• Title/Summary/Keyword: Multiple Response Surface

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Dual Response Surface Optimization using Multiple Objective Genetic Algorithms (다목적 유전 알고리즘을 이용한 쌍대반응표면최적화)

  • Lee, Dong-Hee;Kim, Bo-Ra;Yang, Jin-Kyung;Oh, Seon-Hye
    • Journal of Korean Institute of Industrial Engineers
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    • v.43 no.3
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    • pp.164-175
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    • 2017
  • Dual response surface optimization (DRSO) attempts to optimize mean and variability of a process response variable using a response surface methodology. In general, mean and variability of the response variable are often in conflict. In such a case, the process engineer need to understand the tradeoffs between the mean and variability in order to obtain a satisfactory solution. Recently, a Posterior preference articulation approach to DRSO (P-DRSO) has been proposed. P-DRSO generates a number of non-dominated solutions and allows the process engineer to select the most preferred solution. By observing the non-dominated solutions, the DM can explore and better understand the trade-offs between the mean and variability. However, the non-dominated solutions generated by the existing P-DRSO is often incomprehensive and unevenly distributed which limits the practicability of the method. In this regard, we propose a modified P-DRSO using multiple objective genetic algorithms. The proposed method has an advantage in that it generates comprehensive and evenly distributed non-dominated solutions.

Development of a Multiple Response Surface Method Considering Bias and Variance of Desirability Functions (만족도 함수의 편향과 산포를 고려한 다중반응표면최적화 기법 개발)

  • Jung, Ki-Hyo;Lee, Sang-Ki
    • Journal of Korean Institute of Industrial Engineers
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    • v.38 no.1
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    • pp.25-30
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    • 2012
  • Desirability approaches have been proposed to find an optimum of multiple response problem. The existing desirability approaches use either of mean or min of individual desirability in aggregation of multiple responses. However, in order to find an optimum having high mean and low dispersion among individual desirability, the dispersion needs to be simultaneously considered with its mean. This study proposes bias and variance (BV) method which aggregates bias (ideal target-mean) and variance of individual desirability in multiple response optimization. The proposed BV method was applied to an example to evaluate its usefulness by comparing with existing methods. Evaluation results showed that the solution of BV method was a fairly good compared with DS (Derringer and Suich, 1980) and KL (Kim and Lin, 2000) methods. The BV method can be utilized to multiple response surface problems when decision makers want to find an optimum having high mean and low variance among responses.

A Univariate Loss Function Approach to Multiple Response Surface Optimization: An Interactive Procedure-Based Weight Determination (다중반응표면 최적화를 위한 단변량 손실함수법: 대화식 절차 기반의 가중치 결정)

  • Jeong, In-Jun
    • 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).

Optimization in Multiple Response Model with Modified Desirability Function

  • Cho, Young-Hun;Park, Sung-Hyun
    • International Journal of Quality Innovation
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    • v.7 no.3
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    • pp.46-57
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    • 2006
  • The desirability function approach to multiple response optimization is a useful technique for the analysis of experiments in which several responses are optimized simultaneously. But the existing methods have some defects, and have to be modified to some extent. This paper proposes a new method to combine the individual desirabilities.

Evaluation of Stiffness Profile for Site Response Analysis of Highly-Elevated Earth-fill Embankment (고성토 제방의 부지응답해석을 위한 전단강성 평가)

  • Joh, Sung-Ho;Rahman, Norinah Abd;Hassanul, Raja
    • Proceedings of the KSR Conference
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    • 2010.06a
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    • pp.872-879
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    • 2010
  • High rock-fill embankment is relatively flexible, which makes crest of embankment subject to excessive amplification in displacement due to earthquake loading. To overcome problems related with site response in high embankment, it is essential to evaluate shear-wave velocity profile of the embankment with improved accuracy and reliability. In this aspect, an experimental research was performed to answer how to perform surface-wave tests and to analyze measurements at an embankment site with a sloping ground surface. Unlike flat ground surface, sloping ground may hamper and slow down propagation of surface waves due to multiple reflections and refractions in embankment. To figure out this reasoning for the effect of multiple reflections and refractions due to sloping surface, surface wave tests were performed at a reservoir embankment of Chung-Song in North KyeongSang Province. Parameters involved in surface wave tests at non-flat surface, including source directionality, geometry-related constraint and frequency components in source function, were investigated using field measurements.

