搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于时间序列的网络失效模型

严玉为 蒋沅 杨松青 余荣斌 洪成

引用本文:
Citation:

基于时间序列的网络失效模型

严玉为, 蒋沅, 杨松青, 余荣斌, 洪成

Network failure model based on time series

Yan Yu-Wei, Jiang Yuan, Yang Song-Qing, Yu Rong-Bin, Hong Cheng
PDF
HTML
导出引用
  • 随着网络科学的发展, 静态网络已不能清晰刻画网络的动态过程. 在现实网络中, 个体之间的交互随时间而快速演化. 这种网络模式将时间与交互过程紧密联系, 能够清晰刻画节点的动态过程. 因此, 如何更好地基于时间序列刻画网络行为变化是现有级联失效研究的重要问题. 为了更好地研究该问题, 本文提出一种基于时间序列的失效模型. 通过随机攻击某时刻的节点, 分析了时间、激活比例、连边数、连接概率4个参数对失效的影响并发现网络相变现象. 同时为验证该模型的有效性与科学性, 采用真实网络进行研究. 实验表明, 该模型兼顾时序以及传播动力学, 具有较好的可行性, 为解释现实动态网络的级联传播提供了参考.
    With the development of network science, the static network has been unable to clearly characterize the dynamic process of the network. In real networks, the interaction between individuals evolves rapidly over time. This network model closely links time to interaction process. Compared with static networks, dynamic networks can clearly describe the interaction time of nodes, which has more practical significance. Therefore, how to better describe the behavior changes of networks after being attacked based on time series is an important problem in the existing cascade failure research. In order to better answer this question, a failure model based on time series is proposed in this paper. The model is constructed according to time, activation ratio, number of edges and connection probability. By randomly attacking nodes at a certain time, the effects of four parameters on sequential networks are analyzed. In order to validate the validity and scientificity of this failure model, we use small social networks in the United States. The experimental results show that the model is feasible. The model takes into account the time as well as the spreading dynamics and provides a reference for explaining the dynamic networks in reality.
      通信作者: 蒋沅, jiangyuan@nchu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 61663030, 61663032)和江西省研究生创新专项(批准号: YC2021-S680)资助的课题
      Corresponding author: Jiang Yuan, jiangyuan@nchu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61663030, 61663032) and the Innovation Fund Designated for Graduate Students of Jiangxi Province, China (Grant No. YC2021-S680)
    [1]

    Holme P 2003 Europhys. Lett. 64 427Google Scholar

    [2]

    Holme P, Park S M, Kim B J, Edling C R 2007 Physica A 373 821Google Scholar

    [3]

    Onody R N, Castro P A 2004 Phys. Rev. E 70 037103Google Scholar

    [4]

    Albert R Jeong, H, Barabasi A 1999 Nature 401 130Google Scholar

    [5]

    Perra N, Gonçalves B, Pastor R, Vespignani A 2012 Sci. Rep. 2 469Google Scholar

    [6]

    Liao H, Mariani M S, Medo M, Zhang Y C 2017 Phys. Rep. 689 1Google Scholar

    [7]

    Li A, Cornelius S, Liu Y Y, Wang L, Barabasi, A 2016 Science 358 1042Google Scholar

    [8]

    Steven H 2001 Nature 401 268Google Scholar

    [9]

    Remacle, Jean F, Flaherty, Joseph E, Shephard, Mark S 2003 SIAM Rev. 45 53Google Scholar

    [10]

    杨松青, 蒋沅, 童天驰, 严玉为, 淦各升 2021 物理学报 70 216401Google Scholar

    Yang S Q, Jiang Y, Tong T C, Yan Y W, Gan G S 2021 Acta Phys. Sin. 70 216401Google Scholar

    [11]

    Sole R V, Rosas M, Corominas B, Valverde S 2007 Phys. Rev. E 77 26102Google Scholar

    [12]

    Goh K I, Kahng B, Kim D 2002 Phys. Rev. Lett. 88 108701Google Scholar

    [13]

