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SPARSE APPROACH TO SIMULTANEOUS ANALYSIS AND DESIGN OF GEOMETRICALLY NONLINEAR STRUCTURES

AIAA JOURNAL 1992年第7期30卷 1877-1885页

作者： OROZCO, CE GHATTAS, ON Carnegie Mellon University Pittsburgh Pennsylvania 15213

The problem of increasing the efficiency of the optimization process for nonlinear structures has been examined by several authors in the last ten years. One method proposed to improve the efficiency of this process considers the equilibrium equations as equality constraints of the nonlinear mathematical programming problem. The efficiency of this method, commonly called simultaneous, as compared to the more traditional approach of nesting the analysis and design phases, is reexamined in this paper. It is shown that, when projected Lagrangian methods are used, the simultaneous method is computationally more efficient than the nested, provided the sparsity of at least the Jacobian matrix is exploited. The basic structure of the Hessian and Jacobian matrices for geometrically nonlinear behavior of truss structures is given and numerical results are presented for a series of large problems using both dense and sparse projected Lagrangian methods.

关键词： Trusses sequential quadratic programming Stiffness Matrices Compressive Stress Lagrange Multipliers Structural Optimization Direct Stiffness Method Augmented Lagrangian Method Nonlinear programming Linkages

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Implementation of a robust SQP algorithm

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OPTIMIZATION METHODS & SOFTWARE 2008年第6期23卷 827-846页

作者： Fabien, Brian C. Univ Washington Dept Mech Engn Seattle WA 98195 USA

This paper presents an implementation of a sequential quadratic programming (SQP) algorithm for the solution of nonlinear programming (NLP) problems. In the proposed algorithm, a solution to the NLP problem is found by minimizing the L1 exact penalty function. The search direction for the penalty function minimization is determined by solving a strictly convex quadratic programming (QP) problem. Here, we make the basic SQP algorithm more robust (i) by solving a relaxed, strictly convex, QP problem in cases where the constraints are inconsistent, (ii) by performing a non-monotone line search to improve efficiency, and (iii) by using second-order corrections to avoid the Maratos effect. The robustness of the algorithm is demonstrated via a C language implementation that is applied to numerous parameter optimization and optimal control problems that have appeared in the literature. The results obtained show that both non-monotone line searches and second-order corrections can significantly reduce the amount of work required to solve parameter optimization problems.

关键词： nonlinear programming problem sequential quadratic programming computer code

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Capture set computation of an optimally guided missile

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2001年第6期24卷 1167-1175页

作者： Raivio, T Aalto Univ Syst Anal Lab FIN-02015 Espoo Finland

A game theoretical approach is presented for numerically computing the capture set of an optimally guided medium-range air-to-air missile against a given target. Realistic point mass models are used because long flight times prevent simplifications such as coplanarity or constant speed target. The capture set is obtained by constructing saddle point trajectories on its boundary, or the barrier, numerically. Instead of solving a game of kind, the trajectories are identified by setting up an auxiliary game of degree. The necessary conditions of the auxiliary game are shown to coincide with those of the game of kind. The game of degree is solved from systematically varied initial states with a decomposition method that does not require setting up or solving the necessary conditions. Examples are calculated for a generic fighter and a missile.

关键词： Guided Missiles Computing Nonlinear programming Aerodynamic Drag Heading Angle Transversality Condition Guidance Laws Dynamic Pressure sequential quadratic programming Lagrange Multipliers

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Preliminary study of optimal thrust-limited path-constrained maneuvers

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1996年第6期19卷 1303-1309页

作者： Wenzel, RS Prussing, JE UNIV ILLINOIS DEPT AERONAUT & ASTRONAUT ENGNURBANAIL 61801

Fuel-optimal maneuvers of a constant-specific-impulse, thrust-limited spacecraft in field-free space are analyzed. The simple problem of an optimal maneuver from a state of rest at one location to a state of rest at another location becomes very complex when a path constraint is introduced. Solutions are obtained using a direct numerical optimization method that combines Hermite-Simpson transcription and nonlinear programming. The resulting Lagrange multipliers provide a discrete approximation to the primer vector. The necessary conditions for an optimal solution can then be checked to validate the solution. Fundamental concepts, such as the existence of boundary area or boundary points and the optimal: number of coast arcs, are examined. A comprehensive solution is obtained for symmetric rest-to-rest maneuvers. More general maneuvers are also examined.

