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Robust Calculation of Frequency-Dependent Transmission-Line Transformation Matrices Using the Levenberg-Marquardt Method

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IEEE TRANSACTIONS ON POWER DELIVERY 2014年第4期29卷 1621-1629页

作者： Chrysochos, Andreas I. Papadopoulos, Theofilos A. Papagiannis, Grigoris K. Aristotle Univ Thessaloniki Dept Elect & Comp Engn Power Syst Lab GR-54124 Thessaloniki Greece

This paper presents a new method for the calculation of smooth frequency-dependent transmission-line (TL) transformation matrices. The proposed method, based on the Levenberg-Marquardt algorithm, solves an equivalent real-valued approach of the generalized complex eigenproblem. The implemented formulation incorporates a robust convergence criterion and is applicable to all TL configurations, due to the included numerically well-defined computational scheme. Smooth modal transformation matrices are calculated for overhead and underground TL configurations under different representations of the imperfect earth. Results are compared and validated with the corresponding results obtained from the Newton-Raphson and the sequential quadratic programming methods, revealing the accuracy, efficiency, and robustness of the proposed formulation, even in cases where the other methods fail.

关键词： Eigenproblem Levenberg-Marquardt matrix perturbation theory modal transformation matrices Newton-Raphson sequential quadratic programming

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Feature subset selection by gravitational search algorithm optimization

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INFORMATION SCIENCES 2014年 281卷 128-146页

作者： Han, XiaoHong Chang, XiaoMing Quan, Long Xiong, XiaoYan Li, JingXia Zhang, ZhaoXia Liu, Yi Taiyuan Univ Technol Key Lab Adv Transducers & Intelligent Control Sys Minist Educ China Taiyuan Shanxi Peoples R China

A new method for feature subset selection in machine learning, FSS-MGSA (Feature Subset Selection by Modified Gravitational Search Algorithm), is presented. FSS-MGSA is an evolutionary, stochastic search algorithm based on the law of gravity and mass interactions, and it can be executed when domain knowledge is not available. A wrapper approach, over Naive-Bayes, ID3, K-Nearest Neighbor and Support Vector Machine learning algorithms, is used to evaluate the goodness of each visited solution. The key to the success of the MGSA is to utilize the piecewise linear chaotic map for increasing its diversity of species, and to use sequential quadratic programming for accelerating local exploitation. Promising results are achieved in a variety of tasks where domain knowledge is not available. The experimental results show that the proposed method has the ability of selecting the discriminating input features correctly and can achieve high accuracy of classification, which is comparable to or better than well-known similar classifier systems. Furthermore, the MGSA is tested on ten functions provided by CEC 2005 special session and compared with various modified Gravitational Search Algorithm, Particle Swarm Optimization, and Genetic Algorithm. The obtained results confirm the high performance of the MGSA in solving various problems in optimization. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Feature subset selection Classification Gravitational search algorithm Learning algorithm sequential quadratic programming Chaotic map

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Algorithms for Secrecy Guarantee With Null Space Beamforming in Two-Way Relay Networks

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2014年第8期62卷 2111-2126页

作者： Yang, Yunchuan Sun, Cong Zhao, Hui Long, Hang Wang, Wenbo Beijing Univ Posts & Telecommun Minist Educ Wireless Signal Proc & Network Lab Key Lab Universal Wireless Commun Beijing 100088 Peoples R China Beijing Univ Posts & Telecommun Sch Sci Beijing 100876 Peoples R China

In this paper, we consider a two-way relay network with two sources and multiple cooperative relays in the presence of an eavesdropper. To guarantee the secrecy, a null space beamforming scheme is applied, where the relay beamforming vector lies in the nullspace of the equivalent channel of relay link from two sources to the eavesdropper. Our goal is to obtain the optimal beamforming vector as well as two sources' transmit power subject to various criteria. We propose three different approaches and solve them in an alternating iterative way, where subproblems for solving beamforming and sources' power are formulated in each iteration, respectively. First, we minimize the total transmit power under secrecy rate constraint at two sources. For beamforming vector subproblem, two different methods, semi-definite programming (SDP) and sequential quadratic programming (SQP), are proposed, where we analyze and verify SQP has lower complexity than SDP. Second, we maximize the secrecy sum rate, subject to total transmit power constraint. The beamforming vector subproblem is equivalent to a generalized Rayleigh quotient problem with rank constraint. Third, the problem of minimum per-user secrecy rate maximization under the total power constraint is investigated for user fairness. An iterative procedure utilizing the SDP with bisection search method is proposed to solve beamforming subproblem. In each approach the subproblem with two sources' power is formulated as a single variable problem and solved by Newton's method with line search. Simulation results demonstrate the validity of proposed approaches and algorithms for both symmetric and asymmetric scenarios.

