Modeling and optimization of low-grade Mn bearing ore leaching using response surface methodology and central composite rotatable design

The application of leaching process to extracting Mn from a low-grade manganese ore was investigated using a software based design of experiments. Four main parameters, i.e. sulfuric acid concentration, oxalic acid concentration, time and temperature were considered in a central composite response surface design. The recoveries of Mn and Fe were selected as response of design. The optimum conditions under which the Mn and Fe recoveries were the highest and the time and temperature were the lowest were determined using statistical analysis and analysis of variance （ANOVA）. The results showed that Mn and Fe recoveries were 93.44% and 15.72% under the optimum condition, respectively. Also, sulfuric acid concentration was the most effective parameter affecting the process. The amounts of sulfuric and oxalic acid were obtained to be 7% and 42.50 g/L in optimum condition and the best time and temperature were 65 min and 63 ℃.

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.

Empirical model for bio-extraction of copper from low grade ore using response surface methodology

The copper extraction in shaking bioreactors was modeled and optimized using response surface methodology（RSM）. Influential parameters in the mesophilic bioleaching process of a low-grade copper ore including p H value, pulp density, and initial concentration of ferrous ions were comprehensively studied. The effect of leaching time on the response（copper extraction） at the 1st, 4th, 9th, 14 th and 22 nd days of treatment was modeled and examined. The central composite design methodology（CCD） was used as the design matrix to predict the optimal level of these parameters. Then, the model equation at the 22 nd day was optimized using the quadratic programming（QP） to maximize the total copper extraction within the studied experimental range. Under the optimal condition（initial p H value of 2.0, pulp density of 1.59%, and initial concentration of ferrous ions of 0 g/L）, the total copper extraction predicted by the model is 85.98% which is significantly close to that obtained from the experiment（84.57%）. The results show that RSM could be useful to predict the maximum copper extraction from a low-grade ore and investigate the effects of variables on the final response. Besides, a couple of statistically significant interactions are derived between p H value and pulp density as well as p H value and initial ferrous ion concentration which are precisely interpreted. However, there is no statistically significant interaction between the initial ferrous ion concentration and the pulp density. Additionally, the response at optimal levels of p H value and pulp density is found to be independent on the level of initial ferrous concentration.

Modeling the Effects of Tool Shoulder and Probe Profile Geometries on Friction Stirred Aluminum Welds Using Response Surface Methodology

The present paper discusses the modeling of tool geometry effects on the friction stir aluminum welds using response surface methodology. The friction stir welding tools were designed with different shoulder and tool probe geometries based on a design matrix. The matrix for the tool designing was made for three types of tools, based on three types of probes, with three levels each for defining the shoulder surface type and probe profile geometries. Then, the effects of tool shoulder and probe geometries on friction stirred aluminum welds were experimentally investigated with respect to weld strength, weld cross section area, grain size of weld and grain size of thermo-mechanically affected zone. These effects were modeled using multiple and response surface regression analysis. The response surface regression modeling were found to be appropriate for defining the friction stir weldment characteristics.

Comparative Study of Response Surface Designs with Errors-in-Variables Model

This paper investigates the scaled prediction variances in the errors-in-variables model and compares the performance with those in classic model of response surface designs for three factors.The ordinary least squares estimators of regression coefficients are derived from a second-order response surface model with errors in variables.Three performance criteria are proposed.The first is the difference between the empirical mean of maximum value of scaled prediction variance with errors and the maximum value of scaled prediction variance without errors.The second is the mean squared deviation from the mean of simulated maximum scaled prediction variance with errors.The last performance measure is the mean squared scaled prediction variance change with and without errors.In the simulations,1 000 random samples were performed following three factors with 20 experimental runs for central composite designs and 15 for Box-Behnken design.The independent variables are coded variables in these designs.Comparative results show that for the low level errors in variables,central composite face-centered design is optimal;otherwise,Box-Behnken design has a relatively better performance.

