• Journal of Mechanical Science and Technology
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• v.16 no.2
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• pp.203-210
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• 2002

For effective response surface modeling during sequential approximate optimization (SAO), the normalized and the augmented D-optimality criteria are presented. The normalized D-optimality criterion uses the normalized Fisher information matrix by its diagonal terms in order to obtain a balance among the linear-order and higher-order terms. Then, it is augmented to directly include other experimental designs or the pre-sampled designs. This augmentation enables the trust region managed sequential approximate optimization to directly use the pre-sampled designs in the overlapped trust regions in constructing the new response surface models. In order to show the effectiveness of the normalized and the augmented D-optimality criteria, following two comparisons are performed. First, the information surface of the normalized D-optimal design is compared with those of the original D-optimal design. Second, a trust-region managed sequential approximate optimizer having three D-optimal designs is developed and three design problems are solved. These comparisons show that the normalized D-optimal design gives more rotatable designs than the original D-optimal design, and the augmented D-optimal design can reduce the number of analyses by 30% - 40% than the original D-optimal design.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.9 s.240
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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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.1 s.232
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• pp.45-52
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• 2005

A general approximate optimization technique by sequential design domain(SDD) did not save response values for getting an approximate function in each step. It has a disadvantage at aspect of an expense. In this paper, previous response values are recycled for constructing an approximate function. For this reason, approximation function is more accurate. Accordingly, even if we did not determine move limit, a system is converged to the optimal design. Size and shape optimization using approximate optimization technique is carried out with SDD. Algorithm executing Pro/Engineer and ANSYS are automatically adopted in the approximate optimization program by SDD. Convergence criterion is defined such that optimal point must be located within SDD during the three steps. The PLBA(Pshenichny-Lim-Belegundu-Arora) algorithm is used to solve approximate optimization problems. This algorithm uses the second-order information in the direction finding problem and uses the active set strategy.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.207-220
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• 1999

In this paper, some of the issue about a group sequential method are considered in the Bayesian context. The continuous time optimal stopping boundary can be used to approximate the optimal stopping boundary for group sequential designs. The exact stopping boundary for group sequential design is obtained by using the backward induction method and is compared with the continuous optimal stopping boundary and the corrected continuous stopping boundary.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.16 no.12
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• pp.1156-1166
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• 2004

The shape of plate-fin type heat sink is numerically optimized to acquire the minimum pressure drop under the required temperature rise. In constrained nonlinear optimization problems of thermal/fluid systems, three fundamental difficulties such as high computational cost for function evaluations (i.e., pressure drop and thermal resistance), the absence of design sensitivity information, and the occurrence of numerical noise are commonly confronted. Thus, a sequential approximate optimization (SAO) algorithm has been introduced because it is very hard to obtain the optimal solutions of fluid/thermal systems by means of gradient-based optimization techniques. In this study, the progressive quadratic response surface method (PQRSM) based on the trust region algorithm, which is one of sequential approximate optimization algorithms, is used for optimization and the heat sink is optimized by combining it with the computational fluid dynamics (CFD).

• The Korean Journal of Applied Statistics
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• v.10 no.2
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• pp.353-366
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• 1997

In this paper, we derive an approximate optimal Bayes group sequential design for a given loss function. We use the Monte-Carlo method to compare the ASN(average sample size) function and Bayes risk of approximate optimal Bayes group sequential design, Pocock design and O'Brien and Fleming design. Also introduced is the concept of Bayes efficiency and percentage loss of information due to grouping for the group sequential design and use it to measure the loss of information for different group sizes.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.12
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• pp.3040-3052
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• 2000

For effective construction of second-order response surface models, an efficient quad ratic approximation method is proposed in the context of trust region model management strategy. In the proposed method, although only the linear and quadratic terms are uniquely determined using 2n+1 design points, the two-factor interaction terms are mathematically updated by normalized quasi-Newton formula. In order to show the numerical performance of the proposed approximation method, a sequential approximate optimizer is developed and solves a typical unconstrained optimization problem having 2, 6, 10, 15, 30 and 50 design variables, a gear reducer system design problem and two dynamic response optimization problems with multiple objectives, five objectives for one and two objectives for the other. Finally, their optimization results are compared with those of the CCD or the 50% over-determined D-optimal design combined with the same trust region sequential approximate optimizer. These comparisons show that the proposed method gives more efficient than others.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.4
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• pp.431-437
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• 2003

In this paper, an approximate optimization program based on GUI(graphic user interface) environment is developed. This program is coded by using Fortran and Visual basic. Fortran is used to Progress approximate optimization process. Visual basic is used to make user environment for user to use conveniently. Inside of this program, it uses two independent programs. One is commercial program, ANSYS, and the other is optimization program, PLBA(Pshenichny-Lim-Belegundu Arora). The former is used to obtain approximate equation of stress and displacement of a structure. The latter is used to solve approximate optimization. This algorithm uses second-order information of a function and active set strategy. This program is connecting ANSYS and PLBA. And it progress the process repeatedly until it obtain optimum value. As a method of approximate optimization, sequential design domain(SDD) is introduced. SDD starts with a certain range which is offseted from midpoint of an initial design domain and then SDD of the next step is determined by optimal point of a prior step.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1023-1028
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• 2004

A micro-pressure wave is generated by the high-speed train which enters a tunnel, and it causes explosive noise and vibration at the exit. It is known that train speed, train-tunnel area ratio, nose slenderness and nose shape mainly influence on generating micro-pressure wave. So it is required to minimize it by searching optimal values of such train shape factors and tunnel condition. In this study, response surface model, one of approximation models, is used to perform optimization effectively and analyze sensitivity of design variables. Owen's randomized orthogonal array and D-optimal Design are used to construct response surface model. In order to increase accuracy of model, stepwise regression is selected. Finally SQP(Sequential Quadratic Programming) optimization algorithm is used to minimize the maximum micro-pressure wave by using built approximation model.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.1
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• pp.31-38
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• 2004

Mechanical design process is generally accomplished by design, analysis, and test. Designers use programs fitting purpose, and obtain repeatedly a response of a simulation program, a sub-program for optimization. In this paper, shape optimization using approximate optimization technique is carried out with sequential design domain(SDD). In addition, algorithm executing Pro/Engineer and ANSYS automatically are adopted in the approximate optimization program by SDD. It is difficult for design problem to be approximated accurately for the whole range of design space. However, more or less accurate approximation is constructed if SDD is applied to that case. SDD starts with a certain range which is off-seted from midpoint of an initial design domain and then SDD of the next step is determined by a move limited. Convergence criterion is defined such that optimal point must be located within SDD during the two steps. Also, the PLBA(Pshenichny-Lim-Belegundu-Arora) algorithm is used to solve approximate optimization problems. This algorithm uses the second-order information and the active set strategy, in order to seek the direction of design variables.