随机矩阵理论在高速路关键路径辨识中的应用

doi:10.3778/j.issn.1002-8331.2209-0103

摘要/Abstract

摘要： 高速公路网络是我国各地区相互连接的重要纽带，高速公路网络关键路径辨识对确保高速网络的可靠运行具有重要意义。传统的关键路径分析方法基于拓扑结构，未考虑交通网络的运输量特性；而现有的基于运输量数据的分析方法只考虑部分路径的运输量特性，难以反映交通网络的实际运行情况。利用路径运输量数据，搭建运输量随机矩阵模型，针对高速公路网络异常后的运输量变化特性，定义关键路径评估指数，实现异常影响程度的量化评估，在此基础上提出一种基于数据驱动的高速公路网络关键路径辨识方法。最后，采用辽宁省高速公路网络进行分析，验证了所提方法的合理性和有效性，并将该方法应用于城市路网案例中，进一步证明该方法具有普适性。

关键词: 交通运输, 关键路径辨识, 数据驱动, 复杂网络, 随机矩阵理论

Abstract: Expressway network connects all regions in China, and critical path identification is of great significance to ensure the reliable operation of expressway network. The traditional critical path analysis method is based on topology and does not consider the traffic volume characteristics of the traffic network. The existing analysis methods based on traffic volume data only consider the characteristics of some routes, which is difficult to reflect the actual operation of the expressway network. Using the route traffic volume data to build a random matrix model of traffic volume, according to the change characteristics of traffic volume after the expressway network is abnormal, the critical path evaluation index is defined to realize the quantitative evaluation of the degree of abnormal impact. On this basis, a data-driven critical path identification method for expressway network is proposed. Finally, the rationality and effectiveness of the proposed method are verified by analyzing the expressway network in Liaoning Province, and the method is applied to the urban road network case, which further proves the universality of the method.

Key words: transportation, critical path identification, data-driven, complex network, random matrix theory

张芳, 王菲, 孙宝硕. 随机矩阵理论在高速路关键路径辨识中的应用[J]. 计算机工程与应用, 2024, 60(1): 319-326.

ZHANG Fang, WANG Fei, SUN Baoshuo. Application of Random Matrix Theory in Critical Path Identification of Expressway[J]. Computer Engineering and Applications, 2024, 60(1): 319-326.

