• 응용통계연구
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• 제25권1호
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• pp.215-223
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• 2012

반응표면 방법론은 어떤 공정을 개선하거나 최적화하는데 이용되는 아주 유용한 통계적방법이다. 이러한 최적조건을 추정하기 위하여 최적조건이 있으리라 예상되는 실험구역을 탐색하여 실험을 실시한다. 그런데 이 실험구역은 실험의 환경의 제약 그리고 연구자의 선택 등으로 그 모습이 다양하게 달라질 수 있다. 반응표면 설계는 실험구역의 모양에 따라 보통 둥그런 모양의 "구형설계"와 육면체 모양의 "입방형설계"로 구분한다. 구형설계는 회전성을 만족하거나 회전성에 상당히 근접하는 "유사회전성"을 갖는 특징이 있다. 반응표면 설계에서 가장 많이 사용되는 중심합성설계는 실험구역이 구형인 5수준 실험설계이다. 이 때, 축점의 ${\alpha}$값을 ${\alpha}=\sqrt{k}$ 대신 ${\alpha}=1$로 조정하면 5-수준이 아닌 3-수준 입방형 중심합성설계를 얻을 수 있다. 그러나 입방형 중심합성설계는 실험구역이 구형이 아니므로 회전성을 만족하지 못하는 문제가 있다. 이러한 이유로, 변수들의 수준 수를 3으로 제한하면서 실험구역은 구형인 실험설계가 필요할 때가 많다. 이에 대한 대표적 실험설계가 바로 박스-벤켄 실험설계이다. 이 실험설계는 구형의 실험구역으로 회전성을 만족하나 실험구역의 크기가 변수의 개수가 증가해도 제자리 수준으로 좁은 특징이 있다. 현실적으로 실험구역의 가상 자리 부분에 대한 예측에 관심이 있을 경우 변수의 개수가 많아지면 이에 비례하여 실험구역이 커지는 실험설계가 바람직하다. 본 논문은 3-수준 입방형설계에 비하여 실험구역이 유달리 좁은 박스-벤켄 실험설계를 보완하여 구형설계를 만족하면서도 다른 한편으로는 변수 수에 따라 실험반경이 커지는 3-수준 구형 반응표면 설계를 소개하고자 한다. 이 방법을 기존의 실험설계들과 비교한 결과 변수수가 비교적 작을 경우 실험횟수 등을 고려하여 응용가치가 있음을 확인하였다.

• 대한환경공학회지
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• 제39권10호
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• pp.568-574
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• 2017

본 연구는 폐목재로부터 organosolv 공정을 이용해서 리그닌을 분리할 때 영향을 미치는 주요 3개의 반응조건(반응시간($X_1$), 산 촉매의 농도($X_2$) 및 반응온도($X_3$))을 리그닌 회수율(y) 기준으로 최적화하였다. 중심합성계획법(central composite design, CCD)에 따라 반응온도 $136.4-203.6^{\circ}C$, 산촉매 농도 0-2.5%, 반응시간 26.36-93.64 분의 범위를 가진 실험계획을 수행해서 2차 모델식 및 최적조건을 수립하였다. 2차 모델식은 $y=-79.89+0.91X_1+9.8X_2-2.54{\times}10^{-3}X_1{^2}-2.11X_2{^2}$와 같이 얻었으며, 결정계수(coefficient of determination, $R^2$) 값은 0.8531으로 10% 이내의 유의수준에서 유의성을 나타냈다. 2차 모델식에 따라 예측되는 최고 리그닌 회수율은 12.46 g/100 g of dry wood이며 이때 최적 반응 조건은 반응온도 $178.2^{\circ}C$, 산 촉매 농도 2.32%으로 나타났다. 폐목재 대상 organosolv 공정에서의 리그닌 수율은 반응온도보다는 산 촉매 농도의 영향이 더 크게 나타났으며 반응시간에 의한 영향은 없는 것으로 나타났다. 모델의 변동성 분석(analysis of variance, ANOVA)에 따르면 리그닌 수율(y)에 대한 모델식의 유의확률은 p<0.001로 높은 유의성을 보였다. 최적조건에서 모델의 재현성을 검증한 결과 모델식이 실제공정을 적절하게 모사한 것으로 나타났다.

• 한국지반환경공학회 논문집
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• 제12권4호
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• pp.25-31
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• 2011

본 연구의 목표는 전자빔공정을 통한 1,4-dioxane 처리의 최적화를 이루기 위해 실험계획법을 적용하는 것이다. 주요 인자를 1,4-dioxane removal efficiencies(%), TOC removal efficiencies(%)로 반응표면분석법(RSM) 중 중심합성실험법을 이용하여 수학적으로 표시하였다. 1,4-dioxane의 농도를 "$x_1$", Irradiation intensity를 "$x_2$"로 지정하였다. 1,4-dioxane 농도와 removal efficiencies(%)의 코드화된 회귀방정식은 $y=71.00-10.85x_1+20.67x_2+{1.53x_1}^2-{7.92x_2}^2-1.23x_1x_2$, 1,4-dioxane 농도와 TOC Removal efficiencies(%)의 코드화된 회귀방정식은 $y=44.48-13.25x_1+9.54x_2+{5.43x_1}^2-{1.35x_2}^2+4.45x_1x_2$로 나타났다. 모델 예측식의 $R^2$(Adj.)가 90%이상으로 실험적인 관찰결과 잘 맞는 것으로 나타났다. 마지막으로 조류 Pseudokirchneriella Subcapitata를 이용하여 전자빔에 의한 1,4-dioxane에 대한 독성평가를 실시한 결과 전자빔 조사선량의 증가에 따라 생물학적 방해영향이 저감되었다.

