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Investigation of the Optimization Models Performance in Inverse Transient Leak Detection Method

IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY-TRANSACTIONS OF CIVIL ENGINEERING 2021年第3期45卷 1959-1969页

作者： Mousavifard, Maryam Fasa Univ Fac Engn Dept Civil Engn Fasa Iran

Since one of the most important steps in leak detection method based on inverse transient analysis is optimization, in the current paper the effect of the accurate selection of the optimization model was investigated on inverse transient leak detection method results. Three different optimization models, the logarithmic barrier function method, the mesh adaptive direct search method and the genetic algorithm from three general structures including gradient-based, gradient-free and evolutionary algorithms, were developed. The leak detection model was developed especially for viscoelastic pipes, and during optimization processes by using the three suggested models, the leaks were determined simultaneously with the wave speed, steady flow friction factor and also the coefficients of creep function of the viscoelastic model. In this regard, experimental data with different discharges through the leak and different leak locations were considered. The mesh adaptive direct search model which is based on gradient-free algorithm showed the best operation in determining the location and size of the leaks. It was also shown that the pressure head affected by leaks is not only influenced by mechanical losses but also by waves reflections caused by valve closure.

关键词： Leak detection Inverse transient model Viscoelasticity logarithmic barrier function Mesh adaptive direct search Genetic algorithm

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Demand Response Strategy of Energy Prosumer Based on Robust Optimization Through Aggregator

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IEEE ACCESS 2020年 8卷 202969-202979页

作者： Park, Minsu Lee, Jihoan Won, Dong-Jun Inha Univ Dept Elect & Comp Engn Incheon 22212 South Korea

In this article, the optimal operation strategy for the aggregator to participate in demand response (DR) market is proposed. First, on the day before the occurrence of DR, Customer Baseline Load (CBL)-based load forecasting is performed using historical load data and a day-ahead scheduling is implemented to minimize electric charges by using peak reduction and arbitrage trading. If the demand response occurs, distributed energy resources (DERs) bid power reduction capacity to the aggregator. In Korea tariff system, demand charges determined by peak load are very expensive. Therefore, DERs should not update their peak load due to demand response market participation. The uncertainty of load prediction is modeled using the average value of mean absolute percentage error (MAPE), and robust optimization (RO) is implemented to determine a bidding capacity, thereby preventing the peak form being updated due to prediction error. Then, the aggregator decides the capacity to participate in DR market by considering the bidding capacity and priority. It presents the method to determine the incentive for participation in DR using a logarithmic barrier function. To evaluate the performance of the proposed algorithm simulation was performed by constructing a scenario for prediction error and mandatory reduction capacity.

关键词： Aggregator demand response energy prosumer robust optimization logarithmic barrier function

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Accurate Real-Time Estimation of Power System Transients Using Constrained Symmetric Strong Tracking Square-Root Cubature Kalman Filter

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IEEE ACCESS 2019年 7卷 165692-165709页

作者： Pramanik, Meghabriti Routray, Aurobinda Mitra, Pabitra IIT Kharagpur Adv Technol & Dev Ctr Kharagpur 721302 W Bengal India IIT Kharagpur Dept Elect Engn Kharagpur 721302 W Bengal India IIT Kharagpur Dept Comp Sci & Engn Kharagpur 721302 W Bengal India

The paper presents a fast and accurate algorithm for estimating four significant parameters (i.e., amplitude, frequency, phase angle, and damping factor) of a typical transient signal. The method can be connoted as the constrained symmetric strong tracking square-root cubature Kalman filter (CSSTSCKF). The important aspects of the proposed algorithm are: 1) constraints are imposed on the state vectors by way of a logarithmic barrier function that is either ignored or handled heuristically;2) symmetric sub-optimal multiple fading factors (FFs) are augmented into the predicted covariance matrix to capture sudden changes and to tune the gain matrix in real-time;moreover, symmetry of the covariance matrix is guaranteed by the influence of Cholesky triangular decomposition;3) effect of noise can be adjusted by tuning the soften factor. Several case studies have been simulated to evaluate the proposed algorithm with respect to some of the well-known state-of-the-art methods. The real-time performance has been evaluated by flashing the filter codes into an ARM Cortex-M7 processor board and tracking the real-time signal from the experimental test bench. The results, presented herein, indicate that the CSSTSCKF remarkably outperforms all other considered techniques. Furthermore, the stability analysis of the nonlinear filter has been proved based on the constructor expression considering the boundedness of the estimation errors and other sub-items.

