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On Camera Calibration with linear programming and Loop Constraint linearization

INTERNATIONAL JOURNAL OF COMPUTER VISION 2012年第1期97卷 71-90页

作者： Courchay, Jerome Dalalyan, Arnak S. Keriven, Renaud Sturm, Peter Univ Paris Est IMAGINE LIGM Paris France INRIA Grenoble Lab Jean Kuntzmann Rhone Alpes France

A technique for calibrating a network of perspective cameras based on their graph of trifocal tensors is presented. After estimating a set of reliable epipolar geometries, a parameterization of the graph of trifocal tensors is proposed in which each trifocal tensor is linearly encoded by a 4-vector. The strength of this parameterization is that the homographies relating two adjacent trifocal tensors, as well as the projection matrices depend linearly on the parameters. Two methods for estimating these parameters in a global way taking into account loops in the graph are developed. Both methods are based on sequential linear programming: the first relies on a locally linear approximation of the polynomials involved in the loop constraints whereas the second uses alternating minimization. Both methods have the advantage of being non-incremental and of uniformly distributing the error across all the cameras. Experiments carried out on several real data sets demonstrate the accuracy of the proposed approach and its efficiency in distributing errors over the whole set of cameras.

关键词： Structure from motion Camera calibration sequential linear programming

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Shape optimization of bonded patch to cylindrical shell structures

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2003年第5期58卷 793-820页

作者： Tong, LY Sun, XN Univ Sydney Sch Aerosp Mech & Mechatron Engn Sydney NSW 2006 Australia

Adhesive bonding has been widely used to join or repair metallic and composite structural components to achieve or restore their designated structural stiffness and strengths. However, current analysis methods and empirical databases for composite bonded patch repairs or joints are limited to flat structures, and there exists a very limited knowledge on the effect of curvature on the performance and durability of composite bonded joints and repairs. Recently, a novel finite element formulation was presented for developing adhesive elements for conducting 2.5-D simplified stress analysis of bonded repairs to curved structures. This paper presents the work on optimal shape design of a bonded curved composite patch using the newly developed adhesive element. The sequential linear programming (SLP) method is employed as the optimization algorithm in conjunction with a fully implemented mesh generation algorithm into which new features have been incorporated. The objective of shape optimization is to minimize the maximum stress in the entire adhesive layer to ensure that the bonded patch effectively works together with the parent structure in service. Several different objective functions, related to possible failure mechanisms of the adhesive layer, are proposed to optimize the shape of a bonded patch. Copyright (C) 2003 John Wiley Sons, Ltd.

关键词： adhesive bonding shape optimization sequential linear programming automatic mesh generation finite element analysis adhesive element

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An SLP filter algorithm for probabilistic analytical target cascading

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2010年第6期41卷 935-945页

作者： Han, Jeongwoo Papalambros, Panos Y. Argonne Natl Lab Argonne IL 60439 USA Univ Michigan Dept Mech Engn Ann Arbor MI 48104 USA

Decision-making under uncertainty is particularly challenging in the case of multidisciplinary, multilevel system optimization problems. Subsystem interactions cause strong couplings, which may be amplified by uncertainty. Thus, effective coordination strategies can be particularly beneficial. Analytical target cascading (ATC) is a deterministic optimization method for multilevel hierarchical system design that has been extended to probabilistic formulations. Solving the probabilistic optimization problem requires propagation of uncertainty, namely, evaluating or estimating the output distributions, a task that is computationally expensive for highly nonlinear functions. This article presents the use of sequential linear programming (SLP) for probabilistic ATC. By linearizing and solving a problem successively, the strategy takes advantage of the simplicity and ease of uncertainty propagation for a linear system under the assumption that inputs are normally distributed or can be transformed into equivalent normal distributions. A suspension strategy, developed for a deterministic SLP coordination strategy for ATC, is applied to reduce computational cost by suspending the analyses of subsystems that do not need considerable redesign. The accuracy and effectiveness of the proposed coordination strategy is demonstrated with several numerical examples.