Response Surface Modeling of Fuel Rich and Fuel Lean Catalytic Combustion of the Stabilized Confined Turbulent Gaseous Diffusion Flames

The Response Surface Methodology (RSM) has been applied to explore the thermal structure of the experimentally studied catalytic combustion of stabilized confined turbulent gaseous diffusion flames. The Pt/γAl2O3 and Pd/γAl2O3 disc burners were situated in the combustion domain and the experiments were performed under both fuel-rich and fuel-lean conditions at a modified equivalence (fuel/air) ratio (ø) of 0.75 and 0.25 respectively. The thermal structure of these catalytic flames developed over the Pt and Pd disc burners were inspected via measuring the mean temperature profiles in the radial direction at different discrete axial locations along the flames. The RSM considers the effect of the two operating parameters explicitly (r), the radial distance from the center line of the flame, and (x), axial distance along the flame over the disc, on the measured temperature of the flames and finds the predicted maximum temperature and the corresponding process variables. Also the RSM has been employed to elucidate such effects in the three and two dimensions and displays the location of the predicted maximum temperature.

Modeling and Optimization of Two Clays Acidic Activation for Phosphate Ions Removal in Aqueous Solution by Response Surface Methodology

This work deals with phosphate ions removal in aqueous solution by adsorption carried out using two clays, both in activated form. One, non-swelling clay, rich in kaolinite, is associated with illite and quartz. The other, swelling, richer in montmorillonite, is associated with kaolinite, illite and quartz. Seven factors including these two clays were taken into account in a series of experimental designs in order to model and optimize the acidic activation process favoring a better phosphate removal. In addition to the choice of clay nature, the study was also interested in the identification of the mineral acid, between hydrochloric acid and sulfuric acid, which would promote this acidic activation. Response Surface Methodology (RSM) was used for this purpose by sequentially applying Plackett and Burman Design and Full Factorial Design (FD) for screening. Then, a central composite design (CCD) was used for modeling the activation process. A mathematical surface model has been successfully established. Thus, the best acidic activation conditions were obtained by activating the montmorillonite clay with a 2N sulfuric acid solution, in an acid/clay mass ratio of 7.5 at 100°C for 16H. The phosphate removal maximum rate obtained was estimated at 89.32% ± 0.86%.

A Practical Solution to the Small Sample Size Bias and Uncertainty Problems of Model Selection Criteria in Two-Input Process Multiple Response Surface Methodology Datasets

Multiple response surface methodology (MRSM) most often involves the analysis of small sample size datasets which have associated inherent statistical modeling problems. Firstly, classical model selection criteria in use are very inefficient with small sample size datasets. Secondly, classical model selection criteria have an acknowledged selection uncertainty problem. Finally, there is a credibility problem associated with modeling small sample sizes of the order of most MRSM datasets. This work focuses on determination of a solution to these identified problems. The small sample model selection uncertainty problem is analysed using sixteen model selection criteria and a typical two-input MRSM dataset. Selection of candidate models, for the responses in consideration, is done based on response surface conformity to expectation to deliberately avoid selection of models using the problematic classical model selection criteria. A set of permutations of combinations of response models with conforming response surfaces is determined. Each combination is optimised and results are obtained using overlaying of data matrices. The permutation of results is then averaged to obtain credible results. Thus, a transparent multiple model approach is used to obtain the solution which gives some credibility to the small sample size results of the typical MRSM dataset. The conclusion is that, for a two-input process MRSM problem, conformity of response surfaces can be effectively used to select candidate models and thus the use of the problematic model selection criteria is avoidable.

Using Surface Response Models to Evaluate the Effects of Kinetin on Dioscorea alata Propagated in Wtro