    Holme P, Kim B J, Yoon C N, Han S K 2002 Phys. Rev. E 65 056109Google Scholar

    [14]

    Albert R, Jeong H, Barabasi A. L 2000 Nature 406 387Google Scholar

    [15]

    Zhou T, Wang B H 2005 Chin. Phys. Lett. 22 1072Google Scholar

    [16]

    Motter A E, Lai Y C 2003 Phys. Rev. E 66 065102Google Scholar

    [17]

    Dou B L, Wang X G, Zhang S Y 2010 Physica A 389 2310Google Scholar

    [18]

    Wang J 2012 Nonlinear Dyn. 70 1959Google Scholar

    [19]

    Li S, Li L, Yang Y, Luo Q 2012 Nonlinear Dyn. 69 837Google Scholar

    [20]

    Wang J, Rong L, Liang Z, Zhang Z 2008 Physica A 387 6671Google Scholar

    [21]

    Liu J, Xiong Q Y, Shi X, Wang K, Shi W R 2015 Chin. Phys. B 24 371Google Scholar

    [22]

    唐亮, 焦鹏, 李纪康, 靖可, 靳志宏 2018 控制与决策 33 116Google Scholar

    Tang L, Jiao P, Li J K, Jing K, Le Z H 2018 Control and Decision 33 116Google Scholar

    [23]

    Duan D L, Ling X D, Wu X Y, Ouyang D H, Zhong B 2014 Physica A 2014 416 252Google Scholar

    [24]

    郝羽成, 李成兵, 魏磊 2018 系统工程与电子技术 40 2282Google Scholar

    Hao Y C, Li C, Wei L 2018 Syst. Eng. Electron. 40 2282Google Scholar

  • 图 1  时序网络图 (a)T = 1; (b) T = 2; (c) T = 3; (d) T = 4; (e) T = 5; (f) T = 6; (g) T = All

    Fig. 1.  Sequential network: (a) T = 1; (b) T = 2; (c) T = 3; (d) T = 4; (e) T = 5; (f) T = 6; (g) T = All.

    图 2  时序网络传播示意图 (数字表示节点编号) (a) T = 1; (b) T = 2; (c) T = 3

    Fig. 2.  Propagation of sequential network (number indicates the node number): (a) T = 1; (b) T = 2; (c) T = 3.

    图 3  静态图与时序网络图 (a) 静态图; (b) 静态网络失效图; (c) 时序图

    Fig. 3.  Static diagram and sequential network diagram: (a) Static diagram; (b) static network failure diagram; (c) sequential network.

    图 4  不同激活参数的网络鲁棒性

    Fig. 4.  Robustness of networks under different activation parameters.

    图 5  不同激活参数下的网络生成图 (a) pactive = 0.1; (b) pactive = 0.2; (c) pactive = 0.3; (d) pactive = 0.5; (e) pactive = 0.6; (f) pactive = 1.0

    Fig. 5.  Network diagram with different activation parameters: (a) pactive = 0.1; (b) pactive = 0.2; (c) pactive = 0.3; (d) pactive = 0.5; (e) pactive = 0.6; (f) pactive = 1.0.

    图 6  不同边数以及连接概率下的网络鲁棒性 (a)不同连边数; (b)不同连接概率

    Fig. 6.  Network robustness under different connection numbers and connection probabilities: (a) Different edge numbers; (b) different connection probabilities.

    图 7  不同连接数以及连接概率下的网络生成图 (a) M = 1; (b) M = 2; (c) M = 5; (d) M = 8; (e) M = 10; (f) pcon = 0.1; (g) pcon = 0.2; (h) pcon = 0.5; (i) pcon = 0.6; (j) pcon = 1

    Fig. 7.  Network diagram with different connection numbers and connection Probability: (a)M = 1; (b)M = 2; (c) M = 5; (d) M = 8; (e) M = 10; (f) pcon = 0.1; (g) pcon = 0.2; (h) pcon = 0.5; (i) pcon = 0.6; (j) pcon = 1.

