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Closed-form approximation of the capacity in multi-sector cells: application to LTE tri-sector antenna

IET COMMUNICATIONS 2017年第6期11卷 936-941页

作者： Savaux, Vincent Siaud, Isabelle Legouable, Rodolphe IRT B Com Rennes France

This study deals with the ergodic capacity in multi-sector cells. Due to the presence of the antenna gain pattern in the expression of the capacity, the latter may be difficult to express analytically. To overcome this problem, the authors propose to approximate the antenna gain pattern by means of a piecewise linear function, which leads to a general closed-form formulation of the capacity. The obtained expression is applicable for any used antenna. The simulations results are performed by using the long term evolution (LTE) TR 36.942 antenna specification, showing that the proposed closed-form capacity almost matches the exact one. In addition, the authors provide a practical use case of the method, by considering a scenario where the users are clustered within the area covered by the antenna.

关键词： cellular radio mobile antennas Long Term Evolution approximation theory antenna radiation patterns closed-form approximation multisector cell capacity LTE tri-sector antenna ergodic capacity antenna gain pattern piecewise linear function general closed-form formulation Long Term Evolution LTE TR 36 942 antenna specification closed-form capacity

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Analysis of linear Systems with piecewise linear functions in the Input 35

Analysis of Linear Systems with Piecewise Linear Functions i...

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35th Chinese Control Conference (CCC)

作者： Li, Yuanlong Lin, Zongli Shanghai Jiao Tong Univ Minist Educ Dept Automat Key Lab Syst Control & Informat Proc Shanghai 200240 Peoples R China Univ Virginia Charles L Brown Dept Elect & Comp Engn POB 400743 Charlottesville VA 22904 USA

ISBN: (纸本)9789881563910

This paper revisits the problem of estimating the domain of attraction of linear systems with piecewise linear function in the input. We construct a generalized piecewise quadratic Lyapunov function of the augmented state vector consisting of the system states and the terms that characterize the regional sector conditions of the saturation functions embedded in the piecewise linear function. Conditions are established under which the level sets of the generalized piecewise quadratic Lyapunov function are contractively invariant. Based on these conditions, we formulate a bilinear matrix inequality optimization problem and solve it by using an iterative algorithm that is based on linear matrix inequalities (LMIs) to obtain the largest level set as an estimate of the domain of attraction. Simulation results indicate that the proposed approach indeed has the ability to obtain a significantly larger estimate of the domain of attraction than the existing methods.

关键词： piecewise linear function Domain of attraction Generalized piecewise quadratic Lyapunov functions Stability analysis

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Efficient Pattern Recognition Using the Frequency Response of a Spiking Neuron 9th

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9th Mexican Conference on Pattern Recognition (MCPR)

作者： Valadez-Godinez, Sergio Gonzalez, Javier Sossa, Humberto Inst Politecn Nacl Ctr Invest Computac Av Juan de Dios Batiz S-N Mexico City 07738 DF Mexico

ISBN: (纸本)9783319592268;9783319592251

In previous works, a successful scheme using a single Spiking Neuron (SN) to solve complex problems in pattern recognition has been proposed. This consists in using the firing frequency response to classify a given input pattern, which is multiplied by a weight vector to produce a constant stimulation current. The weight vector is adjusted by an evolutionary strategy where the objective is to obtain an optimal frequency separation. The problem is that the SN has to be numerically simulated several times when the weight vector is being adjusted. In this work, we propose fitting the SN frequency response curve to a piecewise linear function to be used instead of the costly SN simulation. A high fitting degree was found, but, more importantly, the computational cost of the training and testing phases was drastically reduced.

关键词： Spiking Neuron Izhikevich Pattern recognition Curve fitting Frequency Response Curve piecewise linear function Firing Rate Evolutionary strategy Differential evolution Computational cost

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Optimal scheduling of virtual power plant with battery degradation cost

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IET GENERATION TRANSMISSION & DISTRIBUTION 2016年第3期10卷 712-725页

作者： Zhou, Bin Liu, Xi Cao, Yijia Li, Canbing Chung, Chi Yung Chan, Ka Wing Hunan Univ Coll Elect & Informat Engn Changsha 410082 Hunan Peoples R China Univ Saskatchewan Dept Elect & Comp Engn Saskatoon SK S7N 0W0 Canada Hong Kong Polytech Univ Dept Elect Engn Hong Kong Hong Kong Peoples R China

This study proposes a novel optimal generation scheduling model for virtual power plant (VPP) considering the degradation cost of energy storage system (ESS). The VPP is generally formed by a mix of distributed energy resources, and the ESS is an important installation for flexible VPP dispatch due to its controllable and schedulable behaviours. For the operations of battery storage systems, the ambient temperature and depth of discharge have significant impacts on the wear and tear of the ESS as well as battery degradation cost. Furthermore, the battery degradation cost is modelled and approximated by a piecewise linear function, and then incorporated into the proposed optimal VPP scheduling model. Consequently, the optimal VPP scheduling problem is formulated as a two-stage stochastic mixed-integer linear programming in order to maximise the expected profits of the VPP. The proposed model has been successfully implemented and tested through a representative case study, and the influence of battery degradation cost on optimal VPP scheduling has also been thoroughly analysed and demonstrated.

