• 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.

• Structural Engineering and Mechanics
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• v.57 no.4
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• pp.587-602
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• 2016

In structural reliability analysis, the response surface method is widely adopted because of its numerical efficiency. It should be understood that the response function must approximate the actual limit state function accurately in the main region influencing failure probability where it is evaluated. However, the size of main region influencing failure probability was not defined clearly in current response surface methods. In this study, the concept of sub-region of interest is constructed, and an improved response surface method is proposed based on the sub-region of interest. The sub-region of interest can clearly define the size of main region influencing failure probability, so that the accuracy of the evaluation of failure probability is increased. Some examples are introduced to demonstrate the efficiency and the accuracy of the proposed method for both numerical and implicit limit state functions.

• Journal of the Korean Society for Precision Engineering
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• v.19 no.4
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• pp.109-116
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• 2002

The solution of the aircraft wing spar cross-section area optimization problem is obtained by the response surface method. The object function of the problem is wing total weight, design variables are spar cross-section areas, constraints are the conditions that the stresses at the each spar is less than the allowable stress. D-Optimal condition is utilized to obtain the experimental points to construct the response surfaces. D-Optimal experimental points are obtained by the commercial software "Deign-Expert". Response values for the object function and constraints for each experimental point are calculated by the NASTRAN. Response surfaces for object function and constraints are approximated from the response values by the least square method. The optimization solution is obtained by the DOT for the response surfaces of object function and constraints. The optimization results obtained from the response surface are compared with the results obtained by the NASTRAN SOL200.

• Transactions of Materials Processing
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• v.30 no.1
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• pp.27-34
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• 2021

In this study, response surface method (RSM) was used in modeling and multi-objective optimization of the parameters of AA5052-H32 in incremental sheet forming (ISF). The goals of optimization were the maximum forming angle, minimum thickness reduction, and minimum surface roughness, with varying values in response to changes in production process parameters, such as tool diameter, tool spindle speed, step depth, and tool feed rate. A Box-Behnken experimental design (BBD) was used to develop an RSM model for modeling the variations in the forming angle, thickness reduction, and surface roughness in response to variations in process parameters. Subsequently, the RSM model was used as the fitness function for multi-objective optimization of the ISF process based on experimental design. The results showed that RSM can be effectively used to control the forming angle, thickness reduction, and surface roughness.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.9
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• pp.924-933
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• 2007

An impeller is a important part of turbo-machinery. It has a set of twisted surfaces because it consists of many blades. Five-axis machining is required to produce a impeller because of interference between tool and workpiece. It can obtain good surface integrity and high productivity. This paper proposes finish cutting method for machining impeller with 5-axis machining center and optimization of cutting condition by response surface method. Firstly, cutting methods are selected by consideration of operation characteristics. Secondly, response factors are determined as cutting time and cutting error for prediction of productivity. Experiments are projected by central composite design with axis point. Thirdly, regression linear models are estimated as single surface in the leading edge and as dual surface in the hub surface cutting. Finally, cutting conditions are optimized.

• 유체기계공업학회:학술대회논문집
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• 2002.12a
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• pp.439-443
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• 2002

In this study, three-dimensional incompressible viscous flow analysis and optimization using response surface method are presented for the design of a jet fan. Steady, incompressible, three-dimensional Reynolds averaged Wavier-Stokes equations are used as governing equations, and standard k-$\epsilon$ turbulence model is chosen as a turbulence model. Governing equations are discretized using finite volume method. Sweep angles and maximum thickness of blade are used as design variables for the shape optimization of the impeller in response surface method. The experimental points which are needed to construct response surface are obtained from the D-optimal design and Full Factorial design and relations between design variables and response surface are examined.

• Communications for Statistical Applications and Methods
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• v.5 no.3
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• pp.607-621
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• 1998

When fitting a response surface model, the least squares estimates of the model's parameters and the prediction variance will generally depend on how the response surface design is blocked. That is, the choice of a blocking arrangement for a response surface design can have a considerable effect on estimating the mean response and on the size of the prediction variance even if the experimental runs are the same. Therefore, care should be exercised in the selection of blocks. In this paper, we prognose a graphical method for evaluating the effect of blocking in a response surface designs using cuboidal regions in the presence of a fixed block effect. This graphical method can be used to investigate how the blocking has influence on the prediction variance throughout the entire experimental region of interest when this region is cuboidal, and compare the block effect in the cases of the orthogonal and non-orthogonalblockdesigns, resfectively.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.19 no.4
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• pp.582-588
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• 2010

This paper presents the Application of Response Surface Method for Optimal Transfer Conditions of MLCC Alignment System. his paper is composed of two parts: (1) Testing performance verification of MLCC alignment system, compared with manual operation; (2) Applying response surface method to figuring out the optimal transfer conditions of MLCC transfer system. Based on the successfully developed MLCC alignment system, the optimal transfer conditions have been explored by using RSM. The simulations using $ADAMS^{(R)}$ has been performed according to the cube model of CCD. By using $MiniTAB^{(R)}$, we have established the model of response surface based on the simulation results. The optimal conditions resulted from the response optimization tool of $MiniTAB^{(R)}$ has been verified by being assigned to the prototype of MLCC alignment system.

• Journal of Electrical Engineering and Technology
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• v.1 no.4
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• pp.466-471
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• 2006

This raper presents a new optimization method combining the genetic algorithm with the response surface method for the optimum design of a Brushless Direct Current motor. The method utilizes a regression function approximating an objective function and the window moving and zoom-in method so as to complement disadvantages of both the genetic algorithm and response surface method. The results verify that the proposed method is powerful and effective in reducing cogging torque by optimizing only a few decisive design factors compared with the conventional stochastic methods.

• Journal of Korean Society for Quality Management
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• v.25 no.2
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• pp.102-111
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• 1997

In this paper I discuss a method of constructing the confidence region for the logistic response surface model. The construction involves a, pp.ication of a general fitting procedure because the log odds is linear in its parameters. Estimation of parameters of the logistic response surface model can be accomplished by maximum likelihood, although this requires iterative computational method. Using the asymptotic results, asymptotic covariance of the estimators can be obtained. This can be used in the construction of confidence regions for the parameters and for the logistic response surface model.