    图 8  网络鲁棒性

    Fig. 8.  Network robustness.

    图 9  不同时间下的网络鲁棒性

    Fig. 9.  Network robustness under different time.

    图 10  不同时间下的网络生成图 (a) T = 2; (b) T = 5; (c) T = 10; (d) T = 20; (e) T = 30

    Fig. 10.  Network diagram under different times: (a) T = 2; (b) T = 5; (c) T = 10; (d) T = 20; (e) T = 30.

    图 11  不同时间参数的网络鲁棒性

    Fig. 11.  Network robustness under different time.

    图 12  不同时间下的网络图 (a) T = 2; (b) T = 5; (c) T = 10; (d) T = 20; (e) T = 30

    Fig. 12.  Network diagram under different times: (a) T = 2; (b) T = 5; (c) T = 10; (d) T = 20; (e) T = 30.

    图 13  美国小型社交网络级联传递规模图

    Fig. 13.  Scale of transmission through small social networks in the United States

    表 1  激活参数下的网络特征

    Table 1.  Statistical characteristics of the networks under activation parameters.

    pactivenm$\langle {k^{ { { {\rm{in} }/{\rm{out} } } } } } \rangle$
    0.1200320.16
    0.2200680.34
    0.32001910.955
    0.52007873.945
    0.62008434.215
    1.0200320316.015
    下载: 导出CSV

    表 2  不同连接数以及连接概率下的网络特征

    Table 2.  Statistical characteristics of the networks under different connection numbers and connection probabilities.

    Parameternm$\langle {k^{ {\text{in} }/{\text{out} } } } \rangle$
    M = 1200120.060
    M = 2200240.120
    M = 52001430.715
    M = 82005072.535
    M = 102008534.265
    pcon = 0.1200160.080
    pcon = 0.2200450.225
    pcon = 0.52001790.895
    pcon = 0.62002761.380
    pcon = 1.02009834.915
    下载: 导出CSV

    表 3  不同时间下的网络特征

    Table 3.  Statistical characteristics of the networks under different time.

    Tnm$\langle {k^{ {\text{in} }/{\text{out} } } } \rangle$
    2200570.285
    5200680.340
    10200700.350
    20200810.405
    30200710.355
    下载: 导出CSV

    表 4  不同时间下的网络特征

    Table 4.  Statistical characteristics of the networks under different times.

    Tnm$\langle {k^{ {\text{in} }/{\text{out} } } } \rangle$
    22009314.655
    5200525826.290
    102001168958.445
    202001546477.320
    3020023062115.310
    下载: 导出CSV

    表 5  美国小型社交网络的接触时刻

    Table 5.  Contact time of small social networks in the United States.

