• The Journal of Engineering Geology
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• v.12 no.2
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• pp.203-214
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• 2002

The statistical model was introduced to satisfy various experimental condition on the sorption of heavy metals (Pb, Cu, Cd, and Zn) by bentonite. The Box-Behnken model designed statistically was applied to determine relative impact among three variables such as pH, HCO$_3$ contents and heavy metal concentrations on the sorption. The SAS program was used to obtain the statistical solution. The statistical surface response analysis indicates that initial concentration of heavy metals and pH have an important effect on the sorption, and bicarbonate is not a serious variable. The sorption capability about heavy metals of bentonite is in the order of Pb>Cu>Zn>Cd. The precipitation as hydroxyl and carbonate complexes of heavy metals was thermodynamically analyzed as major mechanism of sorption under alkaline pHs and high bicarbonate solution. It was found that there is a little difference between the model prediction on the precipitation of heavy metals and the results of batch sorption experiment. The thermodynamic data of the programs have to revise to obtain the best fit condition between the model prediction and the experimental results.

• The Journal of Engineering Geology
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• v.13 no.3
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• pp.369-378
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• 2003

The statistical modeling was introduced to satisfy various experimental conditions on the sorption of heavy metals (Pb, Cu, Cd, and Zn) by clay minerals, i.e. kaolinite, illite and chlorite. The Box-Behnken model designed statistically was applied to determine a relative impact among three variables such as pH, HCO3(or K) concentration and initial concentration of heavy metals. The SAS program was used to obtain the statistical solution by surface response analysis. The results of a statistical sorption modelling indicated that pH is a strong impact of the variables influencing the sorption of heavy metals. A relative effect between an initial concentration of heavy metals and bicarbonate(or K) concentration is dependent on solution condition. The sorption edge of heavy metals as function of pH shows sigmoidal curve, and a great increase in the range of pH 6～8. The sorption sequence among heavy metals is Cu>Pb>>Zn>Cd. The solution chemistry exerts greater influence on the sorption of heavy metals rather than the crystal chemistry of clay minerals. The potassium exerts some effect into a sorption competition with heavy metals. The research suggests that the statistical modeling is an effective method to demonstrate sorption results in three dimension and to reduce the effort of batch sorption experiment.

• The Korean Journal of Applied Statistics
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• v.25 no.1
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• pp.215-223
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• 2012

Response surface methodology(RSM) is a very useful statistical techniques for improving and optimizing the product process. By this reason, RSM has been utilized extensively in the industrial world, particularly in the circumstances where several product variables potentially influence some quality characteristic of the product. In order to estimate the optimal condition of product variables, an experiment is being conducted defining appropriate experimental region. However, this experimental region can vary with the experimental circumstances and choice of a researcher. Response surface designs can be classified, according to the shape of the experimental region, into spherical and cuboidal. In the spherical case, the design is either rotatable or very near-rotatable. The central composite design(CCD)s widely used in RSM is an example of 5-level and spherical design. The cuboidal CCDs(CCDs with ${\alpha}=1$) is appropriate when an experimental region is cuboidal but this design dose not satisfy the rotatability as it is not spherical. Practically, a 3-level spherical design is often required in the industrial world where various level of experiments are not available. Box-Behnken design(BBD)s are a most popular 3-level spherical designs for fitting second-order response surfaces and satisfy the rotatability but the experimental region does not vary with the number of variables. The new experimental design with expanded experimental region can be considered if the predicting response at the extremes are interested. This paper proposes a new 3-level spherical RSM which are constructed to expand the experimental region together with number of product variables.

• KEPCO Journal on Electric Power and Energy
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• v.1 no.1
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• pp.181-188
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• 2015

The non-contact permanent magnet gear has advantages of high efficiency and improved reliability. It has other advantages of no mechanical friction loss, very little noise and vibration, and no need for lubricant. With these advantages, the non-contact permanent magnet gear that solves the physical contact problem of the mechanical gear has drawn attention. Due to this unique non-contact characteristic, the non-contact permanent magnet gear which is capable of non-contact torque transmission has replaced mechanical gear. The mechanical gears which is in many fields of the modern industry, is used mostly for power transmitting mechanical devices. However, it also has the problem of a low torque density, which requires improvement. In this paper, a novel pole piece shape is proposed in order to improve the problem of low torque density of the non-contact permanent magnet gear. The experiment data required for predicting the relationships among them are obtained using finiteelement Operating method based on two-dimensional (2-D) numerical analysis. Therefore, this paper derived an optimal model for thenon-contact permanent magnet gear with the novel pole piece using the Box-Behnken design, and the validity of the optimal design of the proposed pole piece shape through variance analysis and regression analysis demonstrated. In this paper, we performed the thransfer torque analysis in order to improve the torque density and power density, we have performed on optimal design of proposed pole piece shape using box-behnken.

