Plackett-Burman和Central Composite Design试验设计法优化石榴皮中熊果酸的SFE-CO_2萃取工艺

目的:探讨应用SFE-CO2萃取石榴皮中熊果酸的最佳工艺。方法:以熊果酸得率为考察指标,通过Plackett-Burman(PB)试验设计筛选影响熊果酸得率的显著性因素,最陡爬坡试验逼近熊果酸得率最大区域,Central Composite Design(CCD)试验设计对显著性因素进行响应面优化得到影响熊果酸得率的二阶数学模型,进而得出最佳工艺条件。结果:SFE-CO2萃取石榴皮中熊果酸的最佳工艺条件为:萃取温度46.29℃,萃取时间91.6 min,萃取压力34.49 MPa,在此条件下,验证试验测得熊果酸得率为12.508 mg/g,与模型预测值12.645 mg/g接近。结论:将PB试验和CCD试验设计联合应用于优化石榴皮中熊果酸SFE-CO2萃取工艺,筛选结果具有统计学意义,工艺操作具有可行性。

Analysis of Heat Transfer Performance of Oscillating Heat Pipes Based on a Central Composite Design

Oscillating heat pipes (OHPs) are very promising cooling devices. Their heat transfer performance is af- fected by many factors, and the form of the relationship between the performance and the factors is complex and non-linear. In this paper, the effects of charging ratio, inclination angle, and heat input and their interaction effects on heat transfer performance of a looped copper-water OHP are analyzed. First, suppose that the relationship between the response and the variables approximates a second-order model. And use the central composite design to arrange the ex- periment. Then, the method of least squares is used to estimate the parameters in the second-order model. Finally, multi- variate variance analysis is used to analyze the model. The results show that the assumption is right, that is to say, the re- lationship is well modeled by a second-order function. Among the three main effect variables, the effect of inclination angle is the most significant, but their interaction effects are not significant. In the range of the considered factors, both the optimum charging ratio and the optimum inclination angle increase as the heating water flow rate increases.

Application of response surface methodology and central composite rotatable design for modeling the influence of some operating variables of the lab scale thickener performance

This study discussed the application of response surface methodology(RSM)and central composite rotatable design(CCRD)for modeling and optimization of the influence of some operating variables on the performance of a lab scale thickener for dewatering of tailing in the flotation circuit.Four thickener operating variables,namely feed flowrate,solid percent,flocculant dosage and feedwell height were changed during the tests based on CCRD.The ranges of values of the thickener variables used in the design were a feed flowrate of 9–21 L/min,solid percent of 8%–20%,flocculant dosage of 1.25–4.25 g/t and feedwell height of 16–26 cm.A total of 30 thickening tests were conducted using lab scale thickener on flotation tailing obtained from the Sarcheshmeh copper mine,Iran.The underflow solid percent and bed height were expressed as functions of four operating parameters of thickener.Predicted values were found to be in good agreement with experimental values(R2values of 0.992 and 0.997 for underflow solid percent and bed height,respectively).This study has shown that the RSM and CCRD could effciently be applied for the modeling of thickener for dewatering of flotation tailing.

Modeling and Optimization of Catalytic Dehydration of Ethanol to Ethylene Using Central Composite Design

The central composite design in the modeling and optimization of catalytic dehydration of ethanol to ethylene was performed to improve the ethylene yield.A total of 20 experiments at random were conducted to investigate the effect of reaction temperature,Si/Al ratios of H-ZSM-5 catalyst and liquid hourly space velocity(LHSV) on the ethylene yield.The results show that the relationship between ethylene yield and the three significant independent variables can be approximated by a nonlinear polynomial model,with R-squared of 99.9%and adjusted R-squared of 99.8%.The maximal response for ethylene yield is 93.4%under the optimal condition of 328 ℃,Si/Al ratio 85,and LHSV 3.8 h-1.

