• 대한기계학회논문집A
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• 제29권6호
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• pp.842-851
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• 2005

In this paper, a new method for constrained optimization of noisy functions is proposed. In approximate optimization using response surface methods, if constraints have severe noise, the approximate feasible region defined by approximate constraints is apt to include some of the infeasible region defined by actual constraints. This can cause the approximate optimum to converge into the infeasible region. In the proposed method, the approximate optimization is performed with the approximate constraints shifted by their deviations, which are calculated using a diagonal quadratic response surface method. This can prevent the approximate optimum from converging into the infeasible region. To fit the objective and constraints into diagonal quadratic models, we select the center and 4 additional points along each axis of design variables as experimental points. The deviation of each function is calculated using the differences between the real and approximate function values at the experimental points. A sequential approximate optimization technique based on the trust region algorithm is adopted to manage approximate models. The proposed approach is validated by solving some design problems. The results of the problems show the effectiveness of the proposed method.

• 대한기계학회논문집A
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• 제29권9호
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• pp.1199-1208
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• 2005

Nowadays, it is performed actively to optimize by using an approximate model. This is called the approximate optimization. In addition, the sequential approximate optimization (SAO) is the repetitive method to find an optimum by considering the convergence of an approximate optimum. In some recent studies, it is proposed to increase the fidelity of approximate models by applying the sequential sampling. However, because the accuracy and efficiency of an approximate model is directly connected with the design area and the termination criteria are not clear, sequential sampling method has the disadvantages that could support an unreasonable approximate optimum. In this study, the SAO is executed by using trust region, Kriging model and Optimal Latin Hypercube design (OLHD). Trust region is used to guarantee the convergence and Kriging model and OLHD are suitable for computer experiment. finally, this SAO method is applied to various optimization problems of highly nonlinear mathematical functions. As a result, each approximate optimum is acquired and the accuracy and efficiency of this method is verified by comparing with the result by established method.

• 한국전산구조공학회논문집
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• 제24권5호
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• pp.543-551
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• 2011

본 논문에서는 해양작업 상태의 하중조건을 고려한 부유식 원유생산 저장 하역장치에 설치된 라이져 보강구조의 강도설계에 관련하여 다양한 근사화 기법 기반 설계최적화 및 그 성능을 비교하고자 한다. 설계최적화 문제는 하중조건별 구조강도의 제한조건 하에서 중량을 최소화하여 설계변수인 구조 부재치수가 결정되도록 정식화된다. 비교 연구를 위해 사용된 근사화 기법은 반응표면법 기반 순차적 근사최적화(RBSAO), 크리깅 기반 순차적 근사최적화(KBSAO), 그리고 개선된 이동최소자승법(MLSM) 기반 근사최적화 기법인 CF-MLSM와 Post-MLSM이다. RBSAO와 KBSAO의 적용을 위하여 상용프로세스 통합 설계최적화(PIDO) 코드를 사용하였다. 본 연구에 적용한 MLSM 기반 근사최적화 기법들은 제한조건의 가용성을 보장할 수 있도록 새롭게 개발되었다. 다양한 근사화 모델 기반 설계최적화 기법에 의한 결과는 설계 해의 개선 및 수렴속도 등의 수치적 성능을 기준으로 실제 비근사 설계최적화 결과와 비교 검토하였다.

• 한국해양공학회지
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• 제35권2호
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• pp.131-140
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• 2021

The paper deals with comparative study of various surrogate models based approximate optimization in the structural design of the passive type deck support frame under design load conditions. The passive type deck support frame was devised to facilitate both transportation and installation of 20,000 ton class topside. Structural analysis was performed using the finite element method to evaluate the strength performance of the passive type deck support frame in its initial design stage. In the structural analysis, the strength performances were evaluated for various design load conditions. The optimum design problem based on surrogate model was formulated such that thickness sizing variables of main structure members were determined by minimizing the weight of the passive type deck support frame subject to the strength performance constraints. The surrogate models used in the approximate optimization were response surface method, Kriging model, and Chebyshev orthogonal polynomials. In the context of numerical performances, the solution results from approximate optimization were compared to actual non-approximate optimization. The response surface method among the surrogate models used in the approximate optimization showed the most appropriate optimum design results for the structure design of the passive type deck support frame.

• 대한기계학회논문집A
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• 제22권4호
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• pp.811-825
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• 1998

An approximate line search is presented for dynamic response optimization with Augmented Lagrange Multiplier(ALM) method. This study empolys the approximate a augmented Lagrangian, which can improve the efficiency of the ALM method, while maintaining the global convergence of the ALM method. Although the approximate augmented Lagragian is composed of only the linearized cost and constraint functions, the quality of this approximation should be good since an approximate penalty term is found to have almost second-order accuracy near the optimum. Typical unconstrained optimization algorithms such as quasi-Newton and conjugate gradient methods are directly used to find exact search directions and a golden section method followed by a cubic polynomial approximation is empolyed for approximate line search since the approximate augmented Lagrangian is a nonlinear function of design variable vector. The numberical performance of the proposed approach is investigated by solving three typical dynamic response optimization problems and comparing the results with those in the literature. This comparison shows that the suggested approach is robust and efficient.

