Power systems are the backbone of modern society. As critical facilities for the transmission and conversion of electric power, substations are vital to the stable operation of power systems. Quantifying the residual ...
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Power systems are the backbone of modern society. As critical facilities for the transmission and conversion of electric power, substations are vital to the stable operation of power systems. Quantifying the residual seismic capacity of the substation system is an urgent issue to be addressed. Therefore, this study proposes a reliability assessment process based on network matrix algorithms and efficient simulation methods to evaluate substation systems. A typical 220 kV substation in China with 6 incoming lines and 10 outgoing lines was studied with this assessment process. The results of the case study showed that the redundancy of transformer units, due to their excessive fragility, does not effectively guarantee the complete function of the system after an earthquake. In this work, 220 kV circuit breakers, voltage transformers, and 110 kV disconnect switches were evaluated as the most vulnerable functional equipment in the substation system;improving their seismic performance can significantly improve the seismic reliability of the entire system. Furthermore, the evaluation process demonstrated that substations are more susceptible to earthquakes than individual pieces of equipment, indicating that the redundancy of existing substations is insufficient.
The Convex Hull Membership (CHM) tests whether p is an element of conv(S), wherep and the n points of S lie in R-m. CHM finds applications in Linear Programming, Computational Geometry, and Machine Learning. The Trian...
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The Convex Hull Membership (CHM) tests whether p is an element of conv(S), wherep and the n points of S lie in R-m. CHM finds applications in Linear Programming, Computational Geometry, and Machine Learning. The triangle algorithm (TA), previously developed, in O(1/epsilon(2)) iterations computes p' is an element of conv(S), either an epsilon-approximate solution, or a witness certifying p' is an element of conv(S). We first prove the equivalence of exact and approximate versions of CHM and Spherical-CHM, where p = 0 and vertical bar vertical bar v vertical bar vertical bar = 1 for each v in S. If for some M >= 1 every non-witness with parallel to p'parallel to > epsilon admits v is an element of S satisfying parallel to p' - v parallel to >= root 1 + epsilon/M, we prove the number of iterations improves to O(M/e) and M <= 1/epsilon always holds. Equivalence of CHM and Spherical-CHM implies Minimum Enclosing Ball (MEB) algorithms can be modified to solve CHM. However, we prove (1 + epsilon)-approximation in MEB is Omega(root epsilon)-approximation in Spherical-CHM. Thus, even O(1/epsilon) iteration MEB algorithms are not superior to Spherical-TA. Similar weakness is proved for MEB core sets. Spherical-TA also results a variant of the All Vertex triangle algorithm (AVTA) for computing all vertices of conv(S). Substantial computations on distinct problems demonstrate that TA and Spherical-TA generally achieve superior efficiency over algorithms such as Frank-Wolfe, MEB, and LP-Solver.
The Convex Hull Membership (CHM) problem queries whether a point p in m-dimensional Euclidean space lies in the convex hull of a compact subset S in that Euclidean space. For S finite, CHM forms a basic problem in Com...
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The Convex Hull Membership (CHM) problem queries whether a point p in m-dimensional Euclidean space lies in the convex hull of a compact subset S in that Euclidean space. For S finite, CHM forms a basic problem in Computational Geometry and Linear Programming. It also serves as a query problem in many applications e.g. Topic Modeling, Non-negative Matrix Factorization. The triangle algorithm (TA) invented by Dr. Kalantari is a novel algorithm for CHM, first developed for the case where S is finite and subsequently for the more general case where S is any compact subset. The TA either computes an approximate solution or proves p lies outside of conv(S) by computing a separating hyperplane. The number of iterations of TA to solve CHM is independent of the dimension m and it thus can serve as an efficient oracle in large scale and high dimensional cases of CHM. In this dissertation we mainly investigate the computational aspects of solving three problems via the triangle algorithm, as stated below: 1) Irredundancy problem: We investigate the problem of computing all or a good approximation of vertices of a convex hull given a set of n points in dimension m, known as the irredundancy problem. This problem becomes challenging as m grows, especially for classical algorithms such as Gift Wrapping and QuickHull due to their exponential running times in terms of the dimension. The All Vertex triangle algorithm (AVTA) is proposed to tackle the efficiency issue for the irredundancy problem and its variations. The AVTA leverages on the TA as a membership oracle and progressively recovers vertices of convex hull of S, potentially after the Johnson-Lindenstrauss projection pre-processing. We apply AVTA to design new practical algorithms for two popular machine learning problems: topic modeling and non-negative matrix factorization. Our experimental results show its robustness and efficiency in solving the irredundancy problem and its variations in real world applications. 2
Wireless Multimedia Sensor Networks (WMSNs) have emerged as a significant research topic aimed at improving the flexibility of power distribution networks. The stability of a power distribution network may be greatly ...
