage and connectivity in three- dimensional sensor networks","volume":"26","author":"Zhong","year":"2011","journal-title":"Control Decis."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.adhoc.2018.07.003","article-title":"Connectivity and coverage-based protocols for wireless sensor networks","volume":"80","author":"Boukerche","year":"2018","journal-title":"Ad Hoc Netw."},{"key":"ref_15","first-page":"713","article-title":"Sensor redeployment algorithm based on combined virtual forces in three-dimensional space","volume":"37","author":"Liu","year":"2011","journal-title":"Acta Autom. Sin."},{"key":"ref_16","first-page":"2570","article-title":"Three-dimensional space self-deployment algorithm based on virtual force compensation","volume":"36","author":"Tan","year":"2015","journal-title":"Chin. J. Sci. Instrum."},{"key":"ref_17","first-page":"613","article-title":"Autonomous deployment algorithm of three-dimensional mobile sensor network based on Voronoi diagram","volume":"31","author":"Tang","year":"2018","journal-title":"Chin. J. Sens. Actuators"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1177","DOI":"10.1109\/JSEE.2015.00128","article-title":"Virtual potential field and learning automata-based coverage control algorithm for directional sensor networks","volume":"37","author":"Chen","year":"2015","journal-title":"Syst. Eng. Electron."},{"key":"ref_19","unstructured":"Zou, Y., and Chakrabarty, K. (April, January 30). Sensor deployment and target localization based on virtual forces. Proceedings of the IEEE INFOCOM, San Francisco, CA, USA."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"103019","DOI":"10.1016\/j.jnca.2021.103019","article-title":"A distributed deployment algorithm for communication coverage in wireless robotic networks","volume":"180","author":"Liu","year":"2021","journal-title":"J. Netw. Comput. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Hu, T., and Zhong, S. (2021, January 21\u201323). Research on a virtual force algorithm in Wireless Sensor Network. Proceedings of the International Conference on Frontiers of Electronics, Information and Computation Technologies, Changsha, China.","DOI":"10.1145\/3474198.3478189"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"6665","DOI":"10.1007\/s12652-020-02286-3","article-title":"ERTC: An Enhanced RSSI based Tree Climbing mechanism for well-planned path localization in WSN using the virtual force of Mobile Anchor Node","volume":"12","author":"Thilagavathi","year":"2021","journal-title":"J. Ambient Intell. Humaniz. Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"21999","DOI":"10.1109\/JSEN.2021.3105138","article-title":"Obstacle handling mechanism for mobile anchor assisted localization in wireless sensor networks","volume":"21","author":"Sabale","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"103967","DOI":"10.1016\/j.robot.2021.103967","article-title":"A virtual force interaction scheme for multi-robot environment monitoring","volume":"149","author":"Ji","year":"2022","journal-title":"Robot. Auton. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Wang, S., Yang, X., Wang, X., and Qian, Z. (2019). A virtual force algorithm-L\u00e9vy-embedded grey wolf optimization algorithm for wireless sensor network coverage optimization. Sensors, 19.","DOI":"10.3390\/s19122735"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"19611","DOI":"10.1109\/JSEN.2021.3091619","article-title":"Coverage enhancement strategy for WSNs based on virtual force-directed ant lion optimization algorithm","volume":"21","author":"Yao","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"102694","DOI":"10.1016\/j.adhoc.2021.102694","article-title":"A hybrid coverage control for enhancing UWSN localizability using IBSO-VFA","volume":"123","author":"Luo","year":"2021","journal-title":"Ad Hoc Netw."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Zhang, M., Wang, D., and Yang, J. (2022). Hybrid-flash butterfly optimization algorithm with logistic mapping for solving the engineering constrained optimization problems. Entropy, 24.","DOI":"10.3390\/e24040525"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4521","DOI":"10.3390\/s100504521","article-title":"A multipath routing protocol based on clustering and ant colony optimization for wireless sensor networks","volume":"10","author":"Yang","year":"2010","journal-title":"Sensors"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"100342","DOI":"10.1016\/j.cosrev.2020.100342","article-title":"Nature-inspired algorithms for wireless sensor networks: A comprehensive survey","volume":"39","author":"Singh","year":"2021","journal-title":"Comput. Sci. Rev."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2375","DOI":"10.1109\/JIOT.2021.3094725","article-title":"Three-dimensional coverage optimization of underwater nodes under multi-constraints combined with water flow","volume":"9","author":"Luo","year":"2022","journal-title":"IEEE Internet Things J."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Yan, L., He, Y., and Huangfu, Z. (2021). An uneven node self-deployment optimization algorithm for maximized coverage and energy balance in underwater wireless sensor networks. 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