关键词： Probabilistic analytical target cascading sequential linear programming Complex system design under uncertainty Suspension strategy

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Application of singular value decomposition method to digitally controlled large orbiting platforms

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1998年第4期21卷 551-557页

作者： Ericsson-Jackson, AJ Bainum, PM Xing, GQ Howard Univ Dept Mech Engn Washington DC 20059 USA

The dynamics and control for the specific application of a large orbiting flexible thin square plate are considered. The focus is on the utilization of a singular value decomposition (SVD) method to create a stable reduced-order system. By reviewing the system's singular value bounds in the frequency domain one can properly assess stability robustness parameters that are difficult to characterize effectively in a time-domain setting. This system's open-loop singular values were extremely close to zero, denoting singular system matrices. To alleviate this problem with matrix singularity, the SVD method was applied to transform the original systems. The reduction of actuators/sensors is done partially in the physical sense and partially in the mathematical space. Results show that when the SVD method transformation is applied stable controllable closed-loop system matrices can be designed.

关键词： Singular Value Decomposition Actuators Open Loop Transfer Function Horizon Sensors Frequency Domain linear Quadratic Gaussian Earth Sensors Earth NASA Goddard Space Flight Center sequential linear programming

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Multi-stage risk-based dispatch considering short-term reliability of transmission lines

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IET GENERATION TRANSMISSION & DISTRIBUTION 2020年第19期14卷 4132-4140页

作者： Lou, Xian-Si Guo, Chuang-Xin Ding, Yi Chen, Wei Zhejiang Univ Coll Elect Engn Hangzhou 310027 Peoples R China

The reliability of transmission lines (TLs) has great influences on the safe operation of power systems. Random failures from TLs can be caused by multiple uncertainties such as the high load current. In this study, a multi-stage risk-based dispatch model is proposed to minimise the sum of generation cost and risk cost. Impacts of natural ageing, load current, health condition and disaster weather on the short-term reliability of TLs are studied. For ensuring the operation security of power systems in the post-contingency stage, the dynamic thermal rating (DTR) technology is implemented to improve capacities of TLs for coping with the potential overload. In order to solve this non-linear optimiation problem caused by load current-dependent failure probabilities and thermal rating constraints, a double-iteration solving strategy is proposed. In exterior iterations, the sequential linear programming is applied to decouple bilinear terms of the risk cost and locally linearise failure probabilities. Meanwhile, in interior iterations, the Benders decomposition is utilised to further divide the model into the main problem and the sub-problem for coordinating the preventive and corrective control and checking the feasibility of DTR, respectively. Proposed approaches are validated on a modified IEEE 24-bus test system.

关键词： linear programming power system security power transmission reliability iterative methods power generation dispatch probability power transmission lines post-contingency stage dynamic thermal rating technology nonlinear optimisation problem load current-dependent failure probabilities thermal rating constraints double-iteration solving strategy exterior iterations sequential linear programming decouple bilinear terms risk cost modified IEEE 24-bus test system short-term reliability transmission lines safe operation power systems high load current multistage risk-based dispatch model generation cost natural ageing health condition disaster weather operation security preventive control corrective control

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A linear programming-based optimization algorithm for solving nonlinear programming problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第3期200卷 658-670页

作者： Still, Claus Westerlund, Tapio Abo Akad Univ Proc Design & Syst Engn Lab FIN-20500 Turku Finland

In this paper a linear programming-based optimization algorithm called the sequential Cutting Plane algorithm is presented. The main features of the algorithm are described, convergence to a Karush-Kuhn-Tucker stationary point is proved and numerical experience on some well-known test sets is showed. The algorithm is based on an earlier version for convex inequality constrained problems, but here the algorithm is extended to general continuously differentiable nonlinear programming problems containing both nonlinear inequality and equality constraints. A comparison with some existing solvers shows that the algorithm is competitive with these solvers. Thus, this new method based on solving linear programming subproblems is a good alternative method for solving nonlinear programming problems efficiently. The algorithm has been used as a subsolver in a mixed integer nonlinear programming algorithm where the linear problems provide lower bounds on the optimal solutions of the nonlinear programming subproblems in the branch and bound tree for convex, inequality constrained problems. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Nonlinear programming Cutting plane algorithms sequential linear programming

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Multidisciplinary Design Optimization: A Survey of Architectures

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AIAA JOURNAL 2013年第9期51卷 2049-2075页

作者： Martins, Joaquim R. R. A. Lambe, Andrew B. Univ Michigan Ann Arbor MI 48109 USA Univ Toronto Toronto ON M3H 5T6 Canada