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Wireless Multimedia Sensor Networks (WMSNs) have emerged as a significant research topic aimed at improving the flexibility of power distribution networks. The stability of a power distribution network may be greatly influenced by the precision and energy use of sensor node localization, especially when using Wireless Sensor Networks (WSNs). This work introduces a suggestion for a modified triangle-based localization scheme (MTBLS) with the objective of enhancing the performance of the conventional mid-normal-based localization scheme (MBLS) and the triangle-based localization method (TBLS). The aim of this study is to effectively meet the communication needs associated with smart distribution automation. The proposed strategy aims to create a triangular configuration by establishing a connection between two anchor nodes located on one side of the triangle. The RSSI (Received Signal Strength Indication) value is used to measure the signal strength between the two anchor nodes and the unknown node, which are positioned on the remaining two sides of the triangular configuration. The simulation was performed using the NS-2 Tool, and afterwards, the acquired outcomes were compared with the performance of the existing MBLS and TBLS algorithms. The results indicate that the use of MTBLS has resulted in improved accuracy in the localization of nodes when compared to presently available methods. In addition, there has been a significant decrease in energy consumption across the whole of the power distribution network, which has coincided with a reduction in the quantity of iterations.
The convex hull membership problem (CHMP) consists in deciding whether a certain point belongs to the convex hull of a finite set of points, a decision problem with important applications in computational geometry and...
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The convex hull membership problem (CHMP) consists in deciding whether a certain point belongs to the convex hull of a finite set of points, a decision problem with important applications in computational geometry and in foundations of linear programming. In this study, we review, compare and analyze first -order methods for CHMP, namely, Frank-Wolfe type methods, Projected Gradient methods and a recently introduced geometric algorithm, called triangle algorithm (TA). We discuss the connections between this algorithm and Frank-Wolfe, showing that TA can be interpreted as an inexact Frank-Wolfe. Despite this similarity, TA is strongly based on a theorem of alternatives known as distance duality. By using this theo-rem, we propose suitable stopping criteria for CHMP to be integrated into Frank-Wolfe type and Projected Gradient, specializing these methods to the membership decision problem. Interestingly, Frank-Wolfe in-tegrated with such stopping criteria coincides with a greedy version of the triangle algorithm which is, in its turn, equivalent to an algorithm due to von Neumann. We report numerical experiments on ran-dom instances of CHMP, carefully designed to cover different scenarios, that indicate which algorithm is preferable according to the geometry of the convex hull and the relative position of the query point. Con-cerning potential applications, we present two illustrative examples, one related to linear programming feasibility problems and another related to image classification problems.(c) 2022 Elsevier B.V. All rights reserved.
triangle star identification algorithm is the most widely used and most mature star pattern recognition algorithms. When the number of guide star is relatively huge and the capacity of guide star catalog is relatively...
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ISBN:
(纸本)9781510639560
triangle star identification algorithm is the most widely used and most mature star pattern recognition algorithms. When the number of guide star is relatively huge and the capacity of guide star catalog is relatively large, with the result that the complexity of triangle star identification algorithm increases, the time of star pattern recognition becomes longer, and even the storage space occupied by the algorithm becomes larger. So it is difficult to realize the rapid and effective star identification in star map. In order to improve the efficiency of star identification algorithm and shorten the time of star recognition, it is proposed that a star identification algorithm used on the data structure of hash map and based on the triangle algorithm. The first thing is to make the guide star catalog. Then, all the angular distance values d(m)(ij)(0 < i < j <= N) of the brightest N observed stars in an observed star image and their corresponding star angular distance sets are calculated, and the triangle features, namely angular distance values, are stored in the hash map. In this algorithm, each triangle feature is mapped to an integer, and the hash map of all triangle features is set to reduce the computational complexity of triangle pattern matching, decrease the number of star angular distance matching, and greatly shorten the time of star image recognition. Simulation results show that the star image recognition algorithm based on hash map has better computational complexity and efficiency of performance than traditional triangle algorithm.