• 공업화학
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• 제35권3호
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• pp.248-254
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• 2024

본 연구에서는 전나무와 잣나무 잎으로부터 항균특성을 갖는 기능성 물질을 추출한 후 반응표면분석법 중 중심합성 계획법(CCD-RSM)을 이용하여 최적화하였다. 최적 추출 조건은 전나무의 경우 추출온도(59.5 ℃)와 주정/초순수 부피비(69.5 vol.%)이었으며, 이때 반응치는 추출수율(13.5%), 대장균 억제직경(11.6 mm), 황색포도상구균 억제직경(9.3 mm)로 산출되었다. 또한 잣나무의 경우에는 최적 추출조건인 추출온도(59.2 ℃)와 주정/초순수 부피비(67.8 vol.%)에 서 추출수율(4.8%), 대장균 억제직경(7.9 mm), 황색포도상구균 억제직경(12.5 mm)로 산출되었다. 각 천연물의 최적조건에서 실제 실험 결과 전나무 잎의 추출수율은 13.0%, 대장균 억제직경은 11.7 mm, 황색포도상구균 억제직경은 9.2 mm로 약 ± 2.30% 오차율을 나타내며, 잣나무 잎의 추출수율은 5.1%, 대장균 억제직경은 7.5 mm, 황색포도상구균 억제직경은 12.3 mm로 ± 4.23% 오차율을 나타내었다.

• 한국식품조리과학회지
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• 제26권5호
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• pp.575-585
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• 2010

This study was performed to determine the optimal composition of a muffin administered dried burdock powder and oligosaccharide. The experiment was designed base on CCD (Central Composite Design), and evaluation was carried out by means of RSM (Response Surface Methodology), which included 10 experimental points with 3 replicates for the two independent variables burdock powder and oligosaccharide. The experimental muffin was made according to a traditional recipe, except that the flour was partially replaced with dried burdock powder (5%, 15%, 25%) and the sugar was partially replaced with oligosaccharide (25%, 50%, 75%). The compositional and functional properties of the prepared products were measured, and these values were applied to the mathematical models. Using the F-test, volume, height, pH, yellowness, chewiness, resilience, springiness, cohesiveness, taste, and overall quality were expressed as a linear model, whereas lightness, redness, adhesiveness, color, flavor, and overall quality were expressed as a quadratic model. The polynomial models developed by RSM for sensory evaluation, color, flavor, texture, taste, and overall quality were highly effective in describing the relationships between the factors (p<0.01). The estimated response surfaces confirmed that the amount of burdock powder had significant effects on color, taste, texture, flavor, and overall quality (p<0.01), whereas and the amount of oligosaccharide had significant effects on color and texture (p<0.01). Increased amount of burdock powder led to reductions of the sensory scores for color, taste, texture, flavor, and overall quality at all oligosaccharide levels. The optimal mixing percentage of burdock powder and oligosaccharide muffin were determined to be 5.00% and 46.25%, respectively.

• Membrane and Water Treatment
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• 제7권2호
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• pp.127-141
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• 2016

Electrodialysis (ED) is known to be a useful membrane process for desalination, concentration, separation, and purification in many fields. In this process, it is desirable to work at high current density in order to achieve fast desalination with the lowest possible effective membrane area. In practice, however, operating currents are restricted by the occurrence of concentration polarization phenomena. Many studies showed the occurrence of a limiting current density (LCD). The limiting current density in the electrodialysis process is an important parameter which determines the electrical resistance and the current utilization. Therefore, its reliable determination is required for designing an efficient electrodialysis plant. The purpose of this study is the development of a predictive model of the limiting current density in an electrodialysis process using response surface methodology (RSM). A two-factor central composite design (CCD) of RSM was used to analyze the effect of operation conditions (the initial salt concentration (C) and the linear flow velocity of solution to be treated (u)) on the limiting current density and to establish a regression model. All experiments were carried out on synthetic brackish water solutions using a laboratory scale electrodialysis cell. The limiting current density for each experiment was determined using the Cowan-Brown method. A suitable regression model for predicting LCD within the ranges of variables used was developed based on experimental results. The proposed mathematical quadratic model was simple. Its quality was evaluated by regression analysis and by the Analysis Of Variance, popularly known as the ANOVA.