Multidisciplinary design optimization is a field of research that studies the application of numerical optimization techniques to the design of engineering systems involving multiple disciplines or components. Since the inception of multidisciplinary design optimization, various methods (architectures) have been developed and applied to solve multidisciplinary design-optimization problems. This paper provides a survey of all the architectures that have been presented in the literature so far. All architectures are explained in detail using a unified description that includes optimization problem statements, diagrams, and detailed algorithms. The diagrams show both data and process flow through the multidisciplinary system and computational elements, which facilitate the understanding of the various architectures, and how they relate to each other. A classification of the multidisciplinary design-optimization architectures based on their problem formulations and decomposition strategies is also provided, and the benefits and drawbacks of the architectures are discussed from both theoretical and experimental perspectives. For each architecture, several applications to the solution of engineering-design problems are cited. The result is a comprehensive but straightforward introduction to multidisciplinary design optimization for nonspecialists and a reference detailing all current multidisciplinary design-optimization architectures for specialists.

关键词： MDO Numerical Optimization Lagrange Multipliers sequential Quadratic programming Structural Optimization Computing Structural Analysis Aircraft Design Aerodynamic Loads sequential linear programming

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MULTIOBJECTIVE TRAJECTORY OPTIMIZATION BY GOAL programming WITH FUZZY DECISIONS

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1994年第2期17卷 297-303页

作者： SUZUKI, S YOSHIZAWA, T University of Tokyo Bunkyo-ku Tokyo 113 Japan

A sequential goal programming approach is considered for not only well-defined flight trajectory problems but also ill-defined problems that have no feasible solutions satisfying all design requirements due to strict boundary conditions or tight path constraints. By using a time integration algorithm, trajectory optimization problems am transformed into numerical optimization problems that seek optimal control variables at discrete time points to minimize an objective function and satisfy various design constraints. By defining the target goal values of both the constraints and the objective functions and by prioritizing each goal according to its significance, the GP formulation modifies ill-defined problems as multiobjective design problems. Additionally, a fuzzy decision making method is applied for those goals that are prioritized, not precisely, but in a fuzzy manner. Numerical applications for simple ascent trajectory problems show that this method can efficiently find the trajectories when various kinds of design requirements are imposed for the ill-defined problem.

关键词： Trajectory Optimization Flight Trajectory Numerical Optimization Integration Algorithm sequential Quadratic programming Control Optimization sequential linear programming Propellant Finite Difference Method Interplanetary Mission

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Enhanced multiobjective particle swarm optimization in combination with adaptive weighted gradient-based searching

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ENGINEERING OPTIMIZATION 2008年第9期40卷 789-804页

作者： Izui, Kazuhiro Nishiwaki, Shinji Yoshimura, Masataka Nakamura, Masahiko Renaud, John E. Kyoto Univ Dept Aeronaut & Astronaut Kyoto Japan Univ Notre Dame Aerosp & Mech Engn Notre Dame IN 46556 USA

This article proposes a new multiobjective optimization method for structural problems based on multiobjective particle swarm optimization (MOPSO). A gradient-based optimization method is combined with MOPSO to alleviate constraint-handling difficulties. In this method, a group of particles is divided into two groups - a dominated solution group and a non-dominated solution group. The gradient-based method, utilizing a weighting coefficient method, is applied to the latter to conduct local searching that yields superior non-dominated solutions. In order to enhance the efficiency of exploration in a multiple objective function space, the weighting coefficients are adaptively assigned considering the distribution of non-dominated solutions. A linear optimization problem is solved to determine the optimal weighting coefficients for each non-dominated solution at each iteration. Finally, numerical and structural optimization problems are solved by the proposed method to verify the optimization efficiency.

关键词： structural optimization particle swarm optimization multiobjective optimization hybrid technique sequential linear programming adaptive weighting coefficient

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METHOD FOR NONlinear OPTIMIZATION WITH DISCRETE DESIGN VARIABLES

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AIAA JOURNAL 1989年第11期27卷 1584-1589页

作者： OLSEN, GR VANDERPLAATS, GN VMA ENGN SANTA BARBARACA

A numerical method is presented for the solution of nonlinear discrete optimization problems. The applicability of discrete optimization to engineering design is discussed, and several standard structural optimization problems are solved using discrete design variables. The method uses approximation techniques to create subproblems suitable for linear mixed-integer programming methods. The method employs existing software for continuous optimization and integer programming. © 1989 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Structural Optimization Trusses Finite Element Analysis sequential linear programming Tensile Strength Numerical Optimization Structural Engineering linear programming Sensitivity Analysis Structural Dynamics

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