• Korean Management Science Review
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• v.24 no.2
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• pp.73-80
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• 2007

Robust Design(RD) is a cost-effective methodology to determine the optimal settings of control factors that make a product performance insensitive to the influence of noise factors. To better facilitate the robust design optimization, a dual response surface approach, which models both the process mean and standard deviation as separate response surfaces, has been successfully accepted by researchers and practitioners. However, the construction of response surface approximations has been limited to problems with only a few variables, mainly due to an excessive number of experimental runs necessary to fit sufficiently accurate models. In this regard, an innovative response surface approach has been proposed to investigate robust design optimization problems with larger number of variables. Response surfaces for process mean and standard deviation are partitioned and estimated based on the multi-level approximation method, which may reduce the number of experimental runs necessary for fitting response surface models to a great extent. The applicability and usefulness of proposed approach have been demonstrated through an illustrative example.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2004.04a
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• pp.166-171
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• 2004

In this study, shape optimization of micro-static mixer with a cantilever beam was accomplished for mixing the mixing efficiency by using successive response surface approximations. Variables were chosen as the length of cantilever beam and the angle between horizontal and the cantilever beam. Sequential approximate optimization method was used to deal with both highly nonlinear and non-smooth characteristics of flow field in a micro-static mixer. Shape optimization problem of a micro-static mixer can be divided into a series of simple subproblems. Approximation to solve the subproblems was performed by response surface approximation, which does not require the sensitivity analysis. To verify the reliability of approximated objective function and the accuracy of it, ANOVA analysis and variables selection method were implemented, respectively. It was verified that successive response surface approximation worked very well and the mixing efficiency was improved very much comparing with the initial shape of a micro-static mixer.

• Structural Engineering and Mechanics
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• v.34 no.6
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• pp.779-799
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• 2010

In order to consider high-order effects on the actual limit state function, a new response surface method is proposed for structural reliability analysis by the use of high-order approximation concept in this study. Hermite polynomials are used to determine the highest orders of input random variables, and the sampling points for the determination of highest orders are located on Gaussian points of Gauss-Hermite integration. The cross terms between two random variables, only in case that their corresponding percent contributions to the total variation of limit state function are significant, will be added to the response surface function to improve the approximation accuracy. As a result, significant reduction in computational cost is achieved with this strategy. Due to the addition of cross terms, the additional sampling points, laid on two-dimensional Gaussian points off axis on the plane of two significant variables, are required to determine the coefficients of the approximated limit state function. All available sampling points are employed to construct the final response surface function. Then, Monte Carlo Simulation is carried out on the final approximation response surface function to estimate the failure probability. Due to the use of high order polynomial, the proposed method is more accurate than the traditional second-order or linear response surface method. It also provides much more efficient solutions than the available high-order response surface method with less loss in accuracy. The efficiency and the accuracy of the proposed method compared with those of various response surface methods available are illustrated by five numerical examples.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.9
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• pp.1314-1319
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• 2004

In this study, parameter optimization of micro-static mixer with a cantilever beam was accomplished for maximizing the mixing efficiency by using successive response surface approximations. Variables were chosen as the length of cantilever beam and the angle between horizontal and the cantilever beam. Sequential approximate optimization method was used to deal with both highly nonlinear and non-smooth characteristics of flow field in a micro-static mixer. Shape optimization problem of a micro-static mixer can be divided into a series of simple subproblems. Approximation to solve the subproblems was performed by response surface approximation, which does not require the sensitivity analysis. To verify the reliability of approximated objective function and the accuracy of it, ANOVA analysis and variables selection method were implemented, respectively. It was verified that successive response surface approximation worked very well and the mixing efficiency was improved very much comparing with the initial shape of a micro-static mixer.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.34 no.1
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• pp.42-48
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• 2006

In this study, a repetitive response surface enhancement technique (RRSET) is proposed as a new system approximation method for the efficient multidisciplinary design and optimization (MDO). In order to represent the highly nonlinear behavior of the response with second order polynomials, RRSET introduces a design space transformation using stretching functions and repetitive response surface improvement. The tentative optimal point is repetitively included to the set of experimental points to better approximate the response surface of the system especially near the optimal point, hence a response surface with significantly improved accuracy can be generated with very small experimental points and system iterations. As a system optimizer, the simulated annealing, which generates a global design solution is utilized. The proposed technique is applied to several numerical examples, and demonstrates the validity and efficiency of the method. With its improved approximation accuracy, the RRSET can contribute to resolve large and complex system design problems under MDO environment.

• Journal of Mechanical Science and Technology
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• v.15 no.7
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• pp.876-888
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• 2001

For a large scaled optimization based on response surface methods, an efficient quadratic approximation method is presented in the context of the trust region model management strategy. If the number of design variables is η, the proposed method requires only 2η+1 design points for one approximation, which are a center point and tow additional axial points within a systematically adjusted trust region. These design points are used to uniquely determine the main effect terms such as the linear and quadratic regression coefficients. A quasi-Newton formula then uses these linear and quadratic coefficients to progressively update the two-factor interaction effect terms as the sequential approximate optimization progresses. In order to show the numerical performance of the proposed method, a typical unconstrained optimization problem and two dynamic response optimization problems with multiple objective are solved. Finally, their optimization results compared with those of the central composite designs (CCD) or the over-determined D-optimality criterion show that the proposed method gives more efficient results than others.

• 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.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.1882-1887
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• 2003

The response surface method (RSM) became one of famous meta modeling techniques, however its approximation errors give designers several restrictions. Classical RSM uses the least squares method (LSM) to find the best fitting approximation models from the all given data. This paper discusses how to construct RSM efficiently and accurately using moving least squares method (MLSM) with sensitivity information. In this method, several parameters should be determined during the construction of RSM. Parametric study and optimization for these parameters are performed. Several difficulties during approximation processes are described and numerical examples are demonstrated to verify the efficiency of this method.

• International Journal of Automotive Technology
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• v.3 no.3
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• pp.117-122
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• 2002

Joint stiffness can affect the vibration characteristics of car body structures. Therefore, it should be included in vehicle system model. In this paper, a numerical approximation of joint stiffness is presented considering joint flexibility of thin walled beam-jointed structures. Using the proposed method, it is possible to optimize joint structures considering the change of section shapes in vehicle structures. The numerical approximation of joint stiffness is derived using the response surface method in terms of beam section properties. The study shows that joint stiffnesses can be effectively determined in designing vehicle structures.

• Journal of Electrical Engineering and Technology
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• v.3 no.2
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• pp.207-212
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• 2008

This paper presents a robust and computationally efficient optimal design algorithm for electromagnetic devices by combining an adaptive response surface approximation of the objective function and($1+{\lambda}$) evolution strategy. In the adaptive response surface approximation, the design space is successively reduced with the iteration, and Pareto-optimal sampling points are generated by using Latin hypercube design with the Max Distance and Min Distance criteria. The proposed algorithm is applied to an analytic example and TEAM problem 22, and its robustness and computational efficiency are investigated.