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.

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.

INTEGRATION SHAPE AND SIZING OPTIMIZATION OF COMPOSITE WING STRUCTURE BASED ON RESPONSE SURFACE METHOD

An effective optimization method for the shape/sizing design of composite wing structures is presented with satisfying weight-cutting results. After decoupling, a kind of two-layer cycled optimization strategy suitable for these integrated shape/sizing optimization is obtained. The uniform design method is used to provide sample points, and approximation models for shape design variables. And the results of sizing optimization are construct- ed with the quadratic response surface method （QRSM）. The complex method based on QRSM is used to opti- mize the shape design variables and the criteria method is adopted to optimize the sizing design variables. Compared with the conventional method, the proposed algorithm is more effective and feasible for solving complex composite optimization problems and has good efficiency in weight cutting.

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 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.

Optimizing Bucket Elevator Performance through a Blend of Discrete Element Method, Response Surface Methodology, and Firefly Algorithm Approaches

This research introduces a novel approach to enhancing bucket elevator design and operation through the integration of discrete element method(DEM)simulation,design of experiments(DOE),and metaheuristic optimization algorithms.Specifically,the study employs the firefly algorithm(FA),a metaheuristic optimization technique,to optimize bucket elevator parameters for maximizing transport mass and mass flow rate discharge of granular materials under specified working conditions.The experimental methodology involves several key steps:screening experiments to identify significant factors affecting bucket elevator operation,central composite design(CCD)experiments to further explore these factors,and response surface methodology(RSM)to create predictive models for transport mass and mass flow rate discharge.The FA algorithm is then applied to optimize these models,and the results are validated through simulation and empirical experiments.The study validates the optimized parameters through simulation and empirical experiments,comparing results with DEM simulation.The outcomes demonstrate the effectiveness of the FA algorithm in identifying optimal bucket parameters,showcasing less than 10%and 15%deviation for transport mass and mass flow rate discharge,respectively,between predicted and actual values.Overall,this research provides insights into the critical factors influencing bucket elevator operation and offers a systematic methodology for optimizing bucket parameters,contributing to more efficient material handling in various industrial applications.

Optimization and Characterization of Cellulose Extraction from Grevillea robusta (Silky Oak) Leaves by Soda-Anthraquinone Pulping Using Response Surface Methodology

Response surface methodology (RSM) using the central composite design (CCD) was applied to examine the impact of soda-anthraquinone pulping conditions on Grevillea robusta fall leaves. The pulping factors studied were: NaOH charge 5% to 20% w/v, pulping time 30 to 180 minutes, and the anthraquinone charge 0.1 to 0.5% w/w based on the oven-dried leaves. The responses evaluated were the pulp yield, cellulose content, and the degree of delignification. Various regression models were used to evaluate the effects of varying the pulping conditions. The optimum conditions attained were;NaOH charge of 14.63%, 0.1% anthraquinone, and a pulping period of 154 minutes, corresponding to 20.68% pulp yield, 80.56% cellulose content, and 70.34% lignin removal. Analysis of variance (ANOVA), was used to determine the most important variables that improve the extraction process of cellulose. The experiment outcomes matched those predicted by the model (Predicted R2 = 0.9980, Adjusted R2 = 0.9994), demonstrating the adequacy of the model used. FTIR analysis confirmed the elimination of the non-cellulosic fiber constituents. The lignin and hemicellulose-related bands (around 1514 cm−1, 1604 cm−1, 1239 cm−1, and 1734 cm−1) decreased with chemical treatment, indicating effective cellulose extraction by the soda-anthraquinone method. Similar results were obtained by XRD, SEM and thermogravimetric analysis of the extracted cellulose. Therefore, Grevillea robusta fall leaves are suitable renewable, cost-effective, and environmentally friendly non-wood biomass for cellulose extraction.

Optimal design of butterfly-shaped linear ultrasonic motor using finite element method and response surface methodology

A new method for optimizing a butterfly-shaped linear ultrasonic motor was proposed to maximize its mechanical output. The finite element analysis technology and response surface methodology were combined together to realize the optimal design of the butterfly-shaped linear ultrasonic motor. First, the operation principle of the motor was introduced. Second, the finite element parameterized model of the stator of the motor was built using ANSYS parametric design language and some structure parameters of the stator were selected as design variables. Third, the sample points were selected in design variable space using latin hypercube Design. Through modal analysis and harmonic response analysis of the stator based on these sample points, the target responses were obtained. These sample points and response values were combined together to build a response surface model. Finally, the simplex method was used to find the optimal solution. The experimental results showed that many aspects of the design requirements of the butterfly-shaped linear ultrasonic motor have been fulfilled. The prototype motor fabricated based on the optimal design result exhibited considerably high dynamic performance, such as no-load speed of 873 ram/s, maximal thrust of 27.5 N, maximal efficiency of 43%, and thrust-weight ratio of 45.8.

