Quadratic Response Surface Model Research Articles

Application of Response Surface Methodology for concentration of fluorosilicic acid by extraction technique with benzyl alcohol as extractant

As a kind of alternative of natural fluorinated minerals and raw material for producing anhydrous hydrogen fluoride, fluorosilicic acid has attracted more and more attention. In order to raise its utilization rate, dilute fluorosilicic acid solution coming from chemical enterprises needs to be concentrated. The extraction technology with benzyl alcohol as extraction agent was used to concentrating fluorosilicic acid aqueous solution. In order to determine the optimizing operation conditions of the extracting process, single - factor experiments were carried out to confirm the significant affecting factors and their operating range. Then the Response Surface Methodology (RSM) was conducted to accomplish regression of a nonlinear quadratic polynomial model to the experimental data and statistical analysis. Based on these studies, the optimal technical parameters of extracting process are acquired by optimization of the model using the Design-Expert 13 software. The statistical analysis for the fitting response surface quadratic equation model indicated that the model was reliable and accurate with very low p-values (<0.0001), the predicted values with the model equation had remarkable consistency in experimental data. By a great number of optimizations carried out with the Design Expert 13 software based on the fitting model equation, the optimal extractive processing conditions for concentrating fluorosilicic acid aqueous solution were obtained: the phase ratio 7, the extraction time 120.11 min and the extraction temperature 39.70 °C. The optimal concentration of fluorosilicic acid is 26.68 %. In order to increase the concentration of fluorosilicic acid, three-stage cross-current extraction for dilute fluorosilicic acid solution was carried out at the optimizing extracting conditions, 17.43 wt% fluorosilicic acid solution can be concentrated up to 37.46 wt%. The extractant-benzyl alcohol can be recovered with vacuum distillation and recovery rate reached up to 98 %.

The Application of Converter Sludge and Slag to Produce Ecological Cement Mortars.

The paper presents an analysis of the effective use of a mixture of steel sludge (S1) and slag (S2) from the converter process of steel production for the production of cement mortars. Metallurgical waste used in the research, which is currently deposited in waste landfills and heaps near plants, posing a threat to groundwater (possibility of leaching metal ions present in the waste), was used as a substitute for natural sand in the range of 0-20% by weight of cement (each). The obtained test results and their numerical analysis made it possible to determine the conditions for replacing part of the sand in cement mortars with a mixture of sludge and slag from a basic oxygen furnace (BOF) and to determine the effects of such modification. For the numerical analysis, a full quadratic Response Surface Model (RSM) was utilized for two controlled factors. This model was subsequently optimized through backward stepwise regression, ensuring the inclusion of only statistically significant components and verifying the consistency of residual distribution with the normal distribution (tested via Ryan-Joiner's test, p > 0.1). The designated material models are helpful in designing ecological cement mortars using difficult-to-recycle waste (i.e., sludge and converter slag), which is important for a circular economy. Mortars modified with a mixture of metallurgical waste (up to 20% each) are characterized by a slightly lower consistency, compressive and flexural strength, and water absorption. However, they show a lower decrease in mechanical strength after the freezing-thawing process (frost resistance) compared to control mortars. Mortars modified with metallurgical waste do not have a negative impact on the environment in terms of leaching heavy metal ions. The use of a mixture of sludge and steel slag in the amount of 40% (slag/sludge in a 20/20 ratio) allows you to save 200 kg of sand when producing 1 m3 of cement mortar (cost reduction by approx. EUR 5.1/Mg) and will also reduce the costs of the environmental fee for depositing waste.

On the construction of saturated split-plot designs for quadratic response surface models

Split-plot designs are commonly employed in experiments where the levels of some factors are difficult or costly to adjust. One of the primary objectives of many such experiments is to accurately predict responses using fitted response surfaces. While many split-plot designs have been proposed in the literature for this purpose, most of them require large run sizes and an excessive number of whole plots, resulting in expensive and time-consuming experiments. To address this issue, we conduct a study to determine the minimum requirements for a split-plot design that can be used to fit a response surface. Based on these requirements, we construct saturated or nearly saturated response surface split-plot (RSSP) designs that are cost-effective, featuring the fewest possible run sizes and the smallest number of whole plots. We use a motivating example and conduct simulations. Our study shows that the proposed RSSP designs not only provide cost savings, but also maintain good predictive efficiency.

