Random matrix theory models of electric grid topology

Marvel, Kate; Agvaanluvsan, U.

doi:10.1016/j.physa.2010.08.009

Cited by 10 publications

(5 citation statements)

References 45 publications

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“…This last case is very interesting when studying networks because it aids in understanding the transition from two or more separate networks to one big network through the introduction of intra-networks connections. This case was used to identify new characteristics of electric grid networks [8], where RMT tools were used to describe the interconnection of multiple grids and construct a simple model of a distributed grid, showing the transition from Poisson statistics, an indicator of regularity, to that of a GOE.…”

Section: Random Matrix Approach To Networkmentioning

confidence: 99%

“…Other applications include characterizing the capacity of communication networks [10], modelling multi-path propagation between a transmitting and receiving antenna array [11], and neural networks learning [12]. The authors of [8] suggest that RMT is useful in the study of electric grid networks, and provides a starting point to applications in real-world smart grids.…”

Section: Introductionmentioning

confidence: 99%

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Effect of Unfolding on the Spectral Statistics of Adjacency Matrices of Complex Networks

Abuelenin

Abul-Magd

2012

Procedia Computer Science

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Random matrix theory is finding an increasing number of applications in the context of information theory and communication systems, especially in studying the properties of complex networks. Such properties include short-term and long-term correlation. We study the spectral fluctuations of the adjacency of networks using random-matrix theory. We consider the influence of the spectral unfolding, which is a necessary procedure to remove the secular properties of the spectrum, on different spectral statistics. We find that, while the spacing distribution of the eigenvalues shows little sensitivity to the unfolding method used, the spectral rigidity has greater sensitivity to unfolding.

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Section: Random Matrix Approach To Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effect of Unfolding on the Spectral Statistics of Adjacency Matrices of Complex Networks

Abuelenin

Abul-Magd

2012

Procedia Computer Science

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“…Also, GOE-GUE transition depending on a parameter α, for α = 0, GOE and for α = 1, the ensemble is Gaussian unitary [84] and cross-over transition between Poisson-GOE-GUE [85]. However, the Brody distribution has been widely studied, and there are well-known results for the case of single layer networks to measure the transition/mixture of GOE and Poisson statistics and for real-world networks also [46,47,[52][53][54][55][56][57][59][60][61][62][63][64]. Hence we use Brody distribution in the current article.…”

Section: Model and Techniquesmentioning

confidence: 99%

“…For 0 ≤ p ≤ 1, NNSD shows an intermediate statistics between the Poisson and the GOE [46,47]. However, all the investigations on various spectral properties of adjacency matrices are confined to single layer networks only [52][53][54][55][56][57][59][60][61][62][63][64].…”

Section: Introductionmentioning

confidence: 99%

Random Matrix Analysis of Multiplex Networks

Raghav,

Jalan

2021

Preprint

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We investigate the spectra of adjacency matrices of multiplex networks under random matrix theory (RMT) framework. Through extensive numerical experiments, we demonstrate that upon multiplexing two random networks, the spectra of the combined multiplex network exhibit superposition of two Gaussian orthogonal ensemble (GOE)s for very small multiplexing strength followed by a smooth transition to the GOE statistics with an increase in the multiplexing strength. Interestingly, randomness in the connection architecture, introduced by random rewiring to 1D lattice, of at least one layer may govern nearest neighbor spacing distribution (NNSD) of the entire multiplex network, and in fact, can drive to a transition from the Poisson to the GOE statistics or vice versa. Notably, this transition transpires for a very small number of the random rewiring corresponding to the small-world transition. Ergo, only one layer being represented by the small-world network is enough to yield GOE statistics for the entire multiplex network. Spectra of adjacency matrices of underlying interaction networks have been contemplated to be related with dynamical behaviour of the corresponding complex systems, the investigations presented here have implications in achieving better structural and dynamical control to the systems represented by multiplex networks against structural perturbation in only one of the layers.

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“…In 1967, Marchenko and Pastur have proposed a limit-spectrum distribution (M-P law) for large sample covariance matrices. Now the RMT is in the fields of quantum physics (Backer et al, 2019; Wazir et al, 2010), biomedicine (Korosak and Rupnik, 2019), social science (Chen et al, 2020), grid power distribution (Marvel and Agvaanluvsan, 2010), spectrum sensing (Liu et al, 2019), and so on. Ritto and Fabro (2019) have applied the set of random matrices to rigid body and structural dynamics, which can generate parallel and orthogonal components through tensor decomposition, measure the deviation of the two components from the nominal matrix, and detect model epistemic uncertainties.…”

Section: Introductionmentioning

confidence: 99%

An anomaly detection algorithm of rolling bearing combining random matrix eigenvalues and principal eigenvectors

Wang

Zhu

Zhang

et al. 2022

Transactions of the Institute of Measurement and Control

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An anomaly detection algorithm combining eigenvalues and eigenvectors in random matrix is proposed, which can solve the problem that present algorithms based on random matrix theory overly rely on eigenvalues and ignore useful information contained in eigenvectors. Firtsly, the time window method is used to select the original data of rolling bearing, and the sampling feature matrix is constructed by extracting bearing feature. Secondly, the eigenvalues and principal eigenvector of sampling feature matrix are investigated and combined to construct comprehensive feature index and its corresponding threshold. Finally, an anomaly detection based on comprehensive feature index is proposed to detect the early anomaly of rolling bearing. The application research is carried out by using bearing datasets of intelligent maintenance center and Xi’an Jiaotong University; the result shows that compared with the single eigenvalue index and kurtosis index, the algorithm based on the comprehensive feature index can detect the abnormal condition of bearing earlier. And the accuracy and effectiveness of the anomaly detection algorithm are proved through spectrum analysis, which provides guidance and basis for fault warning and equipment maintenance.

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Random matrix theory models of electric grid topology

Cited by 10 publications

References 45 publications

Effect of Unfolding on the Spectral Statistics of Adjacency Matrices of Complex Networks

Effect of Unfolding on the Spectral Statistics of Adjacency Matrices of Complex Networks

Random Matrix Analysis of Multiplex Networks

An anomaly detection algorithm of rolling bearing combining random matrix eigenvalues and principal eigenvectors

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