Reliability-based design optimization for flexible mechanism with particle swarm optimization and advanced extremum response surface method

To improve the computational efficiency of the reliability-based design optimization(RBDO) of flexible mechanism, particle swarm optimization-advanced extremum response surface method(PSO-AERSM) was proposed by integrating particle swarm optimization(PSO) algorithm and advanced extremum response surface method(AERSM). Firstly, the AERSM was developed and its mathematical model was established based on artificial neural network, and the PSO algorithm was investigated. And then the RBDO model of flexible mechanism was presented based on AERSM and PSO. Finally, regarding cross-sectional area as design variable, the reliability optimization of flexible mechanism was implemented subject to reliability degree and uncertainties based on the proposed approach. The optimization results show that the cross-section sizes obviously reduce by 22.96 mm^2 while keeping reliability degree. Through the comparison of methods, it is demonstrated that the AERSM holds high computational efficiency while keeping computational precision for the RBDO of flexible mechanism, and PSO algorithm minimizes the response of the objective function. The efforts of this work provide a useful sight for the reliability optimization of flexible mechanism, and enrich and develop the reliability theory as well.

EFFECTS OF REACTION AND PROCESSING PARAMETERS ON ETHYLENE POLYMERIZATION USING DIFFERENT ZIEGLER-NATTA CATALYSTS:EMPLOYMENT OF TAGUCHI EXPERIMENTAL DESIGN AND RESPONSE SURFACE METHOD

Different Ziegler-Natta catalysts were employed to polymerize ethylene. To investigate the influences of reaction parameters, namely Al/Ti molar ratio, hydrogen and processing parameters, i.e. ethylene pressure and temperature, a Taguchi experimental design was worked out. An L27 orthogonal array was chosen to take the above-mentioned parameters and relevant interactions into account. Response surface method was the tool used to analyze the experimental design results. Al/Ti, ethylene pressure and temperature were selected as experimental design factors, and catalyst activity and polymerization yield were the response parameters. Increasing pressure, due to an increment in monomer accessibility, and rising Al/Ti, because of higher reduction in the catalysts, cause an increase in both polymerization yield and catalyst activity. Nonetheless, a higher temperature, thanks to reducing ethylene solubility in the slurry medium and partially catalyst destruction, lead to a reduction in both response parameters. A synergistic effect was also observed between temperature and pressure. All catalyst activities will reduce in the presence of hydrogen. Molecular weight also shows a decline in the presence of hydrogen as a transfer agent. However, the polydispersity index remains approximately intact. Using SEM, various morphologies, owing to different catalyst morphologies, were seen for the polyethylene.

Bamboo Fiber Modified Asphalt Mixture Proportion Design and Road Performances Based on Response Surface Method

In order to comprehensively utilize the remaining bamboo residue of bamboo products,this paper presents a research on recycling the bamboo fibers from bamboo residue for improving the performance of the asphalt mixtures.First of all,the basic performance parameters of sinocalamus affinis fiber,phyllostachys pubescens fiber,green bamboo fiber were tested and analyzed,and the optimal content and length were put forward.Then,the mix ratio design of the bamboo fiber modified asphalt mixture was further designed through the response surface method,and was verified the rationality of the mix ratio.Finally,the mixture specimens were made according to the experimental design mix ratio,and the high temperature,low temperature performance and moisture susceptibility of the bamboo fiber modified mixtures asphalt were tested.The results showed that the high temperature performance,low temperature performance and moisture susceptibility of bamboo fiber modified asphalt mixtures were improved compared with the performance of SBS modified asphalt mixture.When the length of bamboo fiber is 7.25 mm and the content of 0.22%,the road performance of the asphalt mixture was optimal.Consequentially,the decomposition of bamboo residue into bamboo fiber and its application in asphalt pavement can improve the reuse of bamboo waste,with remarkable environmental benefits and great promotion value.

Ship Appearance Optimal Design on RCS Reduction Using Response Surface Method and Genetic Algorithms

Radar cross section (RCS) reduction technologies are very important in survivability of the military naval vessels. Ship appearance shaping as an effective countermeasure of RCS reduction redirects the scattered energy from one angular region of interest in space to another region of little interest. To decrease the scattering electromagnetic signals from ship scientifically, optimization methods should be introduced in shaping design. Based on the assumption of the characteristic section design method, mathematical formulations for optimal shaping design were established. Because of the computation-intensive analysis and singularity in shaping optimization, the response surface method (RSM) combined genetic algorithm (GA) was proposed. The poly-nomial response surface method was adopted in model approximation. Then genetic algorithms were employed to solve the surrogate optimization problem. By comparison RCS of the conventional and the optimal design, the superiority and effectiveness of proposed design methodology were verified.

