IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v254y2025ipas0951832024006793.html
   My bibliography  Save this article

Toward the resilience of UAV swarms with percolation theory under attacks

Author

Listed:
  • Hu, Tianzhen
  • Zong, Yan
  • Lu, Ningyun
  • Jiang, Bin

Abstract

Unmanned aerial swarms have been widely applied across various domains. The security of swarms against attacks has been of significance. However, there still exists a lack of quantitatively assessing the unmanned swarm resilience against attacks. Thus, this work adopts the percolation theory to mathematically analyse the resilience of the unmanned aerial swarms after random attacks. In addition to the typically used popularity in the preferential attachment, distance of neighbours is taken into account for modelling unmanned swarms, which is missing in the literature. This improved preferential attachment-based swarm model offers a more precise and realistic description of swarm behaviours. In addition, an attack model is proposed, which can be a description of dynamic attacks. Moreover, this study also utilizes the percolation theory to assess the resilience of swarms after the random attacks. Finally, the simulation results show that the resilience derived using percolation theory aligns with the improved swarm model. The proposed swarm model maintains 79% resilience when 20% of the UAVs are attacked under random attacks, and even 69.4% resilience when 20% of the UAVs are attacked under initial betweenness-based attacks.

Suggested Citation

  • Hu, Tianzhen & Zong, Yan & Lu, Ningyun & Jiang, Bin, 2025. "Toward the resilience of UAV swarms with percolation theory under attacks," Reliability Engineering and System Safety, Elsevier, vol. 254(PA).
    • Handle: RePEc:eee:reensy:v:254:y:2025:i:pa:s0951832024006793
    DOI: 10.1016/j.ress.2024.110608
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832024006793
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2024.110608?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wang, Shuliang & Guo, Zhaoyang & Huang, Xiaodi & Zhang, Jianhua, 2024. "A three-stage model of quantifying and analyzing power network resilience based on network theory," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    2. Liang, Yuanyuan & Xia, Yongxiang & Yang, Xu-Hua, 2022. "Hybrid-radius spatial network model and its robustness analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 591(C).
    3. Bai, Guanghan & Li, Yanjun & Fang, Yining & Zhang, Yun-An & Tao, Junyong, 2020. "Network approach for resilience evaluation of a UAV swarm by considering communication limits," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    4. Sun, Xuting & Hu, Yue & Qin, Yichen & Zhang, Yuan, 2024. "Risk assessment of unmanned aerial vehicle accidents based on data-driven Bayesian networks," Reliability Engineering and System Safety, Elsevier, vol. 248(C).
    5. Andrews, J.D. & Poole, J. & Chen, W.H., 2013. "Fast mission reliability prediction for Unmanned Aerial Vehicles," Reliability Engineering and System Safety, Elsevier, vol. 120(C), pages 3-9.
    6. Zhou, Xinxin & Huang, Yun & Bai, Guanghan & Xu, Bei & Tao, Junyong, 2024. "The resilience evaluation of unmanned autonomous swarm with informed agents under partial failure," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    7. Feng, Qiang & Liu, Meng & Dui, Hongyan & Ren, Yi & Sun, Bo & Yang, Dezhen & Wang, Zili, 2022. "Importance measure-based phased mission reliability and UAV number optimization for swarm," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    8. Xu, Bei & Bai, Guanghan & Liu, Tao & Fang, Yining & Zhang, Yun-an & Tao, Junyong, 2023. "An improved swarm model with informed agents to prevent swarm-splitting," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    9. Hunt, Kyle & Agarwal, Puneet & Zhuang, Jun, 2022. "On the adoption of new technology to enhance counterterrorism measures: An attacker–defender game with risk preferences," Reliability Engineering and System Safety, Elsevier, vol. 218(PB).
    10. Wandelt, Sebastian & Xu, Yifan & Sun, Xiaoqian, 2023. "Measuring node importance in air transportation systems: On the quality of complex network estimations," Reliability Engineering and System Safety, Elsevier, vol. 240(C).
    11. Réka Albert & Hawoong Jeong & Albert-László Barabási, 2000. "Error and attack tolerance of complex networks," Nature, Nature, vol. 406(6794), pages 378-382, July.
    12. Woods, David D., 2015. "Four concepts for resilience and the implications for the future of resilience engineering," Reliability Engineering and System Safety, Elsevier, vol. 141(C), pages 5-9.
    13. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 1999. "Mean-field theory for scale-free random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(1), pages 173-187.
    14. Zhang, Chi & Liu, Tao & Bai, Guanghan & Tao, Junyong & Zhu, Wenjin, 2024. "A dynamic resilience evaluation method for cross-domain swarms in confrontation," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    15. Lu, Qing-Long & Sun, Wenzhe & Dai, Jiannan & Schmöcker, Jan-Dirk & Antoniou, Constantinos, 2024. "Traffic resilience quantification based on macroscopic fundamental diagrams and analysis using topological attributes," Reliability Engineering and System Safety, Elsevier, vol. 247(C).
