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52nd North American Power Symposium (NAPS)

作者： Farokhi-Soofi, Arash Manshadi, Saeed D. San Diego State Univ Dept Elect & Comp Engn San Diego CA 92182 USA

ISBN: (纸本)9781728181929

This paper investigates the impact of the changes in the demand of power systems on the quality of the solution procured by the convex relaxation methods for the AC optimal power flow (ACOPF) problem. This investigation needs various measures to evaluate the tightness of the solution procured by the convex relaxation approaches. Therefore, three tightness measures are leveraged to illustrate the performance of convex relaxation methods under different demand scenarios. The main issue of convex relaxation methods is recovering an optimal solution which is not necessarily feasible for the original non-convex problem in networks with cycles. Thus, a cycle measure is introduced to evaluate the performance of relaxation schemes. The presented case study investigates the merit of using various tightness measures to evaluate the performance of various relaxation methods under different circumstances.

关键词： convex relaxation optimal power flow second-order programming semi-definite programming tightness measures

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An Introduction of a CCA Weighting Matrix to a Closed-Loop Subspace Identification Method 19

An Introduction of a CCA Weighting Matrix to a Closed-Loop S...

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19th IFAC Symposium on System Identification (SYSID)

作者： Ikeda, Kenji Tanaka, Hideyuki Tokushima Univ Tokushima 7708506 Japan Hiroshima Univ Higashihiroshima 7398524 Japan

This paper introduces a CCA (canonical correlation analysis) weighting matrix to an estimation method of the innovations model previously proposed by the authors. A numerical simulation illustrates that the CCA weighting reduces the covariance of the estimate and that the proposed method gives similar or better performance compared to Closed-Loop MOESP and PBSID. Especially, the design parameter called "past horizon" in the proposed method can be set small compared to Closed-Loop MOESP and PBSID. It is also analyzed how the bias of the estimate is reduced. Copyright (C) 2021 The Authors.

关键词： System identification Subspace methods Kalman filters semi-definite programming

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Robustness of rank minimization heuristics for form-finding of tensegrity structures

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COMPUTERS & STRUCTURES 2022年 265卷 106786-106786页

作者： Tkachuk, Anton Karlstad Univ Dept Engn & Phys SE-65888 Karlstad Sweden

The form-finding process for tensegrity structures with a given topology seeks a distribution of force den-sities that satisfies stability and equilibrium conditions. A rank minimization problem regarding the force density matrix can yield feasible distributions of force densities. A direct computation of the matrix rank is difficult and is generally avoided in practice. In a recent contribution by Wang [Engineering Structures 2021;227:111419], a use the trace heuristic for form-finding is proposed. The trace heuristic does not guarantee recovery of the minimal rank. Insufficient rank deficiency leads to a degenerated geometry of the tensegrity. In this contribution, the approach is extended to log-det heuristic and a comparison between both methods is carried out focusing on robustness of the form-finding procedure for tensegri-ties. Robustness of the form-finding procedure is understood here as the ability to recover at least one feasible tensegrity design. Several examples show that the robustness is mainly influenced by the topol-ogy of the structure, constraints on force densities and the admissible set for force densities. Furthermore, the proposed extension with log-det heuristic outperforms the original method in terms of robustness, however it increases the computational cost.(c) 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).

关键词： Rank minimization heuristics Force density matrix Tensegrity structure Form-finding semi-definite programming

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A Convex Parametrization of a New Class of Universal Kernel Functions

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JOURNAL OF MACHINE LEARNING RESEARCH 2020年第1期21卷 1-29页

作者： Colbert, Brendon K. Peet, Matthew M. Arizona State Univ Dept Mech & Aerosp Engn Tempe AZ 85281 USA

The accuracy and complexity of kernel learning algorithms is determined by the set of kernels over which it is able to optimize. An ideal set of kernels should: admit a linear parameterization (tractability);be dense in the set of all kernels (accuracy);and every member should be universal so that the hypothesis space is infinite-dimensional (scalability). Currently, there is no class of kernel that meets all three criteria - e.g. Gaussians are not tractable or accurate;polynomials are not scalable. We propose a new class that meet all three criteria - the Tessellated Kernel (TK) class. Specifically, the TK class: admits a linear parameterization using positive matrices;is dense in all kernels;and every element in the class is universal. This implies that the use of TK kernels for learning the kernel can obviate the need for selecting candidate kernels in algorithms such as SimpleMKL and parameters such as the bandwidth. Numerical testing on soft margin Support Vector Machine (SVM) problems show that algorithms using TK kernels outperform other kernel learning algorithms and neural networks. Furthermore, our results show that when the ratio of the number of training data to features is high, the improvement of TK over MKL increases significantly.