• Journal of Korean Society of Environmental Engineers
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• v.32 no.1
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• pp.33-46
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• 2010

We investigated and estimated at the characteristics of decomposition and by-products of N-Nitrosodimethylamine (NDMA) using a design of experiment (DOE) based on the Box-Behken design in an UV process, and also the main factors (variables) with UV intensity($X_2$) (range: $1.5{\sim}4.5\;mW/cm^2$), NDMA concentration ($X_2$) (range: 100~300 uM) and pH ($X_2$) (rang: 3~9) which consisted of 3 levels in each factor and 4 responses ($Y_1$ (% of NDMA removal), $Y_2$ (dimethylamine (DMA) reformation (uM)), $Y_3$ (dimethylformamide (DMF) reformation (uM), $Y_4$ ($NO_2$-N reformation (uM)) were set up to estimate the prediction model and the optimization conditions. The results of prediction model and optimization point using the canonical analysis in order to obtain the optimal operation conditions were $Y_1$ [% of NDMA removal] = $117+21X_1-0.3X_2-17.2X_3+{2.43X_1}^2+{0.001X_2}^2+{3.2X_3}^2-0.08X_1X_2-1.6X_1X_3-0.05X_2X_3$ ($R^2$= 96%, Adjusted $R^2$ = 88%) and 99.3% ($X_1:\;4.5\;mW/cm^2$, $X_2:\;190\;uM$, $X_3:\;3.2$), $Y_2$ [DMA conc] = $-101+18.5X_1+0.4X_2+21X_3-{3.3X_1}^2-{0.01X_2}^2-{1.5X_3}^2-0.01X_1X_2+0.07X_1X_3-0.01X_2X_3$ ($R^2$= 99.4%, 수정 $R^2$ = 95.7%) and 35.2 uM ($X_1$: 3 $mW/cm^2$, $X_2$: 220 uM, $X_3$: 6.3), $Y_3$ [DMF conc] = $-6.2+0.2X_1+0.02X_2+2X_3-0.26X_1^2-0.01X_2^2-0.2X_3^2-0.004X_1X_2+0.1X_1X_3-0.02X_2X_3$ ($R^2$= 98%, Adjusted $R^2$ = 94.4%) and 3.7 uM ($X_1:\;4.5\;$mW/cm^2$, $X_2:\;290\;uM$, $X_3:\;6.2$) and $Y_4$ [$NO_2$-N conc] = $-25+12.2X_1+0.15X_2+7.8X_3+{1.1X_1}^2+{0.001X_2}^2-{0.34X_3}^2+0.01X_1X_2+0.08X_1X_3-3.4X_2X_3$ ($R^2$= 98.5%, Adjusted $R^2$ = 95.7%) and 74.5 uM ($X_1:\;4.5\;mW/cm^2$, $X_2:\;220\;uM$, $X_3:\;3.1$). This study has demonstrated that the response surface methodology and the Box-Behnken statistical experiment design can provide statistically reliable results for decomposition and by-products of NDMA by the UV photolysis and also for determination of optimum conditions. Predictions obtained from the response functions were in good agreement with the experimental results indicating the reliability of the methodology used.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2006.06a
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• pp.55-60
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• 2006

Draw-bead is applied to control the material flow in a stamping process and improve the product quality by controlling the draw-bead restraining force (DBRF). Actual die design depends mostly on the trial-and-error method without calculating the optimum DBRF. Die design with the predicted value of DBRF can be utilized at the tryout stage effectively reducing the cost of the product development. For the prediction of DBRF, a simulation-based prediction model of the circular draw-bead is developed using the Box-Behnken design with selected shape parameters such as the bead height, the shoulder radius and the sheet thickness. The value of DBRF obtained from each design case by analysis is approximated by a second order regression equation. This equation can be utilized to the calculation of the restraining force and the determination of the draw-bead shape as a prediction model. For the evaluation of the prediction model, the optimum design of DBRF in sheet metal forming is carried out using response surface methodology. The suitable type of the draw-bead is suggested based on the optimum values of DBRF. The prediction model of the circular draw-bead proposes the design method of the draw-bead shape. The present procedure provides a guideline in the tool design stage for sheet metal forming to reduce the cost of the product development.