关键词： Thrust Numerical Optimization Lagrange Multipliers Optimal Control Propellant Hamiltonian Functions sequential quadratic programming Boundary Value Problems Computer Programs Specific Impulse Engine

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Structural optimization technique of a T-tail

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART G-JOURNAL OF AEROSPACE ENGINEERING 2013年第G6期227卷 1009-1020页

作者： Qiu, Ju Sun, Qin Northwestern Polytech Univ Sch Aeronaut Xian 710072 Peoples R China

A T-tail's structural design is a complex engineering problem, and multiple factors are often taken into consideration, especially flutter failure. This approach combining sequential quadratic programming and multi-island genetic algorithm handles this design problem. In the first stage, the use of sequential quadratic programming can rapidly assist in initial design by obtaining a proper model for the next optimization, with the weight as an optimization goal, subjected to constraints in conventional performance. In the second stage, multi-island genetic algorithm is used to optimize the previous result model with special requirements, mainly referring to flutter speed. The optimization-analysis results are compared and discussed with insight into the use of sequential quadratic programming and multi-island genetic algorithm. In light of the second optimization, the special flutter performance of the T-tail is illustrated, again. Improving the torsional stiffness of the horizontal tail increases the flutter speed.

关键词： T-tail optimization technique flutter characteristics sequential quadratic programming multi-island genetic algorithm

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The method for optimisation of gas compressors performance in gas storage systems

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INTERNATIONAL JOURNAL OF OIL GAS AND COAL TECHNOLOGY 2018年第1期17卷 12-33页

作者： Warchol, Michal Swirski, Konrad Ruszczycki, Blazej Wojdan, Konrad Transit Technol SA Warsaw Poland Warsaw Univ Technol Inst Heat Engn Warsaw Poland Polish Acad Sci Nencki Inst Expt Biol Warsaw Poland

We present a computational method for achieving an optimal operation of compressor units used in industrial gas storage systems. The proposed method is capable to operate with a mix of compressor types (i.e., with different operational parameters, different power drives, and different types of construction, e.g., reciprocal and turbocompressors). The goal of the optimisation is to find an optimal compressors configuration and distribution of the compressor loads for each instance of time. The proposed method is based on conversion of a multidimensional discrete-continuous optimisation problem into a set of independent combinatorial and nonlinear optimisation problems. We derive the mathematical foundations of the algorithms. The exemplary results of the application are presented.

关键词： optimisation compressor station dynamic programming sequential quadratic programming SQP gas storage

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An efficient second-order SQP method for structural topology optimization

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2016年第6期53卷 1315-1333页

作者： Rojas-Labanda, Susana Stolpe, Mathias Tech Univ Denmark Dept Wind Energy Frederiksborgvej 399 DK-4000 Roskilde Denmark

This article presents a sequential quadratic programming (SQP) solver for structural topology optimization problems named TopSQP. The implementation is based on the general SQP method proposed in Morales et al. J Numer Anal 32(2):553-579 (2010) called SQP+. The topology optimization problem is modelled using a density approach and thus, is classified as a nonconvex problem. More specifically, the SQP method is designed for the classical minimum compliance problem with a constraint on the volume of the structure. The sub-problems are defined using second-order information. They are reformulated using the specific mathematical properties of the problem to significantly improve the efficiency of the solver. The performance of the TopSQP solver is compared to the special-purpose structural optimization method, the Globally Convergent Method of Moving Asymptotes (GCMMA) and the two general nonlinear solvers IPOPT and SNOPT. Numerical experiments on a large set of benchmark problems show good performance of TopSQP in terms of number of function evaluations. In addition, the use of second-order information helps to decrease the objective function value.