    Source nodeTarget nodeTimeSource nodeTarget nodeTimeSource nodeTarget nodeTime
    ${v_1}$${v_{12}}$4${v_3}$${v_{13}}$2${v_{16}}$${v_{10}}$2
    ${v_1}$${v_{18}}$9${v_3}$${v_{18}}$2${v_{16}}$${v_{12}}$4
    ${v_2}$${v_{10}}$7${v_3}$${v_{25}}$2${v_{16}}$${v_{14}}$2
    ${v_2}$${v_{12}}$1${v_4}$${v_{10}}$4${v_{16}}$${v_{18}}$4
    ${v_2}$${v_{13}}$1${v_4}$${v_{12}}$1${v_{16}}$${v_{32}}$1
    ${v_2}$${v_{14}}$1${v_4}$${v_{27}}$1${v_{17}}$${v_{10}}$3
    ${v_2}$${v_{18}}$1${v_4}$${v_{32}}$4${v_{18}}$${v_{12}}$2
    ${v_3}$${v_{10}}$2${v_5}$${v_{12}}$4${v_{18}}$${v_{13}}$1
    ${v_5}$${v_{13}}$1${v_8}$${v_{10}}$1${v_{18}}$${v_{14}}$2
    ${v_5}$${v_{18}}$5${v_8}$${v_{12}}$2${v_{19}}$${v_{14}}$7
    ${v_5}$${v_{20}}$1${v_8}$${v_{13}}$7${v_{21}}$${v_{13}}$1
    ${v_5}$${v_{27}}$1${v_8}$${v_{15}}$1${v_{21}}$${v_{20}}$4
    ${v_7}$${v_1}$1${v_8}$${v_{18}}$2${v_{22}}$${v_{10}}$3
    ${v_7}$${v_{18}}$1${v_8}$${v_{20}}$2${v_{22}}$${v_{12}}$4
    ${v_7}$${v_{33}}$1${v_8}$${v_{27}}$2${v_{22}}$${v_{13}}$1
    ${v_8}$${v_2}$1${v_8}$${v_{32}}$2${v_{22}}$${v_{18}}$11
    ${v_9}$${v_1}$3${v_{11}}$${v_{10}}$3${v_{22}}$${v_{27}}$3
    ${v_9}$${v_5}$2${v_{11}}$${v_{12}}$1${v_{22}}$${v_{31}}$1
    ${v_9}$${v_{12}}$1${v_{11}}$${v_{14}}$6${v_{24}}$${v_3}$2
    ${v_9}$${v_{18}}$1${v_{11}}$${v_{18}}$1${v_{24}}$${v_6}$1
    ${v_9}$${v_{33}}$2${v_{11}}$${v_{25}}$1${v_{24}}$${v_{10}}$8
    ${v_{10}}$${v_{12}}$1${v_{11}}$${v_{30}}$3${v_{24}}$${v_{12}}$4
    ${v_{10}}$${v_{13}}$1${v_{11}}$${v_{32}}$1${v_{24}}$${v_{13}}$3
    ${v_{10}}$${v_{18}}$2${v_{16}}$${v_2}$1${v_{24}}$${v_{18}}$2
    ${v_{24}}$${v_{25}}$3${v_{28}}$${v_5}$10${v_{33}}$${v_{10}}$2
    ${v_{24}}$${v_{32}}$3${v_{28}}$${v_{12}}$2${v_{33}}$${v_{14}}$2
    ${v_{24}}$${v_{33}}$1${v_{28}}$${v_{23}}$1${v_{33}}$${v_{25}}$1
    ${v_{24}}$${v_{35}}$1${v_{29}}$${v_3}$1${v_{34}}$${v_{10}}$1
    ${v_{25}}$${v_{10}}$1${v_{29}}$${v_{10}}$2${v_{34}}$${v_{12}}$9
    ${v_{25}}$${v_{12}}$5${v_{29}}$${v_{12}}$6${v_{34}}$${v_{13}}$1
    ${v_{25}}$${v_{14}}$4${v_{29}}$${v_{14}}$2${v_{34}}$${v_{14}}$1
    ${v_{25}}$${v_{18}}$2${v_{29}}$${v_{15}}$2${v_{34}}$${v_{18}}$7
    ${v_{26}}$${v_{10}}$3${v_{29}}$${v_{25}}$1${v_{34}}$${v_{20}}$2
    ${v_{26}}$${v_{12}}$1${v_{29}}$${v_{32}}$4${v_{35}}$${v_2}$1
    ${v_{26}}$${v_{14}}$12${v_{30}}$${v_{13}}$1${v_{35}}$${v_6}$1
    ${v_{26}}$${v_{15}}$2${v_{30}}$${v_{14}}$7${v_{35}}$${v_{10}}$2
    ${v_{26}}$${v_{18}}$1${v_{31}}$${v_{10}}$2${v_{35}}$${v_{12}}$2
    ${v_{26}}$${v_{30}}$3${v_{31}}$${v_{13}}$3${v_{35}}$${v_{13}}$1
    ${v_{35}}$${v_{14}}$4${v_{35}}$${v_{25}}$2${v_{35}}$${v_{32}}$3
    ${v_{35}}$${v_{18}}$1
    下载: 导出CSV
  • [1]