Optimization of medium components using response surface methodology (RSM) for mycelium biomass and exopolysaccharide production by <i>Lentinus squarrosulus</i>

The interaction between sucrose, yeast extract and initial pH was investigated to optimize critical medium components for mycelium biomass and production of exopolysaccharide (EPS) of Lentinus squarrosulus using Response Surface Methodology (RSM). A central composite design (CCD) was applied and a polynomial regression model with quadratic term was used to analyse the experimental data using analysis of variance (ANOVA). ANOVA analysis showed that the model was very significant (p Lentinus squarrosulus are as follows: sucrose concentration 114.61 g/L, yeast extract 1.62 g/L and initial pH of 5.81;sucrose concentration 115.8 g/L, yeast extract of 3.39 g/L and initial pH of 6.44 respectively.

Enhacement of the Viability of <i>Lactobacillus</i><i>plantarum</i>during the Preservation and Storage Process Based on the Response Surface Methodology

Objective: The Response Surface Methodology (RSM) is a commonly used system to optimize cell viability of probiotic strains when they are subjected to different preservation and storage processes. Methods and Results: To determine the optimal levels of incorporation of several cry oprotectants (skim milk, sucrose and trehalose) in the freeze-drying process of Lactobacillus plantarum, a range of experiments based on a Rotational Central Composite design (CCD) were conducted. The results were adjusted to a quadratic model, resulting in the presence of interaction between the different variables. Solving a regression equation, we obtained the optimum concentrations of cryoprotective agents: 24.06% milk powder, 6.22% sucrose, 5.63% trehalose. To visualize the interactions between the three variables involved in the study, Design Expert? software was used. Conclusions: The analysis reveals that while trehalose has a direct effect on the viability of L. plantarum, skim milk and sucrose exert quadratic effects. There are also interactions between cryoprotectants, which emphasize the synergies produced between milk and sucrose and between sucrose and trehalose, which allows maintaining the viability of L. plantarum. Significance and Impact of the Study: The addition of new oligosaccharides as trehalose in premixtures for functional feed can maintain the viability of L. plantarum during longer periods of time, ensuring the proper administration of probiotics to their destinations.

Optimization of the Impeller Geometry for an Automotive Torque Converter Using Response Surface Methodology and Desirability Function

Response surface methodology (RSM) based on desirability function approach (DFA) is applied to obtain an optimal design of the impeller geometry for an automotive torque converter. The relative importance of six design parameters including impeller blade number, blade thickness, bias angle, scroll angle, inlet angle and exit angle is investigated using orthogonal design approach. The impeller inlet angle, exit angle and bias angle are found to exert the greatest influence on the overall performance of a torque converter, with two flow area factors being considered, namely 17% and 20%. Then, RSM together with central composite design (CCD) method is used to in-depth evaluate the interaction effect of the three key parameters on converter performance. The results demonstrate that impeller exit angle has the strongest impact on peak efficiency, with larger angles yielding the most favorable results. The stall torque ratio maximization is attainable with the increase of impeller bias angle and inlet angle together with smaller exit angle. In the end, an optimized design for the impeller geometry is obtained with stall torque ratio and peak efficiency increased by 1.62% and 1.1%, respectively. The new optimization method can be used as a reference for performance enhancement in the design process of impeller geometry for an automotive torque converter.

Catalytic Hydrothermal Liquefaction of Water Hyacinth Using Fe3O4/NiO Nanocomposite: Optimization of Reaction Conditions by Response Surface Methodology