关键词： power generation scheduling battery storage plants costing energy storage distributed power generation power generation dispatch approximation theory stochastic programming integer programming linear programming profitability power generation economics power distribution economics virtual power plant battery degradation costing optimal generation scheduling model energy storage system ESS distributed energy resource flexible VPP dispatching battery storage system piecewise linear function optimal VPP scheduling problem two-stage stochastic mixed-integer linear programming

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linear complementarity representation of piecewise linear functions

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IMA JOURNAL OF APPLIED MATHEMATICS 2015年第4期80卷 1178-1198页

作者： Sakurai, Tomoaki Murofushi, Toshiaki Tokyo Inst Technol Dept Computat Intelligence & Syst Sci Midori Ku Yokohama Kanagawa 2268502 Japan

We investigate a representation of piecewise linear function containing a complementarity condition, and call it a linear complementarity representation. This representation is also known as 'Bokh1' or 'state-variable representation' in literature. We discuss two spacial types of representation, called P-representation and ULT-representation, and give an elementary proof to show that either one of these two types of representation completely characterizes any piecewise linear function. We can also demonstrate that a P-representation can be transformed into a ULT-representation, and show how it can be implemented in an algorithmic manner. Furthermore, as an application of linear complementarity representation, we will present a formula of linear complementarity representation of the Choquet integral model over a finite set, which is a model used in the area of decision-making as an aggregation function.

关键词： piecewise linear function linear complementarity representation P-matrix ULT-matrix

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Analysis of linear Systems with piecewise linear functions in the Input

Analysis of Linear Systems with Piecewise Linear Functions i...

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第35届中国控制会议

作者： Yuanlong Li Zongli Lin Department of Automation Shanghai Jiao Tong University Key Laboratory of System Control and Information Processing of Ministry of Education

ISBN: (纸本)9781509009107

This paper revisits the problem of estimating the domain of attraction of linear systems with piecewise linear function in the *** construct a generalized piecewise quadratic Lyapunov function of the augmented state vector consisting of the system states and the terms that characterize the regional sector conditions of the saturation functions embedded in the piecewise linear *** are established under which the level sets of the generalized piecewise quadratic Lyapunov function are contractively *** on these conditions,we formulate a bilinear matrix inequality optimization problem and solve it by using an iterative algorithm that is based on linear matrix inequalities(LMIs) to obtain the largest level set as an estimate of the domain of *** results indicate that the proposed approach indeed has the ability to obtain a significantly larger estimate of the domain of attraction than the existing methods.

关键词： piecewise linear function Domain of attraction Generalized piecewise quadratic Lyapunov functions Stability analysis

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Mathematical programming for piecewise linear regression analysis

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EXPERT SYSTEMS WITH APPLICATIONS 2016年 44卷 156-167页

作者： Yang, Lingjian Liu, Songsong Tsoka, Sophia Papageorgiou, Lazaros G. UCL Dept Chem Engn Ctr Proc Syst Engn London WC1E 7JE England Kings Coll London Sch Nat & Mahtemat Sci Dept Informat London WC2R 2LS England

In data mining, regression analysis is a computational tool that predicts continuous output variables from a number of independent input variables, by approximating their complex inner relationship. A large number of methods have been successfully proposed, based on various methodologies, including linear regression, support vector regression, neural network, piece-wise regression, etc. In terms of piece-wise regression, the existing methods in literature are usually restricted to problems of very small scale, due to their inherent non-linear nature. In this work, a more efficient piece-wise linear regression method is introduced based on a novel integer linear programming formulation. The proposed method partitions one input variable into multiple mutually exclusive segments, and fits one multivariate linear regression function per segment to minimise the total absolute error. Assuming both the single partition feature and the number of regions are known, the mixed integer linear model is proposed to simultaneously determine the locations of multiple break-points and regression coefficients for each segment. Furthermore, an efficient heuristic procedure is presented to identify the key partition feature and final number of break-points. 7 real world problems covering several application domains have been used to demonstrate the efficiency of our proposed method. It is shown that our propbsed piece-wise regression method can be solved to global optimality for datasets of thousands samples, which also consistently achieves higher prediction accuracy than a number of state-of-the-art regression methods. Another advantage of the proposed method is that the learned model can be conveniently expressed as a small number of if-then rules that are easily interpretable. Overall, this work proposes an efficient rule-based multivariate regression method based on piece-wise functions and achieves better prediction performance than state-of-the-arts approaches. This novel method