关键词： kernel functions multiple kernel learning semi-definite programming supervised learning universal kernels

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Solving sparse polynomial optimization problems with chordal structure using the sparse bounded-degree sum-of-squares hierarchy

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DISCRETE APPLIED MATHEMATICS 2020年 275卷 95-110页

作者： Marandi, Ahmadreza de Klerk, Etienne Dahl, Joachim Eindhoven Univ Technol Dept Ind Engn & Innovat Sci Eindhoven Netherlands Tilburg Univ Tilburg Sch Econ & Management Tilburg Netherlands Delft Univ Technol Delft Inst Appl Math Delft Netherlands MOSEK ApS Copenhagen O Denmark

The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser et al. (2017) constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proved by the authors that the sequence converges to the optimal value. In this paper, we modify the hierarchy to deal with problems containing equality constraints directly, without eliminating or replacing them by two inequalities. We also evaluate the sparse-BSOS hierarchy on a well-known bilinear programming problem, called the pooling problem, as well as a discrete-time optimal control problem. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Polynomial optimization Sparse sum-of-squares hierarchy semi-definite programming Pooling problem Chordal sparsity structure Discrete-time optimal control

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Target Localization in Wireless Sensor Networks Based on Received Signal Strength and Convex Relaxation

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SENSORS 2022年第3期22卷 733页

作者： Ding, Weizhong Zhong, Qiubo Wang, Yan Guan, Chao Fang, Baofu Ningbo Univ Technol Robot Inst Ningbo 315048 Peoples R China

A new positioning algorithm based on RSS measurement is proposed. The algorithm adopts maximum likelihood estimation and semi-definite programming. The received signal strength model is transformed to a non-convex estimator for the positioning of the target using the maximum likelihood estimation. The non-convex estimator is then transformed into a convex estimator by semi-definite programming, and the global minimum of the target location estimation is obtained. This algorithm aims at the L-0 known problem and then extends its application to the case of L-0 unknown. The simulations and experimental results show that the proposed algorithm has better accuracy than the existing positioning algorithms.

关键词： target localization maximum likelihood estimation received signal strength semi-definite programming wireless sensor networks

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Exploiting Sparsity for Neural Network Verification 3

Exploiting Sparsity for Neural Network Verification

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3rd Annual Conference on Learning for Dynamics and Control (L4DC)

作者： Newton, Matthew Papachristodoulou, Antonis Univ Oxford Dept Engn Sci Parks Rd Oxford OX1 3PJ England

The problem of verifying the properties of a neural network has never been more important. This task is often done by bounding the activation functions in the network. Some approaches are more conservative than others and in general there is a trade-off between complexity and conservativeness. There has been significant progress to improve the efficiency and the accuracy of these methods. We investigate the sparsity that arises in a recently proposed semi-definite programming framework to verify a fully connected feed-forward neural network. We show that due to the intrinsic cascading structure of the neural network, the constraint matrices in the semi-definite program form a block-arrow pattern and satisfy conditions for chordal sparsity. We reformulate and implement the optimisation problem, showing a significant speed-up in computation, without sacrificing solution accuracy.

关键词： Chordal Sparsity Neural Networks Verification semi-definite programming

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Robust Transceiver Design for Extended Target Detection in a Signal-Dependent Interference Scenario

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IEEE ACCESS 2020年 8卷 122292-122303页

作者： Yao, Yu Miao, Pu Liu, Haitao Chen, Zhi-Min East China Jiaotong Univ Sch Informat Engn Nanchang 330013 Jiangxi Peoples R China Qingdao Univ Sch Elect & Informat Engn Qingdao 266000 Peoples R China East China Jiaotong Univ Sch Mechatron & Vehicle Engn Nanchang 330013 Jiangxi Peoples R China Shanghai Dianji Univ Sch Informat Sci & Engn Shanghai 201200 Peoples R China

Assuming unknown knowledge of target impulse response (TIR), this paper develops robust design methods to optimize the transceiver for the detection of extended targets in the presence of signal-dependent interference. Two different transceiver design schemes comprising single filter and multiple filters methods are presented to handle the fact that the TIR of extended target is unknown at the transmit side. The lowest signal to interference plus noise ratio (SINR) is considered at the receiver side as the performance measure of the system. Two robust design problems are formulated as max-min optimization problems to robustify the system SINR with respect to the unknown TIR. The former is solved using an iterative optimization process alternating between two sequential semi-definite programming (SDP) problems;the latter is solved employing an iterative optimization procedure alternating between a convex and a generalized fractional programming problems. Finally, several numerical examples highlight that the proposed design schemes have better robustness compared to several counterparts which are presented in open literature.