Calibration of Discrete Element Heat Transfer Parameters by Central Composite Design

The efficiency and precision of parameter calibration in discrete element method （DEM） are not satisfactory, and parameter calibration for granular heat transfer is rarely involved. Accordingly, parameter calibration for granular heat transfer with the DEM is studied. The heat transfer in granular assemblies is simulated with DEM, and the effective thermal conductivity （ETC） of these granular assemblies is measured with the transient method in simulations. The measurement testbed is designed to test the ETC of the granular assemblies under normal pressure and a vacuum based on the steady method. Central composite design （CCD） is used to simulate the impact of the DEM parameters on the ETC of granular assemblies, and the heat transfer parameters are calibrated and compared with experimental data. The results show that, within the scope of the considered parameters, the ETC of the granular assemblies increases with an increasing particle thermal conductivity and decreases with an increasing particle shear modulus and particle diameter. The particle thermal conductivity has the greatest impact on the ETC of granular assemblies followed by the particle shear modulus and then the particle diameter. The calibration results show good agreement with the experimental results. The error is less than 4%, which is within a reasonable range for the scope of the CCD parameters. The proposed research provides high efficiency and high accuracy parameter calibration for granular heat transfer in DEM.

Extraction Process Optimization of Total Flavonoids from Mallotus apelta Stems by Central Composite Design/Response Surface Method

[Objectives] To optimize the extraction process of total flavonoids in stems of Mallotus apelta. [Methods]On the basis of singlefactor test,with volume fraction of ethanol,extraction time and ratio of solvent as independent variables,the content of total flavonoids as dependent variables,the completely secondary response surface regression fitting was conducted on the independent and dependent variables,and the Response Surface Method was used to optimize the optimum extraction process of total flavonoids in Mallotus apelta stems and predict the optimum process. [Results] The optimum extraction process of total flavonoids in Mallotus apelta was determined as follows: ethanol concentration of 71. 5%; extraction time of 154. 6 min; solid-liquid ratio of 1∶19. 2; total flavonoids content of 7. 060 mg/g; fitted binomial squared correlation coefficient R^2= 0. 8751.[Conclusions]Composite Design/Response Surface Method could be used in the extraction process optimization of total flavonoids in Mallotus apelta stems,the mathematical model established had high prediction accuracy,the method was simple and operability was good.

Optimization of Extraction Process of Clerodendrum philippinum Schauer var. simplex Mlodenke Total Flavonoids(CPTF) by Central Composite Design-Response Surface Methodology

[Objectives] The research aimed to optimize extraction process of Clerodendrum philippinum Schauer var. simplex Mlodenke total flavonoids( CPTF),and provide reference for its development and utilization. [Methods] Based on single-factor test,ethanol concentration,extraction temperature and extraction time were taken as independent variables,and total flavonoids yield was taken as dependent variable. The test was conducted according to central composite design principle. Multivariate linear regression and binomial equation fitting of the result were conducted,and extraction process of CPTF was optimized by using response surface methodology. [Results]The optimal extraction process of CPTF was as below: ethanol concentration 54. 76%,extraction temperature 83. 92℃,extraction time 102. 64 min,solid-liquid ratio 1:20,extraction for twice. [Conclusions] The extraction process of CPTF by central composite design-response surface methodology was simple and feasible,with reliable prediction result,which was suitable for industrial production.

Optimization of Extraction Process of Total Flavonoids from Akebia trifoliata (Thunb.) Koidz. by Central Composite Design-Response Surface Methodology