• 한국환경보건학회지
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• 제36권4호
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• pp.313-322
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• 2010

The aim of this research was to apply experimental design methodology to optimization of conditions of electrochemical oxidation of Rhodamine B (RhB) and N, N-Dimethyl-4-nitrosoaniline (RNO, indicative of the OH radical). The reactions of electrochemical oxidation of RhB degradation were mathematically described as a function of the parameters of current ($X_1$), NaCl dosage ($X_2$) and pH ($X_3$) and modeled by the use of the central composite design. The application of response surface methodology (RSM) yielded the following regression equation, which is an empirical relationship between the removal efficiency of RhB and RNO and test variables in a coded unit: RhB removal efficiency (%) = $94.21+7.02X_1+10.94X_2-16.06X_3+3.70X_1X_3+9.05X_2X_3-{3.46X_1}^2-{4.67X_2}^2-{7.09X_3}^2$; RNO removal efficiency (%) = $54.78+13.33X_1+14.93X_2- 16.90X_3$. The model predictions agreed well with the experimentally observed result. Graphical response surface and contour plots were used to locate the optimum point. The estimated ridge of maximum response and optimal conditions for the RhB degradation using canonical analysis was 100.0%(current, 0.80 A; NaCl dosage, 2.97% and pH 6.37).

• 한국식생활문화학회지
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• 제34권6호
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• pp.779-784
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• 2019

The purpose of this study was to optimize the rice protein extracted using a response surface methodology. The experiment was designed based on a CCD (Central Composite Design), and the independent variables were the high pressure (X₁, 0-400 MPa) and processing time (X₂, 0-10 minutes). The results of the extraction content (Y₁), residue content (Y₂), and recovery yield (Y₃) were fitted to a response surface methodology model (R²= 0.92, 0.92, and 0.93, respectively). Increasing the pressure and processing time has a positive effect on the extraction content (Y₁), residue content (Y₂), and recovery yield (Y₃). Therefore, these high-pressure conditions (independent variables) can significantly affect the improvement in rice protein extraction efficiency. Thus, the optimal conditions of X₁ and X₂ were 400 MPa and 10 min., respectively. Under these optimal conditions, the predicted values of Y₁, Y₂, and Y₃ were 62.93, 57.53 mg/g, and 91.76%, respectively.

• 한국축산식품학회지
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• 제34권6호
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• pp.836-843
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• 2014

Obesity, a condition in which an abnormally large amount of fat is stored in adipose tissue, causing an increase in body weight, has become a major public health concern worldwide. The purpose of this study was to optimize the process for fermented milk for the production of a functional product with an anti-obesity effect by using Lactobacillus plantarum Q180 isolated from human feces. We used a 3-factor, 3-level central composite design (CCD) combined with the response surface methodology (RSM). Concentration of skim milk powder (%, $X_1$), incubation temperature ($^{\circ}C$, $X_2$), and incubation time (h, $X_3$) were used as the independent factors, whereas pH (pH, $Y_1$), anti-lipase activity (%, $Y_2$) and anti-adipogenetic activity (%, $Y_3$) were used as the dependent factors. The optimal conditions of fermented milk for the highest anti-lipase and anti-adipogenetic activity with pH 4.4 were the 9.5% of skim milk powder, $37^{\circ}C$ of incubation temperature, 28 h of incubation time. In the fermentation condition, the predicted values of pH, anti-lipase activity and anti-adipogenetic activity were 4.47, 55.55, and 20.48%, respectively. However, the actual values of pH, anti-lipase activity and anti-adipogenetic activity were 4.50, 52.86, and 19.25%, respectively. These results demonstrate that 9.5% of skim milk powder and incubation at $37^{\circ}C$ for 28 h were the optimum conditions for producing functional fermented milk with an anti-obesity effect.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2005년도 추계학술대회 논문집
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• pp.869-872
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• 2005

This research studied robust design of column part for LCD transfer system. $1^{st}$ DOE(Design of Experiment)was conducted to find out main effect factors. 36 experiments were performed and their results were shows that the geometric parameters(Low-length, Side-length, Upper-thickness, Middle-thickness)are more important than other factors. The main effect plots shows that the maximum deflection of column is minimized with increasing Low-length, Side-length, under-thickness and Middle-thickness. $2^{nd}$ DOE was conducted to obtain RMS(Response Surface Method)equation 25 experiments were conducted. The CCD(Central Composite Design)technique with four factors were used. The coefficient of determination $(R^2)$ for the calculated RSM equation was 0.986. Optimum design was conducted using the RSM equation Multi-island genetic algorithm was used to optimum design. Optimum value for Low-length. Side-length, Upper-thickness and Middle-thickness were 299.8mm, 180.3mm, 21.7mm, 21.9mm respectively. An approximate value of 5.054mm in deflection was expected to be a maximum under the optimum conditions. Six sigma robust design was conducted to find out guideline for control range of design parameter. To acquire six sigma level reliability, the standard deviation of design parameter should be controlled within 2% of average design value.