关键词： Extended target model robust design semi-definite programming generalized fractional programming max-min fractional problem non-convex quadratic problem

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Robust Adaptive Beamforming Based on Linearly Modified Atomic-Norm Minimization With Target Contaminated Data

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2020年 68卷 5138-5151页

作者： Zhang, Xinyu Jiang, Weidong Huo, Kai Liu, Yongxiang Li, Xiang Natl Univ Def Technol Coll Elect Sci & Technol Changsha 410073 Peoples R China Natl Univ Def Technol Coll Elect Sci & Technol Changsha 410000 Peoples R China

In practice, adaptive beamforming usually faces non-ideal situations where a limited number of snapshots are available, the training data are corrupted by desired target signals, and the array mismatches exist. Traditional methods often degrade significantly under the above situation. In order to solve this problem, a new adaptive beamforming method based on atomic-norm optimization technique is proposed in this paper. In the proposed method, the interference subspace is estimated by minimizing the rank of interference data matrix while making the signals bounded within a ball of Frobenius norm around the observed data. This non-convex problem is solved using alternative optimization which decomposes it into two iterative steps. Each step can be formulated as semi-definite programming, and solved efficiently. Unlike traditional methods, the proposed method can estimate the target signals, target directions, and interference subspace simultaneously. This property guarantees that the proposed beamformer is free from the influence of target signals, and able to adjust pointing direction adaptively. Then it is derived theoretically that the estimation of interference subspace in the proposed method is consistent, and bounded. A fast implementation algorithm based on alternating direction method of multipliers is also derived. Compared with traditional methods, the proposed method not only performs better with target-contaminated training data, and erroneous prior of target direction, but also requires much less snapshots to work. The effectiveness of the proposed method, and its advantages over traditional methods are verified based on simulated, and actual measured radar data.

关键词： Array signal processing Robustness Covariance matrices Optimization Estimation Clutter Robust adaptive beamforming atomic-norm minimization semi-definite programming sparsity recovery

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Cheap Conic OPF Models for Low-Voltage Active Distribution Networks

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IEEE ACCESS 2020年 8卷 99691-99708页

作者： Usman, Muhammad Cervi, Andrea Coppo, Massimilano Bignucolo, Fabio Turri, Roberto Univ Padua Dept Ind Engn I-35131 Padua Italy Univ Padua Interdept Ctr Giorgio Levi Cases Energy Econ & Te I-35131 Padua Italy

The increasing focus on the active participation of low-voltage (LV) active distribution networks (DNs) in electricity markets requires the real-time optimal control of these DNs. To achieve this goal, a cheap semi-definite programming (SDP)-based optimal power flow (OPF) model for active neutral-equipped DNs, hosting both wye- and delta-connected loads, is proposed in this paper, aiming at overcoming the high computational requirement of the primal SDP-based OPF model. The coupled power injections between conductors are explicitly represented for each conductor by utilizing the network admittance matrix-based approach. Furthermore, three novel propositions (P1, P2 and P3) are proposed for the modelling of the constant current component of ZIP end-users in the context of the proposed OPF model. Moreover, the impact of the voltage-angle deviation on the exactness of the P1- and P2-based models is discussed. Simulations are carried out on several LV active DNs for various parameters of ZIP end-users, and the quality of the proposed OPF model is verified through the % optimality gap, power mismatch, voltage violation and root-mean-square error criteria. It is successfully shown that the proposed OPF model provides an optimal and feasible solution for all load types (wye, delta, mixed wye-delta) under a large range of ZIP load parameters. Furthermore, among the three propositions, the P3-based OPF model appears to be the most accurate in terms of determining an optimal and feasible solution. Finally, the reduced computational time of the cheap conic model allows its real-time implementation for medium- and large-sized DNs for which the primal multi-phase SDP-based model is practically difficulty to realize.

关键词： Load modeling Computational modeling Conductors Biological system modeling Solid modeling Real-time systems programming Active distribution networks branch flow methodology conic models neutral conductor optimal power flow semi-definite programming wye- and delta-connected ZIP loads

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