复杂网络的仿真研究及在轮机系统中的应用
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摘要
复杂网络经历了由七桥问题引发的图论、ER随机图模型、小世界网络和无标度网络的发展历程,应用十分广泛,对人类生活影响巨大。然而在分析与应用中尚存在着动态化不强、数据不可靠引起的误判等问题,因此对它的正确分析和应用极为重要。其发展方向主要有随机性和确定性混合、大型化和超网络。由于计算机网络系统的应用,复杂网络已渗透到很多工程领域,包括轮机系统。
首先介绍了复杂网络的定义,阐述了复杂网络的研究内容和复杂性,解释了复杂网络中的三个基本概念：特征路径长度、聚类系数和度分布,并给出了它们的计算流程。然后针对当前研究最多的最近邻耦合网络、随机图模型、WS小世界网络、NW小世界网络和BA无标度网络,给出它们的生成方法、统计性质和仿真流程。用MATLAB进行仿真,得到相应的网络图和特征分布图及特征路径长度、聚类系数和平均度三个网络特征参数值。并以一个在3000KW以上非自动化海船轮机部在最低船员配置下的节点数为7、边数为18的从属关系网络为例做出计算,结论表明在严格执行从属关系下网络不易发生聚类,但处于聚类边缘。神经网络故障诊断法的优点是数据结果可靠、误判率低,缺点是识别维数受到限制。利用复杂网络中的社团结构搜索,将与主机故障相关的热力参数进行分类,选取每类中有代表性的参数用于故障诊断,弥补了神经网络诊断法的不足,分析了降维前后故障诊断的准确率。最后介绍了网络分析软件Pajek的可视化、抽象化和高速计算的三个强大功能和基本操作方法,如求度、求节点间距离、求k近邻、求聚类系数和度分布等。充分利用Pajek对轮机系统的13个子系统组成的网络进行分析,给出定义的宏和运行宏后得到的分析报告,表明主机易发生故障和发电机组故障更易引起其它故障的特点,便于深入细致研究轮机系统。
结尾给出复杂网络在轮机系统中的部分故障诊断应用和子系统组成的网络分析的相关结论,有待于进一步的研究的方面有：在网络分析应用上,还需要更多的数据分析各个子系统,使之形成超网络；对轮机系统故障实行在线诊断；MATLAB和Pajek的数据互导。
Experienced development processes of graph theory caused by the seven bridges problems, ER random graph model, small-world network and scale-free network, complex network is widely used and has a tremendous impact on human life. However, in the analysis and application, some complex networks are not dynamic enough, and unreliable data will cause misjudgment, so it is extremely important to correctly analyze and apply. The main directions are random and deterministic mixed, large scale and super network. Since the application of computer network systems, complex networks have penetrated into many fields of engineering, including marine system.
This paper introduces the definition of complex networks, describes a complex network of content and complexity, explains the complex network of three basic concepts:characteristic path length, clustering coefficient and degree distribution, and gives their calculation process. The generation method, statistical properties and simulation process of the most researched networks-the nearest neighbor coupled network, random graph model, WS small-world network, NW small-world network and BA scale-free network are given. Using MATLAB simulation, the corresponding network maps, characteristics distribution diagrams and the three network characteristics parameter values-characteristic path length, clustering coefficient and average degree-are got. And characteristics parameter values of affiliation network in a more than 3000KW non-automated ship's engine department with the minimum crew configuration which has 7 vertices and 18 arcs are calculated as an example. Conclusions show that the network under strict subordination less prone to clustering, but clustering coefficient has already been at the edge. Neural network fault diagnosis method has the advantages of reliable data and low false positives, and the disadvantage of limited identified dimension. Using community structure search of complex network, the thermal parameters related with the main engine fault are classified. Select a representative parameter for each classification to be used in fault diagnosis. So neural network diagnostics are optimized. Compare the result of fault diagnosis before dimension reduction with after dimension reduction. the three powerful functions of network analysis software Pajek-visualization, abstraction, and high-speed computing-and basic operation methods, such as the calculation of degrees, the distance between vertices, the k-nearest neighbor, the clustering coefficient and degree distribution are introduced. Using Pajek, a network of 13 sub-systems in the marine system is analyzed. The defined macro and the analysis report after running the macro are given, which indicates that the engine prones to more faults and generator faults prones to cause other system faults. This makes it easy to further detailed research in marine systems.
Owing to time constraints, only applications of a complex network in the fault diagnosis of the marine system and network analysis of subsystems in the marine system are completed. The following three aspects need further study:In application of network analysis, more data is needed to analysis subsystems so that a super-network is formed; on-line fault diagnosis of the marine system; MATLAB and Pajek data transconductance.