Kinetin is an important growth hormone used for in vitro propagation, but its dynamic and temporal effects on Dioscoreaalata have not been thoroughly evaluated. In this study, surface response models were developed to better elucidate the effects ofkinetin on D. alata propagated in vitro. Nodal segments were obtained from Akaaba, an important D. alata cultivar in Ghana, andpropagated in vitro under five kinetin rates （0, 2.5, 5, 7.5 and 10 μM）. The models were developed using segmented multipleregression with time and kinetin as the predictors. The effects on plant height, the number of leaves, shoots and roots were assessedwith three-dimensional figures for better observation of temporal trends. The model fit was very good with normalized root meansquared error （NRMSE） = 0.1, R-squared = 0.83 and adjusted R-squared = 0.82, averaged across the different growth parameters.Different kinetin levels elicited the maximum shoot, leaf and root formation, as well as the growth rates over time. Moderate kinetinlevels （2-4 μM） provided better growth at early culturing period. Higher kinetin levels （5-10 μM） suppressed the growth of theplantlets at early stages, but the plantlets recovered from the stress and resumed normal growth thereafter. After 4-5 weeks, thegrowth rates of the moderate kinetin levels （2-4 μM） declined much faster and were lower compared to the higher kinetin levels,except plant height and the number of roots which were still higher at the moderate kinetin level even after eight weeks of culturing.Thus, kinetin requirements vary depending on the growth parameters of interest.

Design optimization of transonic compressor stage using CFD and response surface model

In order to shorten the design period, the paper describes a new optimization strategy for computationally expensive design optimization of turbomachinery, combined with design of experiment (DOE), response surface models (RSM), genetic algorithm (GA) and a 3-D Navier-Stokes solver(Numeca Fine). Data points for response evaluations were selected by improved distributed hypercube sampling (IHS) and the 3-D Navier-Stokes analysis was carried out at these sample points. The quadratic response surface model was used to approximate the relationships between the design variables and flow parameters. To maximize the adiabatic efficiency, the genetic algorithm was applied to the response surface model to perform global optimization to achieve the optimum design of NASA Stage 35. An optimum leading edge line was found, which produced a new 3-D rotor blade combined with sweep and lean, and a new stator one with skew. It is concluded that the proposed strategy can provide a reliable method for design optimization of turbomachinery blades at reasonable computing cost.

Long-term deformation analysis of Shuibuya concrete face rockfill dam based on response surface method and improved genetic algorithm

Due to the size effects of rockfill materials, the settlement difference between numerical simulation and in situ monitoring of rockfill dams is a topic of general concern.The constitutive model parameters obtained from laboratory triaxial tests often underestimate the deformation of high rockfill dams.Therefore, constitutive model parameters obtained by back analysis were used to calculate and predict the long-term deformation of rockfill dams.Instead of using artificial neural networks (ANNs), the response surface method (RSM) was employed to replace the finite element simulation used in the optimization iteration.Only 27 training samples were required for RSM, improving computational efficiency compared with ANN, which required 300 training samples.RSM can be used to describe the relationship between the constitutive model parameters and dam settlements.The inversion results of the Shuibuya concrete face rockfill dam (CFRD) show that the calculated settlements agree with the measured data, indicating the accuracy and efficiency of RSM.

Tunnel flexibility effect on the ground surface acceleration response

Flexibility of underground structures relative to the surrounding medium, referred to as the flexibility ratio, is an important factor that influences their dynamic interaction. This study investigates the flexibility effect of a box-shaped subway tunnel, resting directly on bedrock, on the ground surface acceleration response using a numerical model verified against dynamic centrifuge test results. A comparison of the ground surface acceleration response for tunnel models with different flexibility ratios revealed that the tunnels with different flexibility ratios influence the acceleration response at the ground surface in different ways. Tunnels with lower flexibility ratios have higher acceleration responses at short periods, whereas tunnels with higher flexibility ratios have higher acceleration responses at longer periods. The effect of the flexibility ratio on ground surface acceleration is more prominent in the high range of frequencies. Furthermore, as the flexibility ratio of the tunnel system increases, the acceleration response moves away from the free field response and shifts towards the longer periods. Therefore, the flexibility ratio of the underground tunnels influences the peak ground acceleration （PGA） at the ground surface, and may need to be considered in the seismic zonation of urban areas.