关键词： Null space beamforming physical layer security semi-definite programming sequential quadratic programming

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Solution of the one-dimensional Bratu equation arising in the fuel ignition model using ANN optimised with PSO and SQP

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CONNECTION SCIENCE 2014年第3期26卷 195-214页

作者： Raja, Muhammad Asif Zahoor COMSATS Inst Informat Technol Dept Elect Engn Attock 43600 Pakistan

In this paper, an efficient procedure based on the neural networks methodology is presented for the solution of the fuel ignition model in one dimension. The neural networks were optimised with the particle swarm optimisation algorithm hybridised with sequential quadratic programming. The accuracy and convergence of the scheme are analysed by Monte Carlo simulations and their statistical analyses for three test cases of the problem represented by Bratu-type equations. It was found that the hybrid approach converges in all cases, and can solve the problem with higher accuracy and reliability than most of the methodologies used so far to solve this problem.

关键词： solid fuel ignition model particle swarm optimisation sequential quadratic programming boundary value problems

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Application of three unsupervised neural network models to singular nonlinear BVP of transformed 2D Bratu equation

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NEURAL COMPUTING & APPLICATIONS 2014年第7-8期25卷 1585-1601页

作者： Raja, Muhammad Asif Zahoor Samar, Raza Rashidi, Mohammad Mehdi COMSATS Inst Informat Technol Dept Elect Engn Attock Pakistan Mohammad Ali Jinnah Univ Islamabad Pakistan Shanghai Jiao Tong Univ Dept Mech Engn Univ Michigan Shanghai Jiao Tong Univ Joint Inst Shanghai 200030 Peoples R China Bu Ali Sina Univ Dept Mech Engn Fac Engn Hamadan Iran

In this paper, numerical techniques are developed for solving two-dimensional Bratu equations using different neural network models optimized with the sequential quadratic programming technique. The original two-dimensional problem is transformed into an equivalent singular, nonlinear boundary value problem of ordinary differential equations. Three neural network models are developed for the transformed problem based on unsupervised error using log-sigmoid, radial basis and tan-sigmoid functions. Optimal weights for each model are trained with the help of the sequential quadratic programming algorithm. Three test cases of the equation are solved using the proposed schemes. Statistical analysis based on a large number of independent runs is carried out to validate the models in terms of accuracy, convergence and computational complexity.

关键词： Two-dimensional Bratu equations Neural networks sequential quadratic programming Boundary value problems Nonlinear singular system

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A FILTER METHOD WITH UNIFIED STEP COMPUTATION FOR NONLINEAR OPTIMIZATION

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SIAM JOURNAL ON OPTIMIZATION 2014年第1期24卷 175-209页

作者： Gould, Nicholas I. M. Loh, Yueling Robinson, Daniel P. Rutherford Appleton Lab Dept Comp Sci Didcot OX11 0QX Oxon England Johns Hopkins Univ Dept Appl Math & Stat Baltimore MD 21218 USA

We present a filter line search method for solving general nonlinear and nonconvex optimization problems. The method is of the filter variety but uses a robust (always feasible) subproblem based on an exact penalty function to compute a search direction. This contrasts traditional filter methods that use a (separate) restoration phase designed to reduce infeasibility until a feasible subproblem is obtained. Therefore, an advantage of our approach is that every trial step is computed from subproblems that value reducing both the constraint violation and the objective function. Moreover, our step computation involves subproblems that are computationally tractable and utilize second derivative information when it is available. The formulation of each subproblem and the choice of weighting parameter is crucial for obtaining an efficient, robust, and practical method. Our strategy is based on steering methods designed for exact penalty functions but is fortified with a trial step convexification scheme that ensures that a single quadratic optimization problem is solved per iteration. Moreover, we use local feasibility estimates that emerge during the steering process to define a new and improved margin (envelope) of the filter. Under common assumptions, we show that the iterates converge to a local first-order solution of the optimization problem from an arbitrary starting point.

关键词： filter restoration phase large-scale sequential quadratic programming nonlinear programming

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Optimization of Aircraft Cruise Procedures Using Discrete Trajectory Patterns

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JOURNAL OF AIRCRAFT 2014年第5期51卷 1632-1640页

作者： Valenzuela, Alfonso Rivas, Damian Univ Seville Escuela Tecn Super Ingn Dept Aerosp Engn Seville 41092 Spain

This paper investigates the impact of having discrete flight restrictions on optimizing the cruise procedures commonly flown by airlines, particularly the way by which optimal procedure change when the speeds and altitudes are restricted to take discrete values. Topics covered include the optimization approach based on trajectory patterns developed to optimize the cruise procedures, and minimum direct operating cost (DOC) cruise.