首先介绍了复杂网络的定义,阐述了复杂网络的研究内容和复杂性,解释了复杂网络中的三个基本概念：特征路径长度、聚类系数和度分布,并给出了它们的计算流程。然后针对当前研究最多的最近邻耦合网络、随机图模型、WS小世界网络、NW小世界网络和BA无标度网络,给出它们的生成方法、统计性质和仿真流程。用MATLAB进行仿真,得到相应的网络图和特征分布图及特征路径长度、聚类系数和平均度三个网络特征参数值。并以一个在3000KW以上非自动化海船轮机部在最低船员配置下的节点数为7、边数为18的从属关系网络为例做出计算,结论表明在严格执行从属关系下网络不易发生聚类,但处于聚类边缘。神经网络故障诊断法的优点是数据结果可靠、误判率低,缺点是识别维数受到限制。利用复杂网络中的社团结构搜索,将与主机故障相关的热力参数进行分类,选取每类中有代表性的参数用于故障诊断,弥补了神经网络诊断法的不足,分析了降维前后故障诊断的准确率。最后介绍了网络分析软件Pajek的可视化、抽象化和高速计算的三个强大功能和基本操作方法,如求度、求节点间距离、求k近邻、求聚类系数和度分布等。充分利用Pajek对轮机系统的13个子系统组成的网络进行分析,给出定义的宏和运行宏后得到的分析报告,表明主机易发生故障和发电机组故障更易引起其它故障的特点,便于深入细致研究轮机系统。
结尾给出复杂网络在轮机系统中的部分故障诊断应用和子系统组成的网络分析的相关结论,有待于进一步的研究的方面有：在网络分析应用上,还需要更多的数据分析各个子系统,使之形成超网络；对轮机系统故障实行在线诊断；MATLAB和Pajek的数据互导。
Experienced development processes of graph theory caused by the seven bridges problems, ER random graph model, small-world network and scale-free network, complex network is widely used and has a tremendous impact on human life. However, in the analysis and application, some complex networks are not dynamic enough, and unreliable data will cause misjudgment, so it is extremely important to correctly analyze and apply. The main directions are random and deterministic mixed, large scale and super network. Since the application of computer network systems, complex networks have penetrated into many fields of engineering, including marine system.
This paper introduces the definition of complex networks, describes a complex network of content and complexity, explains the complex network of three basic concepts:characteristic path length, clustering coefficient and degree distribution, and gives their calculation process. The generation method, statistical properties and simulation process of the most researched networks-the nearest neighbor coupled network, random graph model, WS small-world network, NW small-world network and BA scale-free network are given. Using MATLAB simulation, the corresponding network maps, characteristics distribution diagrams and the three network characteristics parameter values-characteristic path length, clustering coefficient and average degree-are got. And characteristics parameter values of affiliation network in a more than 3000KW non-automated ship's engine department with the minimum crew configuration which has 7 vertices and 18 arcs are calculated as an example. Conclusions show that the network under strict subordination less prone to clustering, but clustering coefficient has already been at the edge. Neural network fault diagnosis method has the advantages of reliable data and low false positives, and the disadvantage of limited identified dimension. Using community structure search of complex network, the thermal parameters related with the main engine fault are classified. Select a representative parameter for each classification to be used in fault diagnosis. So neural network diagnostics are optimized. Compare the result of fault diagnosis before dimension reduction with after dimension reduction. the three powerful functions of network analysis software Pajek-visualization, abstraction, and high-speed computing-and basic operation methods, such as the calculation of degrees, the distance between vertices, the k-nearest neighbor, the clustering coefficient and degree distribution are introduced. Using Pajek, a network of 13 sub-systems in the marine system is analyzed. The defined macro and the analysis report after running the macro are given, which indicates that the engine prones to more faults and generator faults prones to cause other system faults. This makes it easy to further detailed research in marine systems.
Owing to time constraints, only applications of a complex network in the fault diagnosis of the marine system and network analysis of subsystems in the marine system are completed. The following three aspects need further study:In application of network analysis, more data is needed to analysis subsystems so that a super-network is formed; on-line fault diagnosis of the marine system; MATLAB and Pajek data transconductance.
引文
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[2]Adrian Cho. Econophysics:Still Controversial After All These Years[J]. Science,2009,325 (5939):408.
[3]A.-L. Barabasi. Scale-Free Networks:A Decade and Beyond[J]. Science,2009,325 (5939): 412-413.