Application of Response Surface Methodology for Optimization of Fluoride Removal Mechanism by Newely Developed Biomaterial

The adsorption capacities of new biomaterials derived from lemon leaf (Citrus sp.) toward fluoride ions have been explored by varying different physicochemical parameters such as pH, initial concentration, adsorbent dose, contact time, stirring rate and temperature. The entire study was done through batch process. Maximum fluoride adsorption of 96.9% - 98.8% was achieved with an initial concentration of 10 mg/L. Langmuir isotherm model well expressed fluoride ad- sorption onto LLD-1, LLD-2 and LLD-3. According to correlation coefficient, the fluoride adsorption onto these 3 ad- sorbents was correlated well with pseudo-second-order kinetic model. From thermodynamic study, the spontaneous nature and feasibility of the adsorption process with negative enthalpy (&#916H0) value also supported the exothermic nature were shown. The rate of fluoride adsorption was mathematically described as a function of experimental parameters and was modeled through Box-Behnken (Response surface methodology). The results showed that the responses of fluoride adsorption were significantly affected by the quadratic term of pH, initial concentration, contact time and temperature and the statistical analysis was performed by ANOVA which indicated good correlation of experimental parameters.

Response Surface Methodology and Artificial Neural Network Methods Comparative Assessment for Fuel Rich and Fuel Lean Catalytic Combustion

Modeling, predictive and generalization capabilities of response surface methodology (RSM) and artificial neural network (ANN) have been performed to assess the thermal structure of the experimentally studied catalytic combustion of stabilized confined turbulent gaseous diffusion flames. The Pt/γAl2O3 and Pd/γAl2O3 disc burners were located in the combustion domain and the experiments were accomplished under both fuel-rich and fuel-lean conditions at a modified equivalence (fuel/air) ratio (ø) of 0.75 and 0.25, respectively. The thermal structure of these catalytic flames developed over the Pt and Pd disc burners was scrutinized via measuring the mean temperature profiles in the radial direction at different discrete axial locations along with the flames. The RSM and ANN methods investigated the effect of the two operating parameters namely (r), the radial distance from the center line of the flame, and (x), axial distance along with the flame over the disc, on the measured temperature of the flames and predicted the corresponding temperatures beside predicting the maximum temperature and the corresponding input process variables. A three-layered Feed Forward Neural Network was developed in conjugation with the hyperbolic tangent sigmoid (tansig) transfer function and an optimized topology of 2:10:1 (input neurons:hidden neurons:output neurons). Also the ANN method has been exploited to illustrate the effects of coded R and X input variables on the response in the three and two dimensions and to locate the predicted maximum temperature. The results indicated the superiority of ANN in the prediction capability as the ranges of & F_Ratio are 0.9181 - 0.9809 & 634.5 - 3528.8 for RSM method compared to 0.9857 - 0.9951 & 7636.4 - 24,028.4 for ANN method beside lower values for error analysis terms.

Analysis of Response Surface in the Study of RE(NO_3)_3-HNO_3-P507-Kerosene Extraction System

RE(NO_3)_3-HNO_3-P507-kerosene extraction system(RE=La,Ce,Pr,Nd,Sm,Eu,Gd,Tb,Dy,Ho,Er, Tm,Yb,Lu,Y)was studied by the response surface technique.14 models for extracting single rare earth ele- ment in a broad range of acidity and initial rare earth concentration were obtained by using the stepwise regression method.Three-dimensional display of the response surface of the model of extracting Er^(3+)was showed as an example,which reveals clearly the dependence of distribution ratio upon both initial acidity and ini- tial rare earth concentration.

Blocking Response Surface Designs Incorporating Neigh-bour Effects

In this paper, blocking in response surface for fitting first order model incorporating neighbour effects has been investigated. The conditions for orthogonal estimation of the parameters of the model have been obtained. A method of constructing designs which ensures the constancy of variance of the parameter estimates of the model has also been given.

Comparative Appraisal of Response Surface Methodology and Artificial Neural Network Method for Stabilized Turbulent Confined Jet Diffusion Flames Using Bluff-Body Burners