参考文献

[1] 叶燕仙. 江苏省货车运输量专项调查验证方案研究[D]. 西安: 长安大学, 2008.
YE Y X. Study on the certification scheme of freight special investigation in Jiangsu province[D]. Xi’an: Chang’an University, 2008.
[2] 冷雪. 辽宁省高速公路交通量特性分析[J]. 北方交通, 2020, 7(3): 78-81.
LENG X. Analysis on traffic volume characteristics of expressway in Liaoning province[J]. Northern Communications, 2020, 7(3): 78-81.
[3] 冯芬玲, 许天鸿. 多式联运网络关键节点识别及性能分析——以珠江西江经济带多式联运网络为例[J]. 铁道科学与工程学报, 2021, 18(12): 3121-3129.
FENG F L, XU T H. Identification and performance analysis of key nodes in multimodal transport network[J]. Journal of Railway Science and Engineering, 2021, 18(12): 3121-3129.
[4] 薛锋, 何传磊, 黄倩. 成都地铁网络的关键节点识别方法及性能分析[J]. 中国安全科学学报, 2019, 29(1): 93-99.
XUE F, HE C L, HUANG Q. Identification of key nodes in Chengdu metro network and analysis of network performance[J]. China Safety Science Journal, 2019, 29(1): 93-99.
[5] 谌微微, 张富贵, 赵晓波. 轨道交通线网拓扑结构模型及节点重要度分析[J]. 重庆交通大学学报 (自然科学版), 2019, 38(7): 107-113.
ZHAN W W, ZHANG F G, ZHAO X B. Topological structure model and node importance analysis of rail transit network[J]. Journal of Chongqing Jiaotong University (Natural Sciences), 2019, 38(7): 107-113.
[6] 张喜平, 李永树, 刘刚, 等. 城市复杂交通网络道路重要性评估方法[J]. 复杂系统与复杂性科学, 2015, 12(3): 7-13.
ZHANG X P, LI Y S, LIU G, et al. Importance evaluation method in urban complex traffic road network[J]. Complex Systems and Complexity Science, 2015, 12(3): 7-13.
[7] 赵建东, 贾卓瑾, 梁营力, 等. 基于浮动车数据的城市区域路网关键路段识别[J]. 北京交通大学学报, 2021, 45(4): 54-60.
ZHAO J D, JIA Z J, LIANG Y L, et al. Identification of key road sections in urban road network based on floating car data[J]. Journal of Beijing Jiaotong University, 2021, 45(4): 54-60.
[8] 徐青刚. 铁路运输系统的网络模型及其抗毁性研究[D]. 南昌: 华东交通大学, 2015.
XU Q G. Network model and research on invulnerability for the railway transportation system[D]. Nanchang: East China Jiaotong University, 2015.
[9] 殷勇, 刘杰. 铁路网络的抗毁性分析研究[J]. 综合运输, 2017, 39(4): 55-59.
YIN Y, LIU J. The survivability of railway network[J]. Comprehensive Transportation, 2017, 39(4): 55-59.
[10] 王延庆. 基于接连失效的复杂网络节点重要性评估[J]. 网络安全技术与应用, 2008, 12(3): 59-61.
WANG Y Q. Importance evaluation of complex network nodes based on successive failures[J]. Network Security, 2008, 12(3): 59-61.
[11] 张建旭, 蒋燕. 基于局部路网交通流重分配的路段关键度计算[J]. 交通运输系统工程与信息, 2016, 16(1): 105-110.
ZHANG J X, JIANG Y. Criticality calculation of road links based on local network traffic flow redistribution[J]. Journal of Transportation Systems Engineering and Information Technology, 2016, 16(1): 105-110.
[12] LALOUX L, CIZEAU P, PPOTTERS M, et al. Random matrix theory and financial correlations[J]. International Journal of Theoretical and Applied Finance, 2000, 3(3): 391-397.
[13] 孙辉, 孙宝硕, 高正男, 等. 基于量测数据时序谱分布特性的电力系统暂态功角稳定在线判别[J]. 电网技术, 2023, 47(3): 1107-1116.
SUN H, SUN B S, GAO Z N, et al. Online identification for power system transient angle stability based on time-series spectral distribution characteristics of measurement data[J]. Power System Technology, 2023, 47(3): 1107-1116.
[14] BRODY T A, FLORES J, FRENCH J B, et al. Random-matrix physics: spectrum and strength fluctuations[J]. Reviews of Modern Physics, 1981, 53(3): 385-479.
[15] 魏大千, 王波, 刘涤尘, 等. 高维随机矩阵描述下的量测大数据建模与异常数据检测方法[J]. 中国电机工程学报, 2015, 35(S1): 59-66.
WEI D Q, WANG B, LIU D C, et al. A method for WAMS big data modeling and abnormal data detection with large random matrices[J]. Proceedings of the CSEE, 2015, 35(S1): 59-66.
[16] 徐心怡, 贺兴, 艾芊, 等. 基于随机矩阵理论的配电网运行状态相关性分析方法[J]. 电网技术, 2016, 40(3): 781-790.
XU X Y, HE X, AI Q, et al. A correlation analysis method for operation status of distribution network based on random matrix theory[J]. Power System Technology, 2016, 40(3): 781-790.
[17] 于海宁, 张宏莉, 余翔湛. 交通网络拓扑结构及特性研究综述[J]. 华中科技大学学报(自然科学版), 2012, 40(S1): 274-279.
YU H N, ZHANG H L, YU X Z. A survey on transportation network topology and its properties[J]. Journal of Huazhong University of Science and Technology (Nature Science Edition), 2012, 40(S1): 274-279.