[4]Listgarten J, Heckerman D. Determining the number of non-spurious arcs in a learned dag model:Investigation of a Bayesian and a frequentist approach[C]. Proceedings of the 23rd
Conference on Uncertainty in Artificial Intelligence. Redmond, WA.,2007.
[5]J. Kleinberg, S. Lawrence. The structure of the Web[J]. Science,2001,294:1849-1850.
[6]John Bohannon. Counterterrorism's New Tool:"Metanetwork" Analysis[J]. Science,2009,325 (5939):409.
[7]Elinor Ostrom. A General Framework for Analyzing Sustainability of Social-Ecological Systems[J]. Science,2009,325 (5939):419.
[8]方锦清,汪小帆,郑志刚.网络科学的理论模型及其应用课题研究的若干进展[J].复杂系统与复杂性科学,2008,12(5)：1-20.
[9]Viktor Mayer Schonberger. Can We Reinvent the Internet?[J]. Science,2009,325 (5939): 396-397.
[10]Douglas B.West著.李建中,骆吉洲译.图论导引[M].北京：机械工业出版社.2006.
[11]李社会,吕岳鹏.随机网络的计算机模拟[J].纺织高校基础科学学报,1998,11(1)：66-70.
[12]M. E. J. Newman. Fast algorithm for detecting community structure in networks[J]. Phys. Rev. E,2004,69:1-5.
[13]M. E. J. Newman. Models of the Small World[J]. Journal of Statistical Physics,2000,101 (3,4):819-841.
[14]Barabasi, A.L.& Albert, R.Emergence of scaling in random networks[J]. Science,1999 (286): 509-512.
[15]John Bohannon. Investigating Networks:The Dark Side[J]. Science,2009,325 (5939): 410-411.
[16]Carter T. Butts. Revisiting the Foundations of Network Analysis[J]. Science,2009,325 (5939)：414.
[17]王志平,王众托.超网络理论及其应用[M].北京：科学出版社,2008.
[18]汪小帆,李翔,陈关荣.复杂网络理论及其应用[M].北京：清华大学出版社,2006.
[19]方锦清,汪小帆,郑志刚等.一门崭新的交叉科学：网络科学(下篇)[J].物理学进展,2007,27(4)：361-448.
[20]Alessandro Vespignani. Predicting the Behavior of Techno-Social Systems[J]. Science,2009, 325 (5939):425.
[21]Frank Schweitzer, Giorgio Fagiolo, Didier Sornettel et al. Economic Networks:The New Challenges[J]. Science,2009,325 (5939):422-424.
[22]J.邦詹森,G.古廷著.姚兵,张忠辅译.有向图的理论、算法及其应用[M].北京：科学出版社,2009.
[23]R. Pastor Satorras, A. Vespignani. Evolution and Structure of the Internet[M]. Cambridge: Cambridge University Pr.,2004.
[24]C. Baldwin, K. Clark. Design Rules:The Power of Modularity [M]. Cambridge:MIT Pr., 2000.
[25]M. E. J. Newman. The structure and function of complex networks[J]. SIAM Review,2003 (45):167-256.
[26]Ahmed, Eric P. Xing. Recovering time-varying networks of dependencies in social and biological studies Amr[J]. PNAS,2009,106 (29):11878-11883.
[27]M. E. J. Newman. Fast algorithm for detecting community structure in networks[J]. Phys. Rev. E,2004 (69):66-133.
[28]M. E. J. Newman, Moore, C.& Watts, D.J.. Mean-field solution of the small-world network model[J]. Phys. Rev. Lett.,2000 (84):3201-3204.
[29]M. E. J. Newman. Finding community structure in networks using the eigenvectors of matrices[J]. Phys. Rev. E,2006,74 (036104):19.
[30]M. E. J. Newman. Analysis of weighted networks[J]. Phys. Rev. E.2004,70 (056131):9.
[31]Wasserman S, RobinsG. An introduction to random graphs, dependence graphs, and p*. Models and Methods in Social Network Analysis[M]. Cambridge:Cambridge Univ Pr.,2005.
[32]Barbour, A.D.& Reinert, G..Small worlds. Preprint cond-mat/0006001 at
[33]Juyong Park, M. E. J. Newman. The statistical mechanics of networks [J]. Phys. Rev. E,2004, 70(066117):15.
[34]杨博,刘大有.复杂网络聚类方法[J].Journal of Software,2009,20 (1):54-66.
[35]赵凤霞,谢福鼎,稽敏.基于复杂网络理论和遗传算法的分类方法[J].计算机应用与软件,2010,27(2)：44-46.
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