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Using the Maximin Criterion in Process Capability Function Approach to Multiple Response Surface Optimization (다중반응표면최적화를 위한 공정능력함수법에서 최소치최대화 기준의 활용에 관한 연구)

  • Jeong, In-Jun
    • 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.

A Weighted Mean Squared Error Approach to Multiple Response Surface Optimization (다중반응표면 최적화를 위한 가중평균제곱오차)

  • Jeong, In-Jun;Cho, Hyun-Woo
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.14 no.2
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    • pp.625-633
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    • 2013
  • Multiple response surface optimization (MRSO) aims at finding a setting of input variables which simultaneously optimizes multiple responses. The minimization of mean squared error (MSE), which consists of the squared bias and variance terms, is an effective way to consider the location and dispersion effects of the responses in MRSO. This approach basically assumes that both the terms have an equal weight. However, they need to be weighted differently depending on a problem situation, for example, in case that they are not of the same importance. This paper proposes to use the weighted MSE (WMSE) criterion instead of the MSE criterion in MRSO to consider an unequal weight situation.

Effects of optimal operating conditions on 2-stage injection PCCI diesel engine using Response Surface Methodology (반응 표면법을 이용한 2 단 분사 PCCI 디젤엔진의 운전조건의 영향도 평가에 대한 연구)

  • Lee, Jae-Hyeon;Kim, Hyung-Min;Lee, Ki-Hyung
    • Proceedings of the KSME Conference
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    • 2008.11b
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    • pp.3044-3048
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    • 2008
  • It is well known that Premixed Charge Compression Ignition (PCCI) diesel engines according to many technologies such a change in injection timing, multiple injection strategy, cooled EGR, intake charging and SCV have the potential to achieve homogeneous mixture in the cylinder which result in lower NOx and PM as well as performance improvements. This may generate merely the infinite number of experimental conditions. The use of Response Surface Methodology (RSM) technique can considerably pull down the number of experimental set and time demand. This paper presents the effects of both fuel injection and engine operation conditions on the combustion and emissions in the PCCI diesel engine system. The experimental results have revealed that a change in fuel injection timing and multiple injection strategy along with various operating conditions affect the combustion, emissions and BSFC characteristics in the PCCI engine.

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Optimal Design of Permanent Magnet Linear Synchronous Motor(PMLSM) Considering Multiple Response by Response Surface Methodology(RSM) (영구자석 선형 동기전동기(PMLSM)의 반응표면법(RSM)을 이용한 다중 반응 최적설계)

  • Kim Sung-Il;Nam Hyuk;Kim Young-Kyoun;Hong Jung-Pyo;Cho Han-Ik
    • Proceedings of the KIEE Conference
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    • summer
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    • pp.1097-1099
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    • 2004
  • This paper deals with the optimal design of a slotless type of permanent magnet linear synchronous motor (PMLSM). Response surface methodology, one of the optimization methods, is used to consider multiple response of the PMLSM. That is, it is applied to obtain more average thrust and less thrust ripple than prototype PMLSM. To analyze quickly, characteristic analysis of the PMLSM is performed by space harmonic method and final results of optimized PMLSM are compare with those of prototype PMLSM through finite element analysis.

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Assessment of Coal Combustion Safety of DTF using Response Surface Method (반응표면법을 이용한 DTF의 석탄 연소 안전성 평가)

  • Lee, Eui Ju
    • Journal of the Korean Society of Safety
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    • v.30 no.1
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    • pp.8-13
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    • 2015
  • The experimental design methodology was applied in the drop tube furnace (DTF) to predict the various combustion properties according to the operating conditions and to assess the coal plant safety. Response surface method (RSM) was introduced as a design of experiment, and the database for RSM was set with the numerical simulation of DTF. The dependent variables such as burnout ratios (BOR) of coal and $CO/CO_2$ ratios were mathematically described as a function of three independent variables (coal particle size, carrier gas flow rate, wall temperature) being modeled by the use of the central composite design (CCD), and evaluated using a second-order polynomial multiple regression model. The prediction of BOR showed a high coefficient of determination (R2) value, thus ensuring a satisfactory adjustment of the second-order polynomial multiple regression model with the simulation data. However, $CO/CO_2$ ratio had a big difference between calculated values and predicted values using conventional RSM, which might be mainly due to the dependent variable increses or decrease very steeply, and hence the second order polynomial cannot follow the rates. To relax the increasing rate of dependent variable, $CO/CO_2$ ratio was taken as common logarithms and worked again with RSM. The application of logarithms in the transformation of dependent variables showed that the accuracy was highly enhanced and predicted the simulation data well.