To improve the speed of the error convergence of the Monte Carlo method in the seismic connectivity reliability assessment of power systems, the quasi-Monte Carlo method sampled by a low-discrepancy sequence is applie...
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To improve the speed of the error convergence of the Monte Carlo method in the seismic connectivity reliability assessment of power systems, the quasi-Monte Carlo method sampled by a low-discrepancy sequence is applied in the reliability evaluation. In addition, a triangle algorithm that can reduce the amount of computation in solving connectivity matrix is proposed to establish a seismic connectivity reliability calculation model with low-discrepancy sequence sampling. The ground motion attenuation model and the magnification effect of site soil were used to perform a seismic hazard analysis of the demonstration area, and the peak ground acceleration and the spatial distribution characteristics of the power system were obtained. Based on the results of the fragility analysis of a 110 kV substation and a 330 kV substation in Xi'an, Shaanxi Province, the standard Monte Carlo simulation and the Sobol sequence quasi-Monte Carlo simulation are carried out. The results show that with the same sampling number, the triangle algorithm has higher operational efficiency. Combining the triangle algorithm with the quasi-Monte Carlo method improves not only the accuracy but also the calculation speed.
As a fine star-field identification algorithm, triangle algorithm is used far and wide currently, but there are some defects in triangle algorithm, such as low search efficiency and high mismatches probability. In all...
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ISBN:
(数字)9781510614062
ISBN:
(纸本)9781510614062;9781510614055
As a fine star-field identification algorithm, triangle algorithm is used far and wide currently, but there are some defects in triangle algorithm, such as low search efficiency and high mismatches probability. In allusion to these defects, a new triangle algorithm based on uncertain sign is presented. This algorithm extracted F and R features of star triangle, and then built a guidance characteristic catalogue which was searched by means of k-vector, promoting the search efficiency, moreover, in order to avoid the occurrence of mismatch, this algorithm would verify guide star triangle's auxiliary information if its uncertain sign is 1. Simulation shows that: compared to the traditional triangle algorithm, this algorithm has a couple of advantages, including the higher rate of correct star recognition, lower mismatches probability, and better real-time adaptability and robustness. And this algorithm can reach 97% on identification rate when the position error is 2 pixels, and average identification time is 38.74ms;the traditional algorithm is 75% when the position error is 2 pixels, and average identification time is 187.26ms.
Wireless sensor networks (WSN) are expected to be used to significantly improve the flexibility and expansibility of power distribution networks. In a WSN enabled power distribution network, the accuracy and energy co...
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Wireless sensor networks (WSN) are expected to be used to significantly improve the flexibility and expansibility of power distribution networks. In a WSN enabled power distribution network, the accuracy and energy consumption of node localisation can critically affect the stability of a power distribution network. In this paper, a triangle-based localisation algorithm (TBLA) is proposed to improves the traditional midnormal-based localisation algorithm (MBLA) to satisfy the communication requirements of the smart distribution automation. The proposed algorithm constructs a triangle by connecting two anchor nodes that position as one side, and then uses the RSSI (Received Signal Strength Indication) ranging value between two anchor nodes and the unknown node as the other two sides. Compared with MBLA, the simulation results reveal that, TBLA has significantly improved the precision of node localisation precision. Meanwhile, the average iterations are reduced by half, decreasing the energy consumption of the entire power distribution network significantly.
Considering that the traditional triangle algorithm needs a large amount of memory to store the navigation star database and the matching time is long,a modified triangle algorithm is *** modified algorithm uses P vec...
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Considering that the traditional triangle algorithm needs a large amount of memory to store the navigation star database and the matching time is long,a modified triangle algorithm is *** modified algorithm uses P vector for the first *** multiple matching results appear,normalized magnitude is used for the second *** navigation star database is converted from traditional triangular characteristic values into P vector and the normalized magnitude characteristic *** this way,the storage capacity of navigation star database is greatly *** simulation results show that the storage capacity and matching time are both reduced by nearly 1/3.
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