关键词： Cholesky triangular decomposition fading factor (FF) inequality constraints logarithmic barrier function power system transient strong tracking square-root cubature Kalman filter (STSCKF)

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Input-to-state stability properties of relaxed barrier function based MPC

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IFAC-PapersOnLine 2015年第23期48卷 302-307页

作者： Feller, Christian Ebenbauer, Christian Institute for Systems Theory and Automatic Control University of Stuttgart Pfaffenwaldring 9 Stuttgart70550 Germany

We analyze robust stability properties of linear model predictive control schemes that are based on relaxed logarithmic barrier functions. It is shown that the corresponding closedloop system is globally exponentially stable in the nominal case as well as input-to-state stable with respect to arbitrary additive disturbances. Possible benefits and the practical relevance of the presented approach are discussed and illustrated by means of a numerical example. © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： System stability Model predictive control Predictive control systems Additive disturbance barrier functions Globally exponentially stable Input to state stable Input to state stability Linear modeling logarithmic barrier function Robust stability

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On the volumetric path

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OPTIMIZATION LETTERS 2012年第4期6卷 687-693页

作者： Mut, Murat Terlaky, Tamas Lehigh Univ Dept Ind & Syst Engn Bethlehem PA 18015 USA

We consider the logarithmic and the volumetric barrier functions used in interior point methods. In the case of the logarithmic barrier function, the analytic center of a level set is the point at which the central path intersects that level set. We prove that this also holds for the volumetric path. For the central path, it is also true that the analytic center of the optimal level set is the limit point of the central path. The only known case where this last property for the logarithmic barrier function fails occurs in case of semidefinite optimization in the absence of strict complementarity. For the volumetric path, we show with an example that this property does not hold even for a linear optimization problem in canonical form.

关键词： logarithmic barrier function Volumetric barrier function Central path Volumetric path Interior point methods Analytic center Volumetric center

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ON INTERIOR logarithmic SMOOTHING AND STRONGLY STABLE STATIONARY POINTS

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SIAM JOURNAL ON OPTIMIZATION 2010年第5期20卷 2137-2156页

作者： Jongen, Hubertus Th. Rueckmann, Jan-J. Rhein Westfal TH Aachen Lehrstuhl Math C D-52056 Aachen Germany Univ Birmingham Sch Math Birmingham B15 2TT W Midlands England

The paper deals with a nonlinear programming problem (P) and, by using a logarithmic barrier function, a parametric family of interior point approximations M(gamma) of its feasible set M, where M(gamma) is described by a single smooth inequality constraint. Assuming that a stationary point (x) over bar of (P) under consideration is strongly stable, it is shown that for all sufficiently small gamma > 0 there exists locally around (x) over bar a uniquely determined stationary point x(gamma) of (P(gamma)), where (P(gamma)) is obtained from (P) by substituting M by M(gamma). In particular, x(gamma) is strongly stable, even nondegenerate, and it has the same stationary index as (x) over bar. Furthermore, it turns out that x(gamma) and its uniquely determined Lagrange multiplier mu(gamma) form a solution pair of a corresponding interior-point problem, where (x(gamma), mu(gamma)) depends continuously differentiable (under linear independence constraint qualification (LICQ)) or continuous (under Mangasarian-Fromovitz constraint qualification (MFCQ)) on the parameter. and x(gamma) converges to (x) over bar as gamma -> 0. The stationary point (x) over bar might be degenerate and, a priori, no strict complementarity is assumed. Finally, a globalization of this one-to-one correspondence between the stationary points of (P) and (P(gamma)) as well as some further topological properties of M and M. are discussed.