    Holme P 2003 Europhys. Lett. 64 427Google Scholar

    [2]

    Holme P, Park S M, Kim B J, Edling C R 2007 Physica A 373 821Google Scholar

    [3]

    Onody R N, Castro P A 2004 Phys. Rev. E 70 037103Google Scholar

    [4]

    Albert R Jeong, H, Barabasi A 1999 Nature 401 130Google Scholar

    [5]

    Perra N, Gonçalves B, Pastor R, Vespignani A 2012 Sci. Rep. 2 469Google Scholar

    [6]

    Liao H, Mariani M S, Medo M, Zhang Y C 2017 Phys. Rep. 689 1Google Scholar

    [7]

    Li A, Cornelius S, Liu Y Y, Wang L, Barabasi, A 2016 Science 358 1042Google Scholar

    [8]

    Steven H 2001 Nature 401 268Google Scholar

    [9]

    Remacle, Jean F, Flaherty, Joseph E, Shephard, Mark S 2003 SIAM Rev. 45 53Google Scholar

    [10]

    杨松青, 蒋沅, 童天驰, 严玉为, 淦各升 2021 物理学报 70 216401Google Scholar

    Yang S Q, Jiang Y, Tong T C, Yan Y W, Gan G S 2021 Acta Phys. Sin. 70 216401Google Scholar

    [11]

    Sole R V, Rosas M, Corominas B, Valverde S 2007 Phys. Rev. E 77 26102Google Scholar

    [12]

    Goh K I, Kahng B, Kim D 2002 Phys. Rev. Lett. 88 108701Google Scholar

    [13]

    Holme P, Kim B J, Yoon C N, Han S K 2002 Phys. Rev. E 65 056109Google Scholar

    [14]

    Albert R, Jeong H, Barabasi A. L 2000 Nature 406 387Google Scholar

    [15]

    Zhou T, Wang B H 2005 Chin. Phys. Lett. 22 1072Google Scholar

    [16]

    Motter A E, Lai Y C 2003 Phys. Rev. E 66 065102Google Scholar

    [17]

    Dou B L, Wang X G, Zhang S Y 2010 Physica A 389 2310Google Scholar

    [18]

    Wang J 2012 Nonlinear Dyn. 70 1959Google Scholar

    [19]

    Li S, Li L, Yang Y, Luo Q 2012 Nonlinear Dyn. 69 837Google Scholar

    [20]

    Wang J, Rong L, Liang Z, Zhang Z 2008 Physica A 387 6671Google Scholar

    [21]

    Liu J, Xiong Q Y, Shi X, Wang K, Shi W R 2015 Chin. Phys. B 24 371Google Scholar

    [22]

    唐亮, 焦鹏, 李纪康, 靖可, 靳志宏 2018 控制与决策 33 116Google Scholar

    Tang L, Jiao P, Li J K, Jing K, Le Z H 2018 Control and Decision 33 116Google Scholar

    [23]

    Duan D L, Ling X D, Wu X Y, Ouyang D H, Zhong B 2014 Physica A 2014 416 252Google Scholar

    [24]

