复杂网络的拓扑识别方法研究
发布时间：2018-12-16 09:08
【摘要】：人类社会日趋网络化,有必要对复杂网络进行深入而全面的了解和分析。复杂网络可能存在不确定性,如未知的节点动力学特性和网络拓扑结构等。在未知网络拓扑情况下,通过观测网络输出数据辨识网络拓扑是复杂网络分析、预测和控制的必要条件,对于深入认识复杂网络进而实现调控具有重要意义。复杂网络拓扑辨识问题的难点如下:①拓扑时变:受噪音、信号传输的拥挤阻塞等因素的影响导致网络的拓扑结构会随时间有所变化,如作战网络中各作战单元之间的连接关系会随时间的变化而变化;②节点动力学参数未知;③节点的状态部分可测:受条件的限制只有部分状态可测量;④当网络规模N很大时,算法计算量激增:对具有N个节点的网络,通常有N2个拓扑参数需要辨识,对于大规模网络,算法的运算量较大,而实际中可能只关心部分重要节点之间的连接关系,因此往往不需要对整个网络拓扑参数进行全部辨识。现有方法在处理节点动力学参数未知只有部分状态可测和时变拓扑的大规模网络局部拓扑辨识问题时都存在着局限性。本文首先对复杂网络拓扑辨识问题进行了阐述,对近年提出的相关方法进行了全面的回顾,具体包括:基于同步方法、基于压缩感知理论方法以及基于互信息理论方法,讨论了各类复杂网络拓扑辨识方法的基本思路,分析了各类方法的特点,通过数值仿真,验证了各类方法的有效性。针对节点状态部分可测的问题,基于输出耦合模型本文利用输出变量驱动响应网络,在只有部分状态可测的情况下,对节点动力学参数未知的时变网络拓扑进行了局部拓扑辨识。依据Lyapunov稳定性理论,分析了响应网络与待辨识网络同步的条件,证明了拓扑辨识方法的可行性。通过多个数值仿真举例,验证了本文方法的有效性。时滞总是出现在各种现实网络中,比如通信网络、生物网络等网络,通常由有限的信号传输速度或容量等因素引起。本文基于压缩感知理论考虑具有耦合时滞的网络拓扑辨识问题,利用相对较少的数据可以达到辨识效果。首先给出了基于压缩感知理论的具有耦合时滞的网络拓扑辨识基本思路。然后分析了状态变量导数的获取方法,通过对比五点公式法和Tikhonov正则化方法可知,由于Tikhonov正则化方法考虑了数据的误差水平,在一定的误差范围内,可以更好的得到近似的导数值。最后利用Tikhonov正则化方法求取状态变量导数,利用多面体面追踪算法(Polytope Faces Pursuit, PFP)对信号进行重构,通过数值仿真,验证了本文方法的有效性。
[Abstract]:As human society becomes more and more networked, it is necessary to understand and analyze the complex network deeply and comprehensively. There may be uncertainties in complex networks, such as unknown node dynamics and network topology. In the case of unknown network topology, identification of network topology by observing network output data is a necessary condition for complex network analysis, prediction and control, which is of great significance for further understanding complex network and realizing regulation and control. The difficulties of complex network topology identification are as follows: (1) topology time-varying: due to the influence of noise, congestion of signal transmission and other factors, the topology of the network will change with time. For example, the connection between each combat unit in the combat network will change with time. The dynamic parameters of 2 nodes are unknown, the state of 3 nodes is partially measurable, and only part of the state can be measured under the restriction of conditions. (4) when the network size N is very large, the computational complexity of the algorithm increases rapidly: for a network with N nodes, there are usually N 2 topological parameters to be identified, but for a large scale network, the computational complexity of the algorithm is large. However, in practice, only the connections between some important nodes may be concerned, so it is not necessary to identify the topology parameters of the whole network. The existing methods have limitations in dealing with the problem of local topology identification of large-scale networks with unknown dynamic parameters and only partially measurable and time-varying topologies. In this paper, the topology identification problem of complex network is discussed, and the related methods proposed in recent years are reviewed, including: based on synchronization method, based on compressed sensing theory and based on mutual information theory. This paper discusses the basic ideas of topology identification methods for complex networks, analyzes the characteristics of these methods, and verifies the effectiveness of these methods by numerical simulation. Based on the output coupling model, the response network is driven by output variables. The local topology identification of time-varying network with unknown node dynamic parameters is presented. Based on the Lyapunov stability theory, the synchronization condition between the response network and the network to be identified is analyzed, and the feasibility of the topology identification method is proved. The effectiveness of this method is verified by several numerical simulation examples. Time delay is always found in various real networks, such as communication networks, biological networks and so on, which are usually caused by limited signal transmission speed or capacity. In this paper, the problem of network topology identification with coupled delay is considered based on the theory of compressed perception, and the identification effect can be achieved by using relatively few data. Firstly, the basic idea of network topology identification with coupled delay based on compressed sensing theory is presented. By comparing the five-point formula method and the Tikhonov regularization method, we can see that because the Tikhonov regularization method considers the error level of the data, it is within a certain error range. The approximate derivative value can be obtained better. Finally, the derivative of state variables is obtained by Tikhonov regularization method, and the signal is reconstructed by polyhedron surface tracing algorithm (Polytope Faces Pursuit, PFP). The effectiveness of this method is verified by numerical simulation.