The present study was conducted to present the comparative modeling, predictive and generalization abilities of response surface methodology (RSM) and artificial neural network (ANN) for the thermal structure of stabilized confined jet diffusion flames in the presence of different geometries of bluff-body burners. Two stabilizer disc burners tapered at 30° and 60° and another frustum cone of 60°/30° inclination angle were employed all having the same diameter of 80 (mm) acting as flame holders. The measured radial mean temperature profiles of the developed stabilized flames at different normalized axial distances (x/dj) were considered as the model example of the physical process. The RSM and ANN methods analyze the effect of the two operating parameters namely (r), the radial distance from the center line of the flame, and (x/dj) on the measured temperature of the flames, to find the predicted maximum temperature and the corresponding process variables. A three-layered Feed Forward Neural Network in conjugation with the hyperbolic tangent sigmoid (tansig) as transfer function and the optimized topology of 2:10:1 (input neurons: hidden neurons: output neurons) was developed. Also the ANN method has been employed to illustrate such effects in the three and two dimensions and shows the location of the predicted maximum temperature. The results indicated the superiority of ANN in the prediction capability as the ranges of R2 and F Ratio are 0.868 - 0.947 and 231.7 - 864.1 for RSM method compared to 0.964 - 0.987 and 2878.8 7580.7 for ANN method beside lower values for error analysis terms.

Analysis of Density of Sintered Iron Powder Component Using the Response Surface Method

The continued growth of ferrous powder metallurgy in automobile and others engineering application is largely de-pendent on the development of higher density materials and improved mechanical properties. Since density is a predominant factor in the performance of powder metallurgy components, it has been primarily considered for the present investigation. An experimental investigation have been undertaken in order to understand the variation of density with respect to the variation of process parameters viz., compaction load, sinter temperature and sintering time. The relation among the various process parameters with density has been observed. A mathematical model has been developed using second order response surface model (RSM) with central composite design (CCD) considering the above mentioned process parameters. The developed mathematical model would help in predicting the variation in density with the change in the level of different parameters influencing the density variation. This model also can be useful for setting of optimum value of the parameters for achieving the target density.

Simulation of an aircraft thermal management system based on vapor cycle response surface model

The modern aircraft Thermal Management System(TMS)faces significant challenges due to increasing thermal loads and limited heat dissipation pathways.To optimize TMS during the conceptual design stage,the development of a modeling and simulation tool is crucial.In this study,a TMS simulation model library was created using MATLAB/SIMULINK.To simplify the complexity of the Vapor Cycle System(VCS)model,a Response Surface Model(RSM)was constructed using the Monte Carlo method and validated through simulation experiments.Taking the F-22 fighter TMS as an example,a thermal dynamic simulation model was constructed to analyze the variation of thermal response parameters in key subsystems and elucidate their coupling relationships.Furthermore,the impact of total fuel flow and ram air flow on the TMS was investigated.The findings demonstrate the existence of an optimal total fuel flow that achieves a balance between maximizing fuel heat sink utilization and minimizing bleed air demand.The adaptive distribution of fuel and ram air flow was found to enhance aircraft thermal management performance.This study contributes to improving modeling efficiency and enhancing the understanding of the thermal dynamic characteristics of TMS,thereby facilitating further optimization in aircraft TMS design.

Performance Improvement of Two-Phase Steam Ejector based on CFD Techniques,Response Surface Methodology and Genetic Algorithm

The steam ejector is a crucial component in the waste heat recovery system.Its performance determines the amount of recovered heat and system efficiency.However,poor ejector performance has always been the main bottleneck for system applications.Therefore,this study proposes an optimization methodology to improve the steam ejector's performance by utilizing computational fluid dynamics(CFD) techniques,response surface methodology(RSM),and genetic algorithm(GA).Firstly,a homogeneous equilibrium model(HEM) was established to simulate the two-phase flow in the steam ejector.Then,the orthogonal test was presented to the screening of the key decision variables that have a significant impact on the entrainment ratio(ER).Next,the RSM was used to fit a response surface regression model(RSRM).Meanwhile,the effect of the interaction of geometric parameters on the performance of the steam ejector was revealed.Finally,GA was employed to solve the RSRM's global optimal ER value.The results show that the RSRM exhibits a good fit for ER(R^(2)=0.997).After RSM and GA optimization,the maximum ejector efficiency is 27.94%,which is 48.38% higher than the initial ejector of 18.83%.Furthermore,the optimized ejector efficiency is increased by 46.4% on average under off-design conditions.Overall,the results reveal that the combination of CFD,RSM,and GA presents excellent reliability and feasibility in the optimization design of a two-phase steam ejector.