    16. Liu, Tao & Bai, Guanghan & Tao, Junyong & Zhang, Yun-An & Fang, Yining, 2024. "A Multistate Network Approach for Resilience Analysis of UAV Swarm considering Information Exchange Capacity," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    17. Kong, Linghao & Wang, Lizhi & Cao, Zhongzheng & Wang, Xiaohong, 2024. "Resilience evaluation of UAV swarm considering resource supplementation," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Hongxu & Zhong, Yuanfu & Zhuang, Xuebin, 2024. "A soft resource optimization method based on autonomous coordination of unmanned swarms system driven by resilience," Reliability Engineering and System Safety, Elsevier, vol. 249(C).
    2. Zhang, Chi & Liu, Tao & Bai, Guanghan & Tao, Junyong & Zhu, Wenjin, 2024. "A dynamic resilience evaluation method for cross-domain swarms in confrontation," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    3. Sun, Qin & Li, Hongxu & Zhong, Yuanfu & Ren, Kezhou & Zhang, Yingchao, 2024. "Deep reinforcement learning-based resilience enhancement strategy of unmanned weapon system-of-systems under inevitable interferences," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    4. Kong, Linghao & Wang, Lizhi & Cao, Zhongzheng & Wang, Xiaohong, 2024. "Resilience evaluation of UAV swarm considering resource supplementation," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    5. Zhou, Xinxin & Huang, Yun & Bai, Guanghan & Xu, Bei & Tao, Junyong, 2024. "The resilience evaluation of unmanned autonomous swarm with informed agents under partial failure," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    6. Song, Xueying & Qi, Lei & Liu, Shiyan & Ding, Shuiting & Li, Daqing, 2024. "Simple analysis of complex system safety based on Finite State Machine Network and phase space theory," Reliability Engineering and System Safety, Elsevier, vol. 249(C).
    7. Wouter Vermeer & Otto Koppius & Peter Vervest, 2018. "The Radiation-Transmission-Reception (RTR) model of propagation: Implications for the effectiveness of network interventions," PLOS ONE, Public Library of Science, vol. 13(12), pages 1-21, December.
    8. Laurienti, Paul J. & Joyce, Karen E. & Telesford, Qawi K. & Burdette, Jonathan H. & Hayasaka, Satoru, 2011. "Universal fractal scaling of self-organized networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3608-3613.
    9. Zhang, Hai-Feng & Wang, Hao-Ren & Xiang, Bing-Bing & Wang, Huan, 2024. "Robustness study of hybrid hypergraphs," Reliability Engineering and System Safety, Elsevier, vol. 252(C).
    10. Deng, Ye & Wang, Zhigang & Xiao, Yu & Shen, Xiaoda & Kurths, Jürgen & Wu, Jun, 2025. "Spatial network disintegration based on spatial coverage," Reliability Engineering and System Safety, Elsevier, vol. 253(C).
    11. Kashin Sugishita & Yasuo Asakura, 2021. "Vulnerability studies in the fields of transportation and complex networks: a citation network analysis," Public Transport, Springer, vol. 13(1), pages 1-34, March.
    12. Cerqueti, Roy & Ferraro, Giovanna & Iovanella, Antonio, 2019. "Measuring network resilience through connection patterns," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 320-329.
    13. Zhang, Jingru & Fang, Zhigeng & Dong, Wenjie & Liu, Sifeng & Chen, Ding, 2024. "A mission success probability assessment framework for phased-mission-systems using extended graphical evaluation and review technique," Reliability Engineering and System Safety, Elsevier, vol. 249(C).
    14. Ying Duan & Xiuwen Fu & Wenfeng Li & Yu Zhang & Giancarlo Fortino, 2017. "Evolution of Scale-Free Wireless Sensor Networks with Feature of Small-World Networks," Complexity, Hindawi, vol. 2017, pages 1-15, July.
    15. Elena Zaitseva & Vitaly Levashenko & Ravil Mukhamediev & Nicolae Brinzei & Andriy Kovalenko & Adilkhan Symagulov, 2023. "Review of Reliability Assessment Methods of Drone Swarm (Fleet) and a New Importance Evaluation Based Method of Drone Swarm Structure Analysis," Mathematics, MDPI, vol. 11(11), pages 1-26, June.
    16. Tran, Huy T. & Balchanos, Michael & Domerçant, Jean Charles & Mavris, Dimitri N., 2017. "A framework for the quantitative assessment of performance-based system resilience," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 73-84.
    17. David L. Alderson, 2008. "OR FORUM---Catching the “Network Science” Bug: Insight and Opportunity for the Operations Researcher," Operations Research, INFORMS, vol. 56(5), pages 1047-1065, October.
    18. Dui, Hongyan & Zhang, Chi & Bai, Guanghan & Chen, Liwei, 2021. "Mission reliability modeling of UAV swarm and its structure optimization based on importance measure," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    19. Wu, Tingwei & Xia, Yongxiang & Liang, Yuanyuan, 2024. "Load cascades in spatial networks: A sandpile model approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 644(C).
    20. Liu, Tao & Bai, Guanghan & Tao, Junyong & Zhang, Yun-An & Fang, Yining, 2024. "A Multistate Network Approach for Resilience Analysis of UAV Swarm considering Information Exchange Capacity," Reliability Engineering and System Safety, Elsevier, vol. 241(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:254:y:2025:i:pa:s0951832024006793. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.