关键词： logarithmic barrier function interior point approximation smoothing strongly stable stationary point degenerate solution of interior-point methods stationary index

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L^p-Norms, Log-barriers and Cramer Transform in Optimization

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SET-VALUED AND VARIATIONAL ANALYSIS 2010年第3-4期18卷 513-530页

作者： Lasserre, Jean B. Santillan Zeron, Eduardo Univ Toulouse LAAS CNRS F-31077 Toulouse 4 France Univ Toulouse LAAS Inst Math F-31077 Toulouse 4 France IPN CINVESTAV Depto Matemat Mexico City 07000 DF Mexico

We show that the Laplace approximation of a supremum by L (p) -norms has interesting consequences in optimization. For instance, the logarithmic barrier functions (LBF) of a primal convex problem P and its dual P (*) appear naturally when using this simple approximation technique for the value function g of P or its Legendre-Fenchel conjugate g (*). In addition, minimizing the LBF of the dual P (*) is just evaluating the Cramer transform of the Laplace approximation of g. Finally, this technique permits to sometimes define an explicit dual problem P (*) in cases when the Legendre-Fenchel conjugate g (*) cannot be derived explicitly from its definition.

关键词： Convex optimization logarithmic barrier function Legendre-Fenchel and Cramer transforms

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Reactive Power Optimization in Smart Grid With Wind Power Generator

Reactive Power Optimization in Smart Grid With Wind Power Ge...

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Asia-Pacific Power and Energy Engineering Conference (APPEEC)

作者： Wei Xiwen Qiu Xiaoyan Xu Jian Li Xingyuan Sichuan Univ Sch Elect Engn & Informat Chengdu Peoples R China

ISBN: (纸本)9781424448135

With the acceleration of smart grid construction, Distributed Generation (DG) integration technology needs to be developed urgently. Reactive power optimization including wind-farm is studied, and the variability and intermittency of wind speed is considered in this paper. The multi-objective reactive power optimization model including network loss, average deviation of voltage and stability margin of static voltage is established. The traditional genetic arithmetic is improved, and logarithmic barrier function in interior point method is introduced into the fitness function. So premature and partial convergence is avoided and the problem that some voltage values easily approach the upper limit in the traditional reactive power optimization is solved. The effectiveness of the proposed method is demonstrated on IEEE-57 bus system with wind farm.

关键词： smart grid wind farm integration reactive power optimization genetic algorithm logarithmic barrier function

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A global continuation algorithm for solving binary quadratic programming problems

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2008年第3期41卷 349-362页

作者： Pan, Shaohua Tan, Tao Jiang, Yuxi S China Univ Technol Sch Math Sci Guangzhou 510640 Peoples R China Dalian Univ Technol Dept Engn Mech Dalian 116024 Peoples R China Dalian Jiaotong Univ Sch Management Dalian 116028 Peoples R China

In this paper, we propose a new continuous approach for the unconstrained binary quadratic programming (BQP) problems based on the Fischer-Burmeister NCP function. Unlike existing relaxation methods, the approach reformulates a BQP problem as an equivalent continuous optimization problem, and then seeks its global minimizer via a global continuation algorithm which is developed by a sequence of unconstrained minimization for a global smoothing function. This smoothing function is shown to be strictly convex in the whole domain or in a subset of its domain if the involved barrier or penalty parameter is set to be sufficiently large, and consequently a global optimal solution can be expected. Numerical results are reported for 0-1 quadratic programming problems from the OR-Library, and the optimal values generated are made comparisons with those given by the well-known SBB and BARON solvers. The comparison results indicate that the continuous approach is extremely promising by the quality of the optimal values generated and the computational work involved, if the initial barrier parameter is chosen appropriately.

关键词： Binary quadratic programming Fischer-Burmeister function logarithmic barrier function Global continuation algorithm

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Why the logarithmic barrier function in convex and linear programming?

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OPERATIONS RESEARCH LETTERS 2000年第4期27卷 149-152页

作者： Lasserre, JB CNRS LAAS F-31077 Toulouse 4 France

关键词： convex programming linear programming interior point methods logarithmic barrier function

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