• Journal of Environmental Science International
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• v.19 no.7
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• pp.889-900
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• 2010

The experimental design and response surface methodology (RSM) have been applied to the investigation of the electro-UV complex process for the disinfection of E. coli in the water. The disinfection reactions of electro-UV process were mathematically described as a function of parameters power ($X_1$), NaCl dosage ($X_2$), initial pH ($X_3$) and disinfection time ($X_4$) being modeled by use of the Box-Behnken technique. The application of RSM using the Box-Behnken technique yielded the following regression equation, which is an empirical relationship between the residual E. coli number and test variables in actual variables: Ln (CFU) = 23.57 - 0.87 power - 1.87 NaCl dosage - 2.13 pH - 2.84 time - 0.09 power time - 0.07 NaCl dosage pH + 0.14 pH time + 0.03 $power^2$ + 0.47 NaCl $dosage^2$ + 0.20 $pH^2$+ 0.33 $time^2$. The model predictions agreed well with the experimentally observed result ($R^2$ = 0.9987). Graphical response surface and contour plots were used to locate the optimum point. The estimated ridge of maximum response and optimal conditions for the E. coli disinfection using canonical analysis was Ln 1.06 CFU (power, 15.40 W; NaCl dosage, 1.95 g/L, pH, 5.94 and time, 4.67 min). To confirm this optimum condition, the obtained number of the residual E. coli after three additional experiments were Ln 1.05, 1.10 and Ln 1.12. These values were within range of 0.62 (95% PI low)~1.50 (95% PI high), which indicated that conforming the reproducibility of the model.

• Journal of Korean Society of Environmental Engineers
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• v.28 no.9
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• pp.917-925
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• 2006

The aim of our research was to apply experimental design methodology in the optimization of photocatalytic degradation of azo dye(Reactive orange 16). The reactions were mathematically described as a function of parameters amount of $TiO_2(x_1)$, and dye concentration($x_2$) being modeled by the use of the Box-Behnken method. The results show that the responses of color removal(%)($Y_1$) in photocatalysis of dyes were significantly affected by the synergistic effect of linear term of $TiO_2(x_1)$ and dye concentration($x_2$). Significant factors and synergistic effects for the $COD_{Cr}$, removal(%)($Y_2$) were the linear term of $TiO_2(x_1)$ and dye concentration($x_2$). However, the quadratic term of $TiO_2(x_1^2)$ and dye concentration($x_2^2$) had an antagonistic effect on $Y_1$ and $Y_2$ responses. Canonical analysis indicates that the stationary point was a saddle point for $Y_1$ and $Y_2$, respectively. The estimated ridge of maximum responses and optimal conditions for $Y_1:(X_1,\;X_2)$=(1.11 g/L, 51.2 mg/L) and $Y_2:(X_1,\;X_2)$=(1.42 g/L, 72.83 mg/L) using canonical analysis was 93% and 73%, respectively.

• Korean Chemical Engineering Research
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• v.56 no.4
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• pp.568-576
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• 2018

In order to investigate the adsorption characteristics of the antibiotics trimethoprim (TMP) by activated carbon (WCAC) prepared from waste citrus peel, the effects of operating parameters on the TMP adsorption were investigated by using a response surface methodology (RSM). Batch experiments were carried out according to a four-factor Box-Behnken experimental design with four input parameters : concentration ($X_1$: 50-150 mg/L), pH ($X_2$: 4-10), temperature ($X_3$: 293-323 K), adsorbent dose ($X_4$: 0.05-0.15 g). The experimental data were fitted to a second-order polynomial equation by the multiple regression analysis and examined using statistical methods. The significance of the independent variables and their interactions was assessed by ANOVA and t-test statistical techniques. Statistical results showed that concentration of TMP was the most effective parameter in comparison with others. The adsorption process can be well described by the pseudo-second order kinetic model. The experimental data of isotherm followed the Langmuir isotherm model. The maximum adsorption amount of TMP by WCAC calculated from the Langmuir isotherm model was 144.9 mg/g at 293 K.

• Microbiology and Biotechnology Letters
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• v.41 no.4
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• pp.398-406
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• 2013

For the maximal production of aphicidal metabolites produced by the Beauveria bassiana Bb08, statistical methods such as the Box-Behnken experimental design and response surface methodology were used. The fungal culture filtrate was sprayed towards 3-star aphids and the mortality was examined. After the statistical analysis of the aphid mortality, the optimal culture conditions were found to be a culture temperature of $26.2^{\circ}C$, medium pH 5.9, flask shaking speed of 209.0 rpm, and culture time of 5.9 days. The expected mortality on days 4, 5, and 6 after spraying the filtrate on to the aphids were 76.8%, 84.9%, and 89.4%, respectively. All 4 factors of the culture conditions significantly affected the production of the aphicidal metabolites, and the order of significance was temperature, pH, culture time and shaking speed.