• 대한기계학회논문집A
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• 제34권11호
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• pp.1603-1611
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• 2010

본 논문에서는 범프 및 브레이크 하중조건 하에서 자동차 넉클의 강도설계에 관한 다양한 회귀모델 기반 근사최적화 기법 및 그 성능을 비교하고자 한다. 최적설계문제는 응력, 변형 및 진동주파수의 제한조건 하에서 중량을 최소화하여 설계변수인 단면치수가 결정되도록 정식화 된다. 비교 연구를 위해 사용된 근사화 기법은 순차적 근사최적화(SAO), 순차적 이점대각이차 근사최적화(STDQAO), 그리고 개선된 이동최소 자승법(MLSM) 기반 근사최적화 기법인 CF-MLSM 와 Post-MLSM 이다. SAO 와 STDQAO 적용을 위하여 상용 프로세스통합 설계최적화(PIDO) 코드를 사용하였다. 본 연구에 적용한 MLSM 기반 근사최적화 기법들은 제한조건의 가용성을 보장할 수 있도록 새롭게 개발되었다. 다양한 근사최적화 기법에 의한 설계결과는 설계 해의 개선 및 수렴속도 등 수치적 성능을 기준으로 실제 비근사최적화 결과와 비교검토 되었다.

• Structural Engineering and Mechanics
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• 제3권4호
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• pp.359-372
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• 1995

This study presents an efficient method for optimum design of plate and shell structures, when the design variables are continuous or discrete. Both sizing and shape design variables are considered. First the structural responses such as element forces are approximated in terms of some intermediate variables. By substituting these approximate relations into the original design problem, an explicit nonlinear approximate design task with high quality approximation is achieved. This problem with continuous variables, can be solved by means of numerical optimization techniques very efficiently, the results of which are then used for discrete variable optimization. Now, the approximate problem is converted into a sequence of second level approximation problems of separable form and each of which is solved by a dual strategy with discrete design variables. The approach is efficient in terms of the number of required structural analyses, as well as the overall computational cost of optimization. Examples are offered and compared with other methods to demonstrate the features of the proposed method.

• 한국기계가공학회지
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• 제14권3호
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• pp.85-91
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• 2015

The press-fit shaft is an important part used in automobiles, vessels, and trains. This study proposes an optimized design method to reduce damage that may occur in the press-fitted shaft by modifying the shape of the boss step of the press-fitted shaft. To reduce the time and cost of running the optimized design method, an approximate design optimization is applied and an optimized algorithm is generated using a genetic algorithm that is widely used in engineering fields and an approximate model using a response surface method. The planned experiments for the data that are needed to generate the approximate model use a central composite design (CCD) and Latin hypercube sampling (LHS), and the results of the approximate optimization using the above two design of experiments are to be compared.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1239-1248
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• 2010

In this paper, an implementable BFGS bundle algorithm for solving a nonsmooth convex optimization problem is presented. The typical method minimizes an approximate Moreau-Yosida regularization using a BFGS algorithm with inexact function and the approximate gradient values which are generated by a finite inner bundle algorithm. The approximate subgradient of the objective function is used in the algorithm, which can make the algorithm easier to implement. The convergence property of the algorithm is proved under some additional assumptions.

• Journal of Mechanical Science and Technology
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• 제15권8호
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• pp.1143-1155
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• 2001

In order to reduce the expensive CPU time for design sensitivity analysis in dynamic response optimization, this study introduces the design sensitivities approximated within estimated confidence radius in dynamic response optimization with ALM method. The confidence radius is estimated by the linear approximation with Hessian of quasi-Newton formula and qualifies the approximate gradient to be validly used during optimization process. In this study, if the design changes between consecutive iterations are within the estimated confidence radius, then the approximate gradients are accepted. Otherwise, the exact gradients are used such as analytical or finite differenced gradients. This hybrid design sensitivity analysis method is embedded in an in-house ALM based dynamic response optimizer, which solves three typical dynamic response optimization problems and one practical design problem for a tracked vehicle suspension system. The optimization results are compared with those of the conventional method that uses only exact gradients throughout optimization process. These comparisons show that the hybrid method is more efficient than the conventional method. Especially, in the tracked vehicle suspension system design, the proposed method yields 14 percent reduction of the total CPU time and the number of analyses than the conventional method, while giving similar optimum values.