[Objectives]To optimize extraction process of total flavonoids from Akebia trifoliata( Thunb.) Koidz.,so as to provide references for development and use of Akebia trifoliata( Thunb.) Koidz. [Methods]The extraction rate of total flavonoids of Akebia trifoliata( Thunb.)Koidz. was taken as observation indicator. On the basis of single factor experiment,central composite design( CCD) was used to evaluate the effects of the extraction temperature,extraction time,and ethanol concentration on the extraction process. Multiple linear regression and binomial fitting were used,and response surface methodology( RSM) was used to select the optimum extraction process. [Results] The optimum extraction process conditions for total flavonoids of Akebia trifoliata( Thunb.) Koidz. was extraction temperature: 83. 92 ℃; extraction time:96. 47 min; ethanol concentration: 63. 92%; extraction times: two times; solid to liquid ratio: 1 ∶ 20; extraction rate of total flavonoids:4. 55%. [Conclusions] The central composite design-response surface methodology( CCD-RSM) is simple,convenient,and feasible for extraction of total flavonoids from Akebia trifoliata( Thunb.) Koidz.,and the prediction results are reliable.

Modeling of biodiesel production: Performance comparison of Box–Behnken, face central composite and full factorial design

The performances of the response surface methodology(RSM)in connection with the Box–Behnken,face central composite or full factorial design(BBD,FCCD or FFD,respectively)were compared for the use in modeling of the NaOH-catalyzed sunflower oil ethanolysis.The influence of temperature,catalyst loading,and ethanol-to-oil molar ratio(EOMR)on fatty acid ethyl esters(FAEE)content was evaluated.All three multivariate strategies were efficient in the statistical modeling and optimization of the influential process variables but BBD and FCCD realization involved less number of experiments,generating smaller costs,requiring less work and consuming shorter time than the corresponding FFD.All three designs resulted in the same optimal catalyst loading(1.25%of oil)and EOMR(12:1).The reduced two-factorinteraction(2 FI)models based on the BBD and FCCD defined a range of optimal reaction temperature(25℃–75℃)and 25℃,respectively while the same model based on the 33 FFD appointed 75℃.The predicted FAEE content of about 97%–98.0%was close to the experimentally obtained FAEE content of about 97.0%–97.6%under the optimal reaction conditions.Therefore,the simpler BBD or FCCD might successfully be applied for statistical modeling of biodiesel production processes instead of the more extensive,more laborious and more expensive FFD.

Optimization of extraction technology of safflower polysaccharide based on central composite design-response surface methodology

Objective:To explore the best extraction technology of safflower polysaccharide by central composite design response surface methodology and evaluate its quality.Methods:Taking the extraction rate of Carthamus tinctorius polysaccharide as the index,taking the ratio of solid to liquid,extraction time,extraction temperature and extraction times as the investigation factors,based on the single factor experiment,the central composite design-response surface methodology was used to optimize the optimum extraction process of Carthamus tinctorius polysaccharide and verify it.Results:The response surface model was established with the extraction rate of Carthamus tinctorius polysaccharide as dependent variable Y,the ratio of solid to liquid,extraction time and extraction temperature as independent variables X,P<0.0001.The optimum extraction process was as follows:the ratio of solid to liquid was 1:16.69,the extraction temperature was 91.39℃,and the extraction working time was 89.78min.Under these conditions,the extraction rate of safflower polysaccharide can reach 7.45%,The experimental results show that RSD is 1.05%,and the model can well predict the experimental results.Conclusion:Central Composite Design-Response Surface Methodology has the advantages of high extraction rate,simple,effective and reasonable process operation,high stability and high precision,which can be fully applied to the resource management and utilization of safflower polysaccharide.

Central Composite Design Method for the Preparation, Stability and Properties of Water-in-Diesel Nano Emulsions

Water in diesel nano-emulsion (WiDNE) due to their nano size, kinetically stable gives its beneficial in commercial and environmental aspects. However, the capability of this fuel strongly depends on the method of preparation, stability and their physic-chemical properties. Central composite design (CCD) method was used to optimize variable interactions in order to obtain maximum stability. Methodology RSM method with six independent variables was selected in order to understand the impacts on droplet size. The response surface and 3D plots of the quadratic polynomial model were created for studying the combination effect on response. Dynamic light scattering DLS technique was used for measuring of droplet sizes. The analysis result by ANOVA was with 95% confidence displaying F value model was 52.82. The results displayed model was fulfilled with the assumptions of ANOVA. This study has relied on Design Expert software to locate the optimum droplet size situations. The measured diameter is 26 nm, with 0.0297 errors between actual conditions and measured value. The optimum blend properties of prepared WiDNE fuel were compared with conventional diesel. Improvements in physical properties were observed in presence of water in WiDNE.