This research aimed at optimizing the reaction conditions for the catalytic hydrothermal liquefaction (HTL) of water hyacinth using iron oxide/nickel oxide nanocomposite as catalysts. The iron oxide/nickel oxide nanocomposite was synthesized by the co-precipitation method and used in the hydrothermal liquefaction of water hyacinth. The composition and structural morphology of the synthesized catalysts were determined using X-ray diffraction (XRD), transmission electron microscopy (TEM), scanning electron microscopy (SEM), and atomic absorption spectroscopy (AAS). The particle size distribution of the catalyst nanoparticles was determined by the Image J software. Three reaction parameters were optimized using the response surface methodology (RSM). These were: temperature, residence time, and catalyst dosage. A maximum bio-oil yield of 59.4 wt% was obtained using iron oxide/nickel oxide nanocomposite compared to 50.7 wt% obtained in absence of the catalyst. The maximum bio-oil yield was obtained at a temperature of 320°C, 1.5 g of catalyst dosage, and 60 min of residence time. The composition of bio-oil was analyzed using gas chromatography-mass spectroscopy (GC-MS) and elemental analysis. The GC-MS results showed an increase of hydrocarbons from 58.3% for uncatalyzed hydrothermal liquefaction to 88.66% using iron oxide/nickel oxide nanocomposite. Elemental analysis results revealed an increase in the hydrogen and carbon content and a reduction in the Nitrogen, Oxygen, and Sulphur content of the bio-oil during catalytic HTL compared to HTL in absence of catalyst nanoparticles. The high heating value increased from 33.5 MJ/Kg for uncatalyzed hydrothermal liquefaction to 38.6 MJ/Kg during the catalytic HTL. The catalyst nanoparticles were recovered from the solid residue by sonication and magnetic separation and recycled. The recycled catalyst nanoparticles were still efficient as hydrothermal liquefaction (HTL) catalysts and were recycled four times. The application of iron oxide/ nickel oxide nanocomposites in the HTL of water hyacinth increases the yield of bio-oil and improves its quality by reducing hetero atoms thus increasing its energy performance as fuel. Iron oxide/nickel oxide nanocomposites used in this study are widely available and can be easily recovered magnetically and recycled. This will potentially lead to an economical, environmentally friendly, and sustainable way of converting biomass into biofuel.

Improvement of xylanase production by Aspergillus niger XY-1 using response surface methodology for optimizing the medium composition

Objective: To study the optimal medium composition for xylanase production by Aspergillus niger XY-1 in solid-state fermentation (SSF). Methods: Statistical methodology including the Plackett-Burman design (PBD) and the central composite design (CCD) was employed to investigate the individual crucial component of the medium that significantly affected the enzyme yield. Results: Firstly, NaNO3, yeast extract, urea, Na2CO3, MgSO4, peptone and (NH4)2SO4 were screened as the significant factors positively affecting the xylanase production by PBD. Secondly, by valuating the nitrogen sources effect, urea was proved to be the most effective and economic nitrogen source for xylanase production and used for further optimization. Finally, the CCD and response surface methodology (RSM) were applied to determine the optimal concentration of each sig-nificant variable, which included urea, Na2CO3 and MgSO4. Subsequently a second-order polynomial was determined by multiple regression analysis. The optimum values of the critical components for maximum xylanase production were obtained as follows: x1 (urea)=0.163 (41.63 g/L), x2 (Na2CO3)=?1.68 (2.64 g/L), x3 (MgSO4)=1.338 (10.68 g/L) and the predicted xylanase value was 14374.6 U/g dry substrate. Using the optimized condition, xylanase production by Aspergillus niger XY-1 after 48 h fermentation reached 14637 U/g dry substrate with wheat bran in the shake flask. Conclusion: By using PBD and CCD, we obtained the optimal composition for xylanase production by Aspergillus niger XY-1 in SSF, and the results of no additional expensive medium and shortened fermentation time for higher xylanase production show the potential for industrial utilization.

Influence of Operating Parameters on Unbalance in Rotating Machinery Using Response Surface Method

Wide range of rotating machinery contains an inherent amount of unbalance which leads to increase in the vibration level and related faults.In this work,the effect of different operating conditions viz.the unbalanced weight,radius,speed and position of the rotor disc on the unbalance in rotating machine are studied experimentally and analyzed by using Response Surface Methodology(RSM).RSM is a technique which consists of mathematical and statistical methods to develop the relationship between the inputs and outputs of a system by distinct functions.L27 Orthogonal Array(OA)was developed by using Design of Experiments(DOE)according to which experimentation has been carried out.Three accelerometer sensors were mounted to record the vibration responses(accelerations)in radially vertical,horizontal and axial directions.The responses recorded as root mean square values are then analysed using RSM.The relationship between response and operating factors has been established by developing a second order,non-linear mathematical model.Analysis of variance(ANOVA)has been performed for verification of the developed mathematical models.Results obtained from the analysis show that the unbalance weight and speed are most significant operating conditions that contribute the most to the effect the unbalance has on the rotating spindle.

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.

Optimization of Dielectric Barrier Discharge Process for Decolorization of Reactive Blue 19 by Means of Response Surface Methodology

The decolorization of reactive blue 19(RB-19)as a model dye from aqueous solutions has been studied by means of the dielectric barrier discharge(DBD)process.The independent parameters of input power,initial dye concentration and initial pH value were evaluated respectively.Experimental data were optimized by means of a 33 factorial design and response surface methodology(RSM).The dye was quickly removed during the treatment,yielding 96.9%of decolorization efficiency under optimized conditions.Therefore,the total organic carbon(TOC)and chemical oxygen demand(CODcr)results indicated that only the chromophore was destroyed rather than completed oxidation.This was confirmed with UV-vis and tertiary butanol assessments during the DBD treatment.