Response surface optimization of hydrogen-rich syngas production by methane dry reforming over bimetallic Mn-Ni/La2O3 catalyst in a fixed bed reactor

The present work utilizes a response surface optimization technique to optimize hydrogen-rich syngas production through the process of methane dry reforming (DRM). This optimization is achieved by employing a bimetallic Mn–Ni/La2O3 catalyst. The study aimed to evaluate the impact of three key parameters, namely reaction temperature, time on stream (TOS), and gas hourly space velocity (GHSV), on the hydrogen to carbon monoxide (H2/CO) ratio in syngas during the DRM. The Mn–Ni/La2O3 catalyst, synthesized using the sequential wet impregnation technique, exhibited suitable physicochemical properties necessary for DRM reaction, as evidenced by the obtained characterization data. Among the five models examined, it was found that the quadratic versus 2FI model substantially fit the experimental data, as evidenced by a p-value <0.05. The analysis of variance (ANOVA) conducted on the quadratic response surface model compared to the 2FI model demonstrated that both the reaction temperature and the TOS had a significant impact on the H2/CO ratio in the syngas. The only significant interaction factor was the relationship between the reaction temperature and the TOS. Under the specified optimal circumstances of 15 000 ml/g.h, 850 °C, and 258.15 min, an H2/CO ratio of 0.98 was achieved. The resulting H2/CO ratio of 0.98 is almost 1, indicating its suitability as a feedstock for methanol production in the Fischer-Tropsch synthesis (FTS).

On E–Optimality Design for Quadratic Response Surface Model

On E–Optimality Design for Quadratic Response Surface Model

Statistical optimization of two-phase hollow fiber liquid-phase microextraction for preconcentration of strychnine in the clinical and postmortem biological fluids prior to gas chromatography-mass spectroscopy detection

Strychnine is a herbal alkaloid whose role in military and doping applications as well as the nervous system stimulation and cancer therapy has been confirmed. Because of its lethal nature, even at low dosages, developing a rapid, sensitive, and accurate method for determination of this alkaloid in the clinical and postmortem samples is of great importance. In this study, a green analytical method based on the two-phase hollow fiber liquid-phase microextraction (HF-LPME) combined with gas chromatography-mass spectrometry (GC–MS) was presented for preconcentration and determination of strychnine in biological fluids. A Box-Behnken design (BBD) with three variables, including extraction time (30–90 min), solution pH (9.0–11.0), and ionic strength (1.0–3.0 mol/L) was employed to maximize the extraction efficiency of strychnine by 1-octanol. The results were satisfactorily fitted to a quadratic response surface model (R2 = 0.979, F = 34.4) which predicted the optimum conditions of operation (extraction time of 89 min, pH = 11.0, and ionic strength of 3.0 mol/L). Based on the results, the studied variables and the interaction between pH and extraction time showed highly significant effects on the process efficiency. The calibration curve was linear in the concentration range of 2.7–1000.0 µg/L (R2 = 0.9978) and the limits of detection and quantitation were found to be 0.8 and 2.7 µg/L, respectively. Moreover, the method was successfully applied to different real samples, including urine (clinical sample), bile and stomach contents, blood, and vitreous humor (postmortem samples), and relative recoveries were obtained in the range of 93.8 % to 99.8 %. The findings of this study suggest that the environmentally friendly HF-LPME method which uses a small amount of a chlorine-free solvent, is a sensitive, cost-effective, simple, and efficient preconcentration method for trace determination of strychnine in biological fluids.

Buckling Defect Optimization of Constrained Ring Rolling of Thin-Walled Conical Rings with Inner High Ribs Combining Response Surface Method with FEM

A buckling defect will appear on the outer surface of the deformed ring during the constrained ring rolling (CRR) of an aluminum alloy thin-wall conical ring with inner high ribs (AATWCRIHR) if the geometrical dimension of the ribs does not match the wall thickness. To avoid the buckling defect, a quantitative method for characterizing the degree of the buckling defect is proposed using the area of the buckling profile. Then, an orthogonal experimental scheme was designed, taking the width of the middle rib, thickness of wall, and height of the middle rib as the design variables and defining the area of the buckling profile as the optimization objective. Subsequently, a quadratic polynomial response surface model was established by combining the optimization algorithm with the finite element method (FEM), and the geometrical dimension of the middle ribs of the deformed AATWCRIHR is optimized. Moreover, the optimal parameter combination to minimize the area of the buckling profile is obtained and verified using FE simulation. The results show that the AATWCRIHR after optimization does not generate the buckling defect during constrained ring rolling, and it is proven that the quantitative buckling defect representation method and the optimization design method based on the response surface model and the finite element simulation results are feasible for the constrained ring-rolling process of the AATWCRIHR.

Macro–micro investigation on stabilization sludge as subgrade filler by the ternary blending of steel slag and fly ash and calcium carbide residue

This study investigates the efficacious utilization of sludge as a subgrade filler through in-situ shallow stabilization, employing cementitious industrial waste materials including steