• Knowledge Management Research
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• v.21 no.1
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• pp.27-40
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• 2020

Response surface methodology (RSM) empirically studies the relationship between a response variable and input variables in the product or process development phase. The ultimate goal of RSM is to find an optimal condition of the input variables that optimizes (maximizes or minimizes) the response variable. RSM can be seen as a knowledge management tool in terms of creating and utilizing data, information, and knowledge about a product production and service operations. In the field of product or process development, most real-world problems often involve a simultaneous consideration of multiple response variables. This is called a multiple response surface (MRS) problem. Various approaches have been proposed for MRS optimization, which can be classified into loss function approach, priority-based approach, desirability function approach, process capability approach, and probability-based approach. In particular, the loss function approach is divided into univariate and multivariate approaches at large. This paper focuses on the univariate approach. The univariate approach first obtains the mean square error (MSE) for individual response variables. Then, it aggregates the MSE's into a single objective function. It is common to employ the weighted sum or the Tchebycheff metric for aggregation. Finally, it finds an optimal condition of the input variables that minimizes the objective function. When aggregating, the relative weights on the MSE's should be taken into account. However, there are few studies on how to determine the weights systematically. In this study, we propose an interactive procedure to determine the weights through considering a decision maker's preference. The proposed method is illustrated by the 'colloidal gas aphrons' problem, which is a typical MRS problem. We also discuss the extension of the proposed method to the weighted MSE (WMSE).

• Food Science and Biotechnology
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• v.16 no.4
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• pp.557-564
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• 2007

We prepared caviar analogs encapsulated by calcium-alginate gel membranes as a means to replace higher priced natural caviars. Processing the caviar analogs (beluga type) was optimized by response surface methodology with central composite design. Concentrations of sodium alginate ($X_1$) and $CaCl_2\;(X_2)$ were chosen as the independent variables. In order to compare characteristics of the caviar analogs with the natural caviar, sphericity ($Y_1$), diameter ($Y_2$), membrane thickness ($Y_3$), rupture strength ($Y_4$), rupturing deformation ($Y_5$), and sensory score ($Y_6$) were used as the dependent variables. The sphericity of the caviar analogs showed a similar value to that of natural caviar (over 94%) in the range of independent variables. Generally, the $CaCl_2$ concentration ($X_2$) affected all dependent variables to a greater extent than the sodium alginate concentration ($X_l$), For the multiple response optimization of the 5 dependent variables ($Y_1,\;Y_2,\;Y_4,\;Y_5$, and $Y_6$), the desirability function was defined as the following conditions: target values ($Y_1\;=\;100%,\;Y_2\;=\;3.0\;mm,\;Y_4\;=\;1,470\;g,\;Y_5\;=\;1.1\;mm,\;and\;Y_6\;=\;10\;points$). Membrane thickness ($Y_3$) was eliminated from the dependent variables for multiple response optimization because it could not be measured with an image analyzer. The values of the independent variables as evaluated by multiple response optimization were $X_1\;=\;-0.093$ (78%) and $X_2\;=\;-0.322$ (1.07%), respectively.

• Advances in materials Research
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• v.5 no.2
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• pp.67-80
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• 2016

The objective of the present work is to optimize process parameters namely, cutting speed, feed rate, and depth of cut in milling of AISI 304 stainless steel. In this work, experiments were carried out as per the Taguchi experimental design and an $L_{27}$ orthogonal array was used to study the influence of various combinations of process parameters on surface roughness (Ra) and material removal rate (MRR). As a dynamic approach, the multiple response optimization was carried out using grey relational analysis (GRA) and desirability function analysis (DFA) for simultaneous evaluation. These two methods are considered in optimization, as both are multiple criteria evaluation and not much complicated. The optimum process parameters found to be cutting speed at 63 m/min, feed rate at 600 mm/min, and depth of cut at 0.8 mm. Analysis of variance (ANOVA) was employed to classify the significant parameters affecting the responses. The results indicate that depth of cut is the most significant parameter affecting multiple response characteristics of GFRP composites followed by feed rate and cutting speed. The experimental results for the optimal setting show that there is considerable improvement in the process.

• Journal of Korean Society for Quality Management
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• v.34 no.4
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• pp.93-101
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• 2006

Robust parameter design is an off-line production technique for reducing variation and improving the quality of products and processes by using product arrays. However, the use of the product arrays usually requires a large number of runs. To overcome the drawback of the product array, the combined array can be used. Also optimizing multiple responses is increasingly important in industry. Using simultaneous optimization measures, we can deal with the multiple response case. In this paper we compare the simultaneous optimization using the Taguchi's product array with using the combined array. And models possible to set on combined arrays are also investigated and compared with the cases of product arrays.

• 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.

• Journal of computational fluids engineering
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• v.15 no.2
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• pp.79-85
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• 2010

Aerodynamic design optimization of rotor airfoil has been performed with advanced design method for improved aerodynamic characteristics of ONERA airfoils. A multiple response surface method is used to consider various requirements in rotor airfoil design. Shape functions for mean camber line are proposed to extend possible design domain. Numerical simulations are performed using KFLOW, a Navier-Stokes solver with shear stress transport turbulence model. The present design method provides favorable configurations for the high performance rotor airfoil. Resulting optimized airfoils give better aerodynamic performance than the baseline airfoils.

• 한국전산유체공학회:학술대회논문집
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• 2010.05a
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• pp.55-59
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• 2010

Aerodynamic design optimization of rotor airfoil has been performed with advanced design method for improved aerodynamic characteristics of ONERA airfoils as a baseline. A multiple response surface method is used to consider various consider various constraints in rotor airfoil design. Airfoil surface and mean camber line are modified using various shape functions. Numerical simulations are performed using KFLOW, a Navier-Stokes solver with shear stress transport turbulence model. The present design method provides favorable configurations for the high performance rotor airfoil. Resulting optimized air foils give better aerodynamic performance than the baseline airfoils.

• Knowledge Management Research
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• v.20 no.3
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• pp.39-47
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• 2019

Response surface methodology (RSM) is a group of statistical modeling and optimization methods to improve the quality of design systematically in the quality engineering field. Its final goal is to identify the optimal setting of input variables optimizing a response. RSM is a kind of knowledge management tool since it studies a manufacturing or service process and extracts an important knowledge about it. In a real problem of RSM, it is a quite frequent situation that considers multiple responses simultaneously. To date, many approaches are proposed for solving (i.e., optimizing) a multi-response problem: process capability function approach, desirability function approach, loss function approach, and so on. The process capability function approach first estimates the mean and standard deviation models of each response. Then, it derives an individual process capability function for each response. The overall process capability function is obtained by aggregating the individual process capability function. The optimal setting is given by maximizing the overall process capability function. The existing process capability function methods usually use the arithmetic mean or geometric mean as an aggregation operator. However, these operators do not guarantee the Pareto optimality of their solution. Moreover, they may bring out an unacceptable result in terms of individual process capability function values. In this paper, we propose a maximin-based process capability function method which uses a maximin criterion as an aggregation operator. The proposed method is illustrated through a well-known multiresponse problem.

• Transactions of the Korean Society of Automotive Engineers
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• v.23 no.6
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• pp.583-590
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• 2015

Automobile crash optimization is nonlinear dynamic response structural optimization that uses highly nonlinear crash analysis in the time domain. The equivalent static loads (ESLs) method has been proposed to solve such problems. The ESLs are the static load sets generating the same displacement field as that of nonlinear dynamic analysis. Linear static response structural optimization is employed with the ESLs as multiple loading conditions. Nonlinear dynamic analysis and linear static structural optimization are repeated until the convergence criteria are satisfied. Nonlinear dynamic crash analysis for frontal analysis may not have boundary conditions, but boundary conditions are required in linear static response optimization. This study proposes a method to use the inertia relief method to overcome the mismatch. An optimization problem is formulated for the design of an automobile frontal structure and solved by the proposed method.

• Journal of Korean Society for Quality Management
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• v.23 no.3
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• pp.84-92
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• 1995

A method is proposed for the simultaneous optimization of several response functions that depend on the same set of controllable variables and are adequately represented by a response surface model (polynomial regression model) with the same degree and with constraint that the individual responses have the target values. First, the multiple responses data are checked for linear dependencies among the responses by eigenvalue analysis. Thus a set of responses with no linear functional relationships is used in developing a function that measures the distance estimated responses from the target values. We choose the optimal condition that minimizes this measure. Also, under the different degree of importance two step procedures are proposed.