復(fù)雜網(wǎng)絡(luò)的拓?fù)渥R(shí)別方法研究
發(fā)布時(shí)間：2018-12-16 09:08
【摘要】：人類社會(huì)日趨網(wǎng)絡(luò)化,有必要對(duì)復(fù)雜網(wǎng)絡(luò)進(jìn)行深入而全面的了解和分析。復(fù)雜網(wǎng)絡(luò)可能存在不確定性,如未知的節(jié)點(diǎn)動(dòng)力學(xué)特性和網(wǎng)絡(luò)拓?fù)浣Y(jié)構(gòu)等。在未知網(wǎng)絡(luò)拓?fù)淝闆r下,通過(guò)觀測(cè)網(wǎng)絡(luò)輸出數(shù)據(jù)辨識(shí)網(wǎng)絡(luò)拓?fù)涫菑?fù)雜網(wǎng)絡(luò)分析、預(yù)測(cè)和控制的必要條件,對(duì)于深入認(rèn)識(shí)復(fù)雜網(wǎng)絡(luò)進(jìn)而實(shí)現(xiàn)調(diào)控具有重要意義。復(fù)雜網(wǎng)絡(luò)拓?fù)浔孀R(shí)問(wèn)題的難點(diǎn)如下:①拓?fù)鋾r(shí)變:受噪音、信號(hào)傳輸?shù)膿頂D阻塞等因素的影響導(dǎo)致網(wǎng)絡(luò)的拓?fù)浣Y(jié)構(gòu)會(huì)隨時(shí)間有所變化,如作戰(zhàn)網(wǎng)絡(luò)中各作戰(zhàn)單元之間的連接關(guān)系會(huì)隨時(shí)間的變化而變化;②節(jié)點(diǎn)動(dòng)力學(xué)參數(shù)未知;③節(jié)點(diǎn)的狀態(tài)部分可測(cè):受條件的限制只有部分狀態(tài)可測(cè)量;④當(dāng)網(wǎng)絡(luò)規(guī)模N很大時(shí),算法計(jì)算量激增:對(duì)具有N個(gè)節(jié)點(diǎn)的網(wǎng)絡(luò),通常有N2個(gè)拓?fù)鋮?shù)需要辨識(shí),對(duì)于大規(guī)模網(wǎng)絡(luò),算法的運(yùn)算量較大,而實(shí)際中可能只關(guān)心部分重要節(jié)點(diǎn)之間的連接關(guān)系,因此往往不需要對(duì)整個(gè)網(wǎng)絡(luò)拓?fù)鋮?shù)進(jìn)行全部辨識(shí)�，F(xiàn)有方法在處理節(jié)點(diǎn)動(dòng)力學(xué)參數(shù)未知只有部分狀態(tài)可測(cè)和時(shí)變拓?fù)涞拇笠?guī)模網(wǎng)絡(luò)局部拓?fù)浔孀R(shí)問(wèn)題時(shí)都存在著局限性。本文首先對(duì)復(fù)雜網(wǎng)絡(luò)拓?fù)浔孀R(shí)問(wèn)題進(jìn)行了闡述,對(duì)近年提出的相關(guān)方法進(jìn)行了全面的回顧,具體包括:基于同步方法、基于壓縮感知理論方法以及基于互信息理論方法,討論了各類復(fù)雜網(wǎng)絡(luò)拓?fù)浔孀R(shí)方法的基本思路,分析了各類方法的特點(diǎn),通過(guò)數(shù)值仿真,驗(yàn)證了各類方法的有效性。針對(duì)節(jié)點(diǎn)狀態(tài)部分可測(cè)的問(wèn)題,基于輸出耦合模型本文利用輸出變量驅(qū)動(dòng)響應(yīng)網(wǎng)絡(luò),在只有部分狀態(tài)可測(cè)的情況下,對(duì)節(jié)點(diǎn)動(dòng)力學(xué)參數(shù)未知的時(shí)變網(wǎng)絡(luò)拓?fù)溥M(jìn)行了局部拓?fù)浔孀R(shí)。依據(jù)Lyapunov穩(wěn)定性理論,分析了響應(yīng)網(wǎng)絡(luò)與待辨識(shí)網(wǎng)絡(luò)同步的條件,證明了拓?fù)浔孀R(shí)方法的可行性。通過(guò)多個(gè)數(shù)值仿真舉例,驗(yàn)證了本文方法的有效性。時(shí)滯總是出現(xiàn)在各種現(xiàn)實(shí)網(wǎng)絡(luò)中,比如通信網(wǎng)絡(luò)、生物網(wǎng)絡(luò)等網(wǎng)絡(luò),通常由有限的信號(hào)傳輸速度或容量等因素引起。本文基于壓縮感知理論考慮具有耦合時(shí)滯的網(wǎng)絡(luò)拓?fù)浔孀R(shí)問(wèn)題,利用相對(duì)較少的數(shù)據(jù)可以達(dá)到辨識(shí)效果。首先給出了基于壓縮感知理論的具有耦合時(shí)滯的網(wǎng)絡(luò)拓?fù)浔孀R(shí)基本思路。然后分析了狀態(tài)變量導(dǎo)數(shù)的獲取方法,通過(guò)對(duì)比五點(diǎn)公式法和Tikhonov正則化方法可知,由于Tikhonov正則化方法考慮了數(shù)據(jù)的誤差水平,在一定的誤差范圍內(nèi),可以更好的得到近似的導(dǎo)數(shù)值。最后利用Tikhonov正則化方法求取狀態(tài)變量導(dǎo)數(shù),利用多面體面追蹤算法(Polytope Faces Pursuit, PFP)對(duì)信號(hào)進(jìn)行重構(gòu),通過(guò)數(shù)值仿真,驗(yàn)證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.
【學(xué)位授予單位】：西安理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O157.5
本文編號(hào)：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.
【學(xué)位授予單位】：西安理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O157.5
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