关键词： Topology optimization sequential quadratic programming Minimum compliance Second-order method Hessian approximation

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Orthogonal frequency division multiplexing linear frequency modulation signal design with optimised pulse compression property of spatial synthesised signals

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IET RADAR SONAR AND NAVIGATION 2016年第7期10卷 1319-1326页

作者： Li, Hui Zhao, Yongbo Cheng, Zengfei Feng, Da-Zheng Xidian Univ Natl Lab Radar Signal Proc Xian Peoples R China

Orthogonal frequency division multiplexing (OFDM) linear frequency modulation (LFM) waveform is widely studied due to its application potentials in multiple-input-multiple-output (MIMO) radar, but its effective design is still a challenge. Considering the critical role, the pulse compression property of spatial synthesised signals plays in MIMO radar, a detailed analysis is made using OFDM LFM signals, resulting in the radical reasons for the high grating sidelobes. Then, a joint optimisation method for OFDM LFM signal design based on genetic algorithm and sequential quadratic programming is proposed to degrade the sidelobe level dramatically. Furthermore, to nullify the grating sidelobes thoroughly, a modification is performed through optimising the relaxed frequency steps of the OFDM LFM waveform, which involves a balance between sidelobe property and orthogonality. Numerical results validate the theoretic analysis and show the superior performance of the designed OFDM LFM waveforms in pulse compression properties of spatial synthesised signals.

关键词： signal synthesis OFDM modulation MIMO radar radar signal processing genetic algorithms quadratic programming optimised pulse compression spatial synthesised signals orthogonal frequency division multiplexing OFDM linear frequency modulation LFM multiple-input-multiple-output radar MIMO radar OFDM LFM signals genetic algorithm sequential quadratic programming

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Predictive planning of optimal velocity and state of charge trajectories for hybrid electric vehicles

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CONTROL ENGINEERING PRACTICE 2017年 61卷 229-243页

作者： Heppeler, Gunter Sonntag, Marcus Wohlhaupter, Uli Sawodny, Oliver Univ Stuttgart Inst Syst Dynam Waldburstr 17-19 D-70569 Stuttgart Germany Daimler AG Stuttgart Germany

The combination of electric motors and internal combustion engines in hybrid electric vehicles (HEV) can considerably improve the fuel efficiency compared to conventional vehicles. In order to use its full potential, a predictive intelligent control system using information about impending driving situations has to be developed, to determine the optimal gear shifting strategy and the torque split between the combustion engine and the electric motor. To further increase fuel efficiency, the vehicle velocity can be used as an additional degree of freedom and the development of a predictive algorithm calculating good choices for all degrees of freedom over time is necessary. In this paper, an optimization-based algorithm for combined energy management and economic driving over a limited horizon is proposed. The results are compared with results from an offline calculation, which determine the overall fuel savings potential through the use of a discrete dynamic programming algorithm. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Hybrid vehicles Dynamic programming sequential quadratic programming Energy management Potential analysis Velocity optimization Predictive control Economic driving

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An inexact restoration strategy for the globalization of the sSQP method

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2013年第3期54卷 595-617页

作者： Fernandez, D. Pilotta, E. A. Torres, G. A. Univ Nacl Cordoba Fac Matemat Astron & Fis CIEM CONICET RA-5000 Cordoba Argentina

A globally convergent algorithm based on the stabilized sequential quadratic programming (sSQP) method is presented in order to solve optimization problems with equality constraints and bounds. This formulation has attractive features in the sense that constraint qualifications are not needed at all. In contrast with classic globalization strategies for Newton-like methods, we do not make use of merit functions. Our scheme is based on performing corrections on the solutions of the subproblems by using an inexact restoration procedure. The presented method is well defined and any accumulation point of the generated primal sequence is either a Karush-Kuhn-Tucker point or a stationary (maybe feasible) point of the problem of minimizing the infeasibility. Also, under suitable hypotheses, the sequence generated by the algorithm converges Q-linearly. Numerical experiments are given to confirm theoretical results.

关键词： sequential quadratic programming Nonlinear programming Global convergence Augmented Lagrangian

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