• 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.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.24 no.3
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• pp.302-307
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• 2015

The automobile is an important means of transportation. For this reason, the automotive wheel is also an important component in the automotive industry because it acts as a load support and is closely related to safety. Thus, the wheel design is a very important safety aspect. In this paper, an optimal design for minimizing automotive wheel stress and increasing wheel safety is described. To study the optimal design, a central composite design (CCD) and D-optimal design theory are applied, and the approximate function using the response surface method (RSM) is generated. The optimal solutions using the non-dominant sorting genetic algorithm (NSGA-II) are then derived. Comparing CCD and D-optimal solution accuracy and verified the CCD can deduce more accuracy optimal solutions.

• 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.

• 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.

• 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).

• Transactions of the Korean Society of Mechanical Engineers A
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• v.39 no.5
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• pp.535-541
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• 2015

In this study, an approximate multi-objective optimization of a wall-mounted monitor bracket arm was performed. The rotation angle of the bracket arm was determined considering the inplane degree of freedom. We then formulated an optimization problem on maximum stress and deflection. Analyses of mean and design parameters were conducted for sensitivity regarding performance with orthogonal array and response surface method (RSM). RSM models of objective and constraint functions were generated using central composite (CCD) and D-optimal design. The accuracy of approximate models was evaluated through $R^2$ value. The obtained optimal solutions by non-dominant sorting genetic algorithm (NSGA-II) were validated through the finite element analysis and we compared the obtained optimal solution by CCD and D-optimal design.

• Journal of the Korean Society for Precision Engineering
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• v.32 no.9
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• pp.815-824
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• 2015

In this study, we conducted the approximate multi-objective optimization of gap sizes of pressurized-water reactor (PWR) annular fuels. To determine the contacting tendency of the inner-outer gaps between the annular fuel pellets and cladding, thermoelastic-plastic-creep (TEPC)analysis of PWR annular fuels was performed, using in-house FE code. For the efficient heat transfer at certain levels of stress, we investigated the tensile, compressive hoop stress and temperature, and optimized the gap sizes using the non-dominant sorting genetic algorithm (NSGA-II). For this, response surface models of objective and constraint functions were generated, using central composite (CCD) and D-optimal design. The accuracy of approximate models was evaluated through $R^2$ value. The obtained optimal solutions by NSGA-II were verified through the TEPC analysis, and we compared the obtained optimum solutions and generated errors from the CCD and D-optimal design. We observed that optimum solutions differ, according to design of experiments (DOE) method.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.19 no.5
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• pp.27-37
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• 2020

Structural optimization problems with discrete design variables require more function calculations (or finite element analyses) than those in the continuous design space. In this study, a method to find an optimal solution in the discrete design of the truss structure is presented, reducing the number of function calculations. Because a continuous optimal solution is the Karush-Kuhn-Tucker point that satisfies the optimality condition, it is assumed that the discrete optimal solution is around the continuous optimum. Then, response values such as weight, displacement, and stress are predicted using approximate models-referred to as hybrid metamodels-within specified design ranges. The discrete design method using the hybrid metamodels is used as a post-process of the continuous optimization process. Standard truss design problems of 10-bar, 25-bar, 15-bar, and 52-bar are solved to show the usefulness of this method. The results are compared with those of existing methods.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.10 s.241
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• pp.1139-1147
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• 2005

The shape optimal design of the plate-fin type heat sink with vortex generator is performed to minimize the pressure loss subjected to the desired maximum temperature numerically. Evaluation of the performance function, in general, is required much computational cost in fluid/thermal systems. Thus, global approximate optimization techniques have been introduced into the optimization of fluid/thermal systems. In this study, Kriging method Is used to obtain the optimal solutions associated with the computational fluid dynamics (CFD). The results show that when the temperature .rise is less than 40 K, the optimal design variables are $B_1=2.44\;mm,\;B_2=2.09\;mm$, and t=7.58 mm. Kriging method can dramatically reduce computational time by 1/6 times compared to SQP method so that the efficiency of Kriging method can be validated.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.24 no.3
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• pp.256-264
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• 2012

A general procedure for the optimal design of a micro-channel heat exchanger for heat pump systems is presented. For this design, a performance analysis program that can reflect the various geometric variables of the micro-channel heat exchanger was developed. The deviation between simulated and experiment results of previous research was within 4% for the heat transfer rate. To prove the feasibility of the optimal design process, the performance of the reference heat exchanger was compared to that of the optimized heat exchanger. The $JF_{air}$ and PECv of the optimized heat exchanger were enhanced by 14% and 26%, respectively.