关键词： Boeing 767 Aerodynamic Drag Cruise Altitude ATC Fuel Consumption Nonlinear programming Calibrated Airspeed sequential quadratic programming Direct Operating Cost Lift Coefficient

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Reduced-Order Modeling of Steady Flows Subject to Aerodynamic Constraints

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AIAA JOURNAL 2014年第2期52卷 255-266页

作者： Zimmermann, Ralf Vendl, Alexander Goertz, Stefan Tech Univ Carolo Wilhelmina Braunschweig Inst Computat Math D-38106 Braunschweig Germany German Aerosp Ctr DLR Inst Aerodynam & Flow Technol Aeroloads Predict Grp D-38108 Braunschweig Germany

A novel reduced-order modeling method based on proper orthogonal decomposition for predicting steady, turbulent flows subject to aerodynamic constraints is introduced. Model-order reduction is achieved by replacing the governing equations of computational fluid dynamics with a nonlinear weighted least-squares optimization problem, which aims at finding the flow solution restricted to the low-order proper orthogonal decomposition subspace that features the smallest possible computational fluid dynamics residual. As a second and new ingredient, aerodynamic constraints are added to the nonlinear least-squares problem. It is demonstrated that the constrained nonlinear least-squares problem can be solved almost as efficiently as its unconstrained counterpart and outperforms all alternative approaches known to the authors. The method is applied to data fusion, seeking to combine the use of computational fluid dynamics with wind-tunnel or flight testing to improve the prediction of aerodynamic loads. It is also demonstrated that it can be used to compute aerodynamic loads for a given aerodynamic configuration subject to aerodynamic design or performance targets. Exemplary results considering both applications are computed for the NACA 64A010 airfoil and the DLR-F15 high-lift configuration.

关键词： Flow Conditions CFD Aerodynamic Shape Optimization NACA 64A010 Model Order Reduction Data Fusion Flight Testing Wind Tunnel Tests sequential quadratic programming Lift Coefficient

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A MATRIX-FREE TRUST-REGION SQP METHOD FOR EQUALITY CONSTRAINED OPTIMIZATION

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SIAM JOURNAL ON OPTIMIZATION 2014年第3期24卷 1507-1541页

作者： Heinkenschloss, Matthias Ridzal, Denis Rice Univ Dept Computat & Appl Math Houston TX 77005 USA Sandia Natl Labs Albuquerque NM 87185 USA

We develop and analyze a trust-region sequential quadratic programming (SQP) method for the solution of smooth equality constrained optimization problems, which allows the inexact and hence iterative solution of linear systems. Iterative solution of linear systems is important in large-scale applications, such as optimization problems with partial differential equation constraints, where direct solves are either too expensive or not applicable. Our trust-region SQP algorithm is based on a composite-step approach that decouples the step into a quasi-normal and a tangential step. The algorithm includes critical modifications of substep computations needed to cope with the inexact solution of linear systems. The global convergence of our algorithm is guaranteed under rather general conditions on the substeps. We propose algorithms to compute the substeps and prove that these algorithms satisfy global convergence conditions. All components of the resulting algorithm are specified in such a way that they can be directly implemented. Numerical results indicate that our algorithm converges even for very coarse linear system solves.

关键词： sequential quadratic programming trust-region large-scale optimization matrix free inexact linear system solvers PDE-constrained optimization Krylov subspace methods

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Extended Monte Carlo Simulation for Parametric Global Sensitivity Analysis and Optimization

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AIAA JOURNAL 2014年第4期52卷 867-878页

作者： Wei, Pengfei Lu, Zhenzhou Song, Jingwen Northwestern Polytech Univ Sch Aeronaut Xian 710072 Peoples R China

Estimating the functional relation between the probabilistic response of a computational model and the distribution parameters of the model inputs is especially useful for 1)assessing the contribution of the distribution parameters of model inputs to the uncertainty of model output (parametric global sensitivity analysis), and 2)identifying the optimized distribution parameters of model inputs to efficiently and cheaply reduce the uncertainty of model output (parametric optimization). In this paper, the extended MonteCarlo simulation method is developed for this purpose, which provides four benefits to the parametric global sensitivity analysis and parametric optimization problems. First, the extended MonteCarlo simulation method is able to provide an unbiased or progressive unbiased estimate for the model whose behavior is even mainly governed by high nonlinearity or interaction terms. Second, only one set of model input-output samples is needed for implementing the method;thus, the computational burden is free of input dimensionality. Third, the extended MonteCarlo simulation is a derivative-free method. Fourth, the extended MonteCarlo simulation method enables us to solve problems with dependent and non-normally distributed model inputs. Additionally, the R-indices are introduced for conquering the overparameterized problem in the optimization process. An analytical example and two engineering examples are used to demonstrate the power of the proposed methods.

关键词： Monte Carlo Simulation Sensitivity Analysis Derivative Free Method Wing Box Finite Element Modeling Computing Cumulative Distribution Function sequential quadratic programming Structural System Numerical Integration

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