• Computational Structural Engineering
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• v.5 no.1
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• pp.133-142
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• 1992

This paper presents a method to apply the linear goal programming, which has rarely been used to the structural opimization problem due to its unique formulation, to large scale nonlinear structural optimization. The method can be used as a multicriteria optimization tool since goal programming removes the difficulty in defining an objective function and constraints. The method uses the finite element analysis, linear goal programming techniques and successive linearization to obtain the solution for the nonlinear goal optimization problems. The general formulation of the structural optimization problem into a nonlinear goal programming form is presented. The successive linearization method for the nonlinear goal optimization problem is discussed. To demonstrate the validity of the method, as a design tool, the minimum weight structural optimization problems with stress constraints are solved for the cases of 10, 25 and 200 trusses and compared with the results of the other works.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.2
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• pp.15-21
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• 2004

A Conjugate Gradiant (CG) method is proposed for unconstained optimization which is invariant to a nonlinear scaling of a strictly convex quadratic function. The technique has the same properties as the classical CG-method when applied to a quadratic function. The algorithm derived here is based on a logarithmic model and is compared to the standard CG method of Fletcher and Reeves [3]. Numerical results are encouraging and indicate that nonlinear scaling is promising and deserves further investigation.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.347-354
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• 2004

Using an efficient adjoint variable method, we develop a unified design sensitivity analysis (DSA) method considering both steady state nonlinear heat conduction and geometrical nonlinear elasticity problems. Design sensitivity expressions with respect to thermal conductivity and Young's modulus are derived. Beside the temperature and displacement adjoint equations, another coupled one is defined regarding the obtained adjoint displacement field as the adjoint load in temperature field. The developed DSA method is shown to be very efficient and further extended to a topology design optimization method for the nonlinear weakly coupled thermo-elasticity problems using a density approach.

• Journal of Mechanical Science and Technology
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• v.20 no.10
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• pp.1557-1566
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• 2006

We present a procedure for the application of global orthogonal polynomial into an atmospheric re-entry maneuvering problem. This trajectory optimization is imbedded in a family of canonically parameterized optimal control problem. The optimal control problem is transcribed to nonlinear programming via global orthogonal polynomial and is solved a sparse nonlinear optimization algorithm. We analyze the optimal trajectories with respect to the performance of re-entry maneuver.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.37 no.1
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• pp.42-54
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• 2009

Contrast to the 6-DOF nonlinear dynamic modeling of nonlinear tracking problem, 3-DOF point-mass modeling of flight mechanics is efficient and adequate for applying the trajectory optimization problem. There exist limitations to apply an optimal trajectory from point-mass modeling as a reference trajectory directly to conduct the nonlinear tracking control, In this paper, new matching trajectory optimization scheme is proposed to compensate those differences of mismatching. To verify performance of proposed method, full ascent three-dimensional flight trajectories are obtained by reflecting the real constraints of flight conditions and airship performance with and without jet stream condition. Then, they are compared with the optimal trajectories obtained from conventional method.

• ETRI Journal
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• v.45 no.1
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• pp.119-130
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• 2023

We propose a quantized gradient search algorithm that can achieve global optimization by monotonically reducing the quantization step with respect to time when quantization is composed of integer or fixed-point fractional values applied to an optimization algorithm. According to the white noise hypothesis states, a quantization step is sufficiently small and the quantization is well defined, the round-off error caused by quantization can be regarded as a random variable with identically independent distribution. Thus, we rewrite the searching equation based on a gradient descent as a stochastic differential equation and obtain the monotonically decreasing rate of the quantization step, enabling the global optimization by stochastic analysis for deriving an objective function. Consequently, when the search equation is quantized by a monotonically decreasing quantization step, which suitably reduces the round-off error, we can derive the searching algorithm evolving from an optimization algorithm. Numerical simulations indicate that due to the property of quantization-based global optimization, the proposed algorithm shows better optimization performance on a search space to each iteration than the conventional algorithm with a higher success rate and fewer iterations.

• Journal of Electrical Engineering and Technology
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• v.11 no.6
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• pp.1863-1871
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• 2016

This paper presents an application of fractional order controller for the control of multi input multi output twin rotor aerodynamic system. Dynamics of the considered system are highly nonlinear and there exists a significant cross-coupling between the horizontal and vertical axes (pitch & yaw). In this paper, a fractional order model of twin rotor aerodynamic system is identified using input output data from nonlinear system. Based upon identified fractional order model, a fractional order PID controller is designed to control the angular position of level bar of twin rotor aerodynamic system. The parameters of controller are tuned using Nelder-Mead optimization and compared with particle swarm optimization techniques. Simulation results on the nonlinear model show a significant improvement in the performance of fractional order PID controller as compared to a classical PID controller.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.3
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• pp.225-242
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• 2016

The phase-type representation is strongly connected with the positive realization in positive system. We attempt to transform phase-type representation into sparse mono-cyclic positive representation with as low order as possible. Because equivalent positive representations of a given phase-type distribution are non-unique, it is important to find a simple sparse positive representation with lower order that leads to more effective use in applications. A Hypo-Feedback-Coxian Block (HFCB) representation is a good candidate for a simple sparse representation. Our objective is to find an HFCB representation with possibly lower order, including all the eigenvalues of the original generator. We introduce an efficient nonlinear optimization method for computing an HFCB representation from a given phase-type representation. We discuss numerical problems encountered when finding efficiently a stable solution of the nonlinear constrained optimization problem. Numerical simulations are performed to show the effectiveness of the proposed algorithm.

• Journal of Mechanical Science and Technology
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• v.17 no.10
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• pp.1496-1506
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• 2003

The SIMP (solid isotropic material with penalization) approach is perhaps the most popular density variable relaxation method in topology optimization. This method has been very successful in many applications, but the optimization solution convergence can be improved when new variables, not the direct density variables, are used as the design variables. In this work, we newly propose S-shape functions mapping the original density variables nonlinearly to new design variables. The main role of S-shape function is to push intermediate densities to either lower or upper bounds. In particular, this method works well with nonlinear mathematical programming methods. A method of feasible directions is chosen as a nonlinear mathematical programming method in order to show the effects of the S-shape scaling function on the solution convergence.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.05a
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• pp.111-114
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• 2004

기존의 도함수에 기초한 수치적 최적화 기법들(derivative-based optimization)은 비선형 최적화 문제를 풀기 위해 목적식의 1차 도함수의 정보를 이용하여 정류점(stable point)인 최적해를 찾아 나가는 방식을 취하고 있다. 그러나 이런 방법들은 목적식의 국부 최적해(local minimum)을 찾는 것은 보장하나, 전역 최적해(global minimum)를 찾는 데에는 실패할 경우가 많다. 국부 최적해와 전역 최적해는 모두 목적식의 1차 도함수가 '0'인 값을 가지는 특징이 있으므로, 국부 또는 전역 최적해를 구하는 구하는 과정은 목적식의 1차 도함수가 '0'인 해를 찾는 방정식 문제로 변환될 수 있다. 따라서 본 논문에서는 비선형 방정식의 해를 찾는데 좋은 성능을 보이는 Homotopy 방법을 이용하여 목적식의 1차 도함수에 관한 비선형 방정식을 풀고, 이를 통해 비선형 최적화 문제의 모든 국부 최적해를 찾아냄으로써 전역 최적화 문제를 해결하는 방법을 제안하고자 한다. 제안된 방법론을 다양한 전역 최적화 문제에 적용한 결과, 기존의 방법들에 비해 더 좋은 성능을 보임을 알 수 있었다.