    郝羽成, 李成兵, 魏磊 2018 系统工程与电子技术 40 2282Google Scholar

    Hao Y C, Li C, Wei L 2018 Syst. Eng. Electron. 40 2282Google Scholar

  • [1] 杨武华, 王彩琳, 张如亮, 张超, 苏乐. 高压IGBT雪崩鲁棒性的研究. 物理学报, 2023, 72(7): 078501. doi: 10.7498/aps.72.20222248
    [2] 赵豪, 冯晋霞, 孙婧可, 李渊骥, 张宽收. 连续变量Einstein-Podolsky-Rosen纠缠态光场在光纤信道中分发时纠缠的鲁棒性. 物理学报, 2022, 71(9): 094202. doi: 10.7498/aps.71.20212380
    [3] 潘倩倩, 刘润然, 贾春晓. 具有弱依赖组的复杂网络上的级联失效. 物理学报, 2022, (): . doi: 10.7498/aps.71.20210850
    [4] 潘倩倩, 刘润然, 贾春晓. 具有弱依赖组的复杂网络上的级联失效. 物理学报, 2022, 71(11): 110505. doi: 10.7498/aps.70.20210850
    [5] 蒋文君, 刘润然, 范天龙, 刘霜霜, 吕琳媛. 多层网络级联失效的预防和恢复策略概述. 物理学报, 2020, 69(8): 088904. doi: 10.7498/aps.69.20192000
    [6] 韩伟涛, 伊鹏, 马海龙, 张鹏, 田乐. 异质弱相依网络鲁棒性研究. 物理学报, 2019, 68(18): 186401. doi: 10.7498/aps.68.20190761
    [7] 李军, 李大超. 基于优化核极限学习机的风电功率时间序列预测. 物理学报, 2016, 65(13): 130501. doi: 10.7498/aps.65.130501
    [8] 高彦丽, 陈世明. 一种全局同质化相依网络耦合模式. 物理学报, 2016, 65(14): 148901. doi: 10.7498/aps.65.148901
    [9] 彭兴钊, 姚宏, 杜军, 王哲, 丁超. 负荷作用下相依网络中的级联故障. 物理学报, 2015, 64(4): 048901. doi: 10.7498/aps.64.048901
    [10] 田中大, 李树江, 王艳红, 高宪文. 短期风速时间序列混沌特性分析及预测. 物理学报, 2015, 64(3): 030506. doi: 10.7498/aps.64.030506
    [11] 陈世明, 吕辉, 徐青刚, 许云飞, 赖强. 基于度的正/负相关相依网络模型及其鲁棒性研究. 物理学报, 2015, 64(4): 048902. doi: 10.7498/aps.64.048902
    [12] 欧阳博, 金心宇, 夏永祥, 蒋路茸, 吴端坡. 疾病传播与级联失效相互作用的研究:度不相关网络中疾病扩散条件的分析. 物理学报, 2014, 63(21): 218902. doi: 10.7498/aps.63.218902
    [13] 袁铭. 带有层级结构的复杂网络级联失效模型. 物理学报, 2014, 63(22): 220501. doi: 10.7498/aps.63.220501
    [14] 陈世明, 邹小群, 吕辉, 徐青刚. 面向级联失效的相依网络鲁棒性研究. 物理学报, 2014, 63(2): 028902. doi: 10.7498/aps.63.028902
    [15] 姚天亮, 刘海峰, 许建良, 李伟锋. 基于最大Lyapunov指数不变性的混沌时间序列噪声水平估计. 物理学报, 2012, 61(6): 060503. doi: 10.7498/aps.61.060503
    [16] 吴建军, 徐尚义, 孙会君. 混合交通流时间序列的去趋势波动分析. 物理学报, 2011, 60(1): 019502. doi: 10.7498/aps.60.019502
    [17] 修春波, 徐勐. 基于混沌算子网络的时间序列多步预测研究. 物理学报, 2010, 59(11): 7650-7656. doi: 10.7498/aps.59.7650
    [18] 董昭, 李翔. 离散时间序列的网络模体分析. 物理学报, 2010, 59(3): 1600-1607. doi: 10.7498/aps.59.1600
    [19] 曾高荣, 裘正定. 数字水印的鲁棒性评测模型. 物理学报, 2010, 59(8): 5870-5879. doi: 10.7498/aps.59.5870
    [20] 吴延东, 谢洪波. 一种新的时间序列确定性辨识方法. 物理学报, 2007, 56(11): 6294-6300. doi: 10.7498/aps.56.6294
计量
  • 文章访问数:  3476
  • PDF下载量:  96
  • 被引次数: 0
出版历程
  • 收稿日期:  2021-08-09
  • 修回日期:  2021-12-09
  • 上网日期:  2022-01-26
  • 刊出日期:  2022-04-20

/

返回文章
返回