Central-Composite Design响应面实验设计用于金盏菊提取工艺的研究

目的:确定金盏菊最佳提取工艺条件。方法:以金盏菊中总黄酮含量及浸膏得率为考察指标,应用中心组合(Central composite design,CCD)响应面实验设计,考察药材与提取溶剂的比例(料液比)、乙醇浓度、提取时间对金盏花提取效率的影响。结果:根据二项式拟合方程,确定金盏花最佳提取工艺条件为药材与溶剂的比例为1∶12,乙醇浓度为68%,提取时间为1.8 h,提取两次。结论:中心组合响应面实验设计能够对金盏菊的提取工艺进行优化筛选。

Central Composite Design响应面法优化厚裂凤仙花总黄酮提取工艺研究

为厚裂凤仙花中总黄酮资源的开发利用,本文采用单因素与星点-效应面法相结合的方式,考察提取溶剂浓度、料液比、提取时间、提取次数对厚裂凤仙花中总黄酮提取率的影响。优选出厚裂凤仙花总黄酮最佳提取方法为:甲醇体积分数80%,料液比为1︰64,提取时间为50 min;提次数为3次;验证实验结果表明,总黄酮平均提取率为5.51 mg/g,与实验模型RSD值为0.79%。建立的模型与实际方案有较高拟合度,可作为苗药厚裂凤仙花总黄酮提取工艺参数。

基于响应面法中BBD法和CCD法的丙烷回收参数优化对比

为优化丙烷回收工艺运行参数,以丙烷回收率和单位综合能耗为响应值,采用响应曲面法中的Box-Behnken设计(BBD)和中心复合设计(central composite design,CCD)试验优化工艺参数,从方差分析、帕累托图分析、响应面分析和优化结果4个方面优选最佳试验方法。结果显示,CCD法建立的二次响应回归模型的显著性优于BBD法,且CCD法响应曲面分析参数交互作用的显著性结果与方差分析一致。CCD法优化得到的最佳工艺如下:脱乙烷塔压力为3250 kPa,低温分离器温度为-55.6℃,液相回流比为98%,丙烷回收率为98.1%,单位综合能耗为114.1 kgce/10^(4)m^(3)(1 kgce=29.3076 MJ)。在最优工艺参数条件下,丙烷回收率增加了4.36%,产品收益达到3.548万元/d,且预测误差均小于0.2%。

基于PB-CCD设计的丹参提取工艺的研究及主要成分含量测定

目的基于Plackett-Burman-central composite design(PB-CCD)设计优化丹参水提工艺。方法基于试验优化设计,采用PB-CCD设计对影响提取工艺的7种因素进行优化,采用液质联用色谱法(HPLC-ESI/MS)测定丹参水提液中丹酚酸B、丹参素钠、丹参酮ⅡA、隐丹参酮的含量作为评价指标。结果确定了基于PB-CCD设计的丹参提取的最佳工艺条件为浸泡时间0.5 h,提取时间1 h,提取温度100℃,液固比6:1,p H值7.0,提取次数3次,浓缩温度100℃。丹参药材中丹酚酸B、丹参素钠、丹参酮ⅡA、隐丹参酮的含量分别为18.91、2.142、0.1935、0.3188 mg·g^(-1)。结论基于PB-CCD设计确定的丹参提取的最佳工艺,模型预测性良好,试验设计有较高的可靠性。