关键词： Regression analysis Surrogate model piecewise linear function Mathematical programming Optimisation

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On solvability recognition for interval linear systems of equations

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OPTIMIZATION LETTERS 2016年第2期10卷 247-260页

作者： Shary, Sergey P. Sharaya, Irene A. Novosibirsk State Univ Inst Computat Technol SB RAS Novosibirsk 630090 Russia

The paper considers the problem of recognizing solvability (nonemptiness of the solution set) for interval systems of linear algebraic equations. We introduce a quantitative measure of the membership of a point in the solution set, the so-called "recognizing functional" of the solution set. As the result, the decision on solvability of the interval linear systems reduces to global maximization of the recognizing functional. Additionally, the specific value of this maximum and its argument provide us with important quantitative information of the solvability supply or its deficiency, which can used for the correction of the interval system in a desired sense.

关键词： Interval system of linear equations Solvability Solution set Solvability measure Recognizing functional piecewise linear function

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Slope estimation in noisy piecewise linear functions

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SIGNAL PROCESSING 2015年 108卷 576-588页

作者： Ingle, Atul Bucklew, James Sethares, William Varghese, Tomy Univ Wisconsin Dept Elect & Comp Engn Madison WI 53706 USA Univ Wisconsin Dept Med Phys Madison WI 53705 USA

This paper discusses the development of a slope estimation algorithm called MAPSLOPE for piecewise linear data that is corrupted by Gaussian noise. The number and locations of slope change points (also known as breakpoints) are assumed to be unknown a priori though it is assumed that the possible range of slope values lies within known bounds. A stochastic hidden Markov model that is general enough to encompass real world sources of piecewise linear data is used to model the transitions between slope values and the problem of slope estimation is addressed using a Bayesian maximum a posteriori approach. The set of possible slope values is discretized, enabling the design of a dynamic programming algorithm for posterior density maximization. Numerical simulations are used to justify choice of a reasonable number of quantization levels and also to analyze mean squared error performance of the proposed algorithm. An alternating maximization algorithm is proposed for estimation of unknown model parameters and a convergence result for the method is provided. Finally, results using data from political science, finance and medical imaging applications are presented to demonstrate the practical utility of this procedure. (C) 2014 Elsevier B.V. All rights reserved.

关键词： piecewise linear function MAP estimation Dynamic programming optimization EM algorithm Alternating maximization

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Two-stage piecewise linear model for investigating doseresponse relationship in meta-analysis:methodology,examples,and applicationShort title:Two-stage piecewise linear model for dose-response meta-analysis

Two-stage piecewise linear model for investigating doserespo...

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2017年中国卫生统计学学术年会

作者： Chang Xu Lehana Thabane Chao Zhang Tong-Zu Liu Ling Li Ke Deng Xin Sun Chinese Evidence-Based Medicine Center and Chinese Cochrane Center West China HospitalSichuan University Department of Clinical Epidemiology and Biostatistics McMaster University Center for Evidence-Based Medicine and Clinical Research Taihe HospitalHubei University of Medicine Department of Urology Zhongnan Hospital of Wuhan UniversityWuhan University

Background:Dose-response meta-analysis(DRMA)is widely employed to establishing the potential dose-response relationship between continuous exposures and disease ***,no method is readily available for exploring the relation between a discrete exposure and a binary or continuous ***:We proposed a two-stage piecewise linear(PL)DRMA model as a solution to this *** used sleep(a continuous exposure)and parity(a discrete exposure)data to illustrate how to apply PL model in DRMA using the Stata code *** also empirically compared the slopes of PL model with restricted cubic spline(RCS)model by sleep ***:PL DRMA model fitted well in our two *** sleep duration,our meta-analysis showed that the relative risk(RR)of all-cause mortality was 1.02(95%CI:1.01,1.04)for every 1-hour reduction of sleep duration among people who slept less than 7 hours,and 1.15(95%CI:1.06,1.25)for every 1-hour increase of sleep duration among people who slept more than 7 *** parity and risk of rheumatoid arthritis:among women with 3 or less births,the RR was 0.88(95%CI:0.77,1.00)for every 1-birth increment;otherwise(3 or more births),the RR was 1.10(95%CI:0.99,1.23)for every 1-birth *** slopes of PL model fitted well to RCS curve based on sleep ***:piecewise linear function is a simple and valid method for DRMA and can be used for discrete *** also represents a superior model to linear model in DRMA and may be an alternative model to non-linear model.

关键词： piecewise linear function dose-response meta-analysis discrete exposure two-stage approach

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