【学位授予单位】：西安理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5
本文编号：2382112
[Abstract]:As human society becomes more and more networked, it is necessary to understand and analyze the complex network deeply and comprehensively. There may be uncertainties in complex networks, such as unknown node dynamics and network topology. In the case of unknown network topology, identification of network topology by observing network output data is a necessary condition for complex network analysis, prediction and control, which is of great significance for further understanding complex network and realizing regulation and control. The difficulties of complex network topology identification are as follows: (1) topology time-varying: due to the influence of noise, congestion of signal transmission and other factors, the topology of the network will change with time. For example, the connection between each combat unit in the combat network will change with time. The dynamic parameters of 2 nodes are unknown, the state of 3 nodes is partially measurable, and only part of the state can be measured under the restriction of conditions. (4) when the network size N is very large, the computational complexity of the algorithm increases rapidly: for a network with N nodes, there are usually N 2 topological parameters to be identified, but for a large scale network, the computational complexity of the algorithm is large. However, in practice, only the connections between some important nodes may be concerned, so it is not necessary to identify the topology parameters of the whole network. The existing methods have limitations in dealing with the problem of local topology identification of large-scale networks with unknown dynamic parameters and only partially measurable and time-varying topologies. In this paper, the topology identification problem of complex network is discussed, and the related methods proposed in recent years are reviewed, including: based on synchronization method, based on compressed sensing theory and based on mutual information theory. This paper discusses the basic ideas of topology identification methods for complex networks, analyzes the characteristics of these methods, and verifies the effectiveness of these methods by numerical simulation. Based on the output coupling model, the response network is driven by output variables. The local topology identification of time-varying network with unknown node dynamic parameters is presented. Based on the Lyapunov stability theory, the synchronization condition between the response network and the network to be identified is analyzed, and the feasibility of the topology identification method is proved. The effectiveness of this method is verified by several numerical simulation examples. Time delay is always found in various real networks, such as communication networks, biological networks and so on, which are usually caused by limited signal transmission speed or capacity. In this paper, the problem of network topology identification with coupled delay is considered based on the theory of compressed perception, and the identification effect can be achieved by using relatively few data. Firstly, the basic idea of network topology identification with coupled delay based on compressed sensing theory is presented. By comparing the five-point formula method and the Tikhonov regularization method, we can see that because the Tikhonov regularization method considers the error level of the data, it is within a certain error range. The approximate derivative value can be obtained better. Finally, the derivative of state variables is obtained by Tikhonov regularization method, and the signal is reconstructed by polyhedron surface tracing algorithm (Polytope Faces Pursuit, PFP). The effectiveness of this method is verified by numerical simulation.
【学位授予单位】：西安理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5
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