基于PB-CCD设计的桔梗种子预处理工艺

以桔梗种子为试材,采用Plackett-Burman-Central Composite Design(PB-CCD)设计优化桔梗种子预处理的工艺。以萌发率为指标,采用PB设计试验,研究浸泡时间、浸泡温度、GA3浓度、预冻时间和料液比对桔梗种子萌发的影响;采用CCD设计对筛选出的因素进一步优化,确定桔梗种子预处理的最佳工艺。结果表明:桔梗种子预处理的最佳工艺条件为浸泡时间18h,GA3浓度3g·L^(-1),浸泡温度27℃。利用该优化方案对桔梗种子进行预处理,萌发率为92.3%,与模型预测基本一致,表明优化的工艺条件有较高的可靠性。

利用CCD优化C/N和pH对污泥厌氧发酵产沼气的影响

采用响应面中心组合设计,研究了pH和C/N对污泥厌氧发酵产沼气的影响,并利用回归方程对其产气量进行模拟。结果表明,当pH 6.50～8.00时,C/N 20～30之间变化时,产气量随之发生明显变化,当pH 7.25和C/N 25时,污泥单位产气量最高;以pH为因素A,C/N为因素B,单位产气量为响应值R1,进行响应面分析,建立模型得到二次系数方程,根据方程预测,当pH 7.09和C/N 25时,其理论最高产气量可达345 m L/g,而实际验证试验的产气量结果为（348±6）m L/g,与预测值相差仅0.8%,可见该方法确定的最佳条件合理,可以很好地用于污泥厌氧发酵条件的优化。

Effect of Variable Selection on Multidisciplinary Design Optimization:a Flight Vehicle Example

Different multidisciplinary design optimization （MDO） problems are formulated and compared. Two MDO formulations are applied to a sounding rocket in order to optimize the performance of the rocket. In the MDO of the referred vehicle, three disciplines have been considered, which are trajectory, propulsion and aerodynamics. A special design structure matrix is developed to assist data exchange between disciplines. This design process uses response surface method （RSM） for multidisciplinary optimization of the rocket. The RSM is applied to the design in two categories： the propulsion model and the system level. In the propulsion model, RSM determines an approximate mathematical model of the engine output parameters as a function of design variables. In the system level, RSM fits a surface of objective function versus design variables. In the first MDO problem formulation, two design variables are selected to form propulsion discipline. In the second one, three new design variables from geometry are added and finally, an optimization method is applied to the response surface in the system level in order to find the best result. Application of the first developed multidisciplinary design optimization procedure increased accessible altitude （performance index） of the referred sounding rocket by twenty five percents and the second one twenty nine.

Optimization of Process Parameters for in High-Energy Ball Milling of CNTs/Al2024 Composites Through Response Surface Methodology

The mathematical models are developed to evaluate the ultimate tensile strength( UTS) and hardness of CNTs / Al2024 composites fabricated by high-energy ball milling. The effects of the preparation variables which are milling time,rotational speed,mass fraction of CNTs and ball to powder ratio on UST and hardness of CNTs / Al2024 composites are investigated. Based on the central composite design( CCD),a quadratic model is developed to correlate the fabrication variables to the UST and hardness. From the analysis of variance( ANOVA),the most influential factor on each experimental design response is identified. The optimum conditions for preparing CNTs / Al2024 composites are found as follows: 1. 53 h milling time,900 r / min rotational speed,mass fraction of CNTs 2. 87% and Ball to powder ratio 25 ∶ 1. The predicted maximum UST and hardness are 273.30 MPa and 261.36 HV,respectively. And the experimental values are 283.25 MPa and256.8 HV,respectively. It is indicated that the predicted UST and hardness after process optimization are found to agree satisfactory with the experimental values.

Stamping Robust Design Method and Its Application

The application of the robust design to stamping is discussed in the paper. The regression equation of the quality index and its influencing factors can be attained by using method of central composite design. Stamping computer simulation takes the place of real stamping experiments to fulfill the special experimental conditions. The real stamping experiments prove the correctness and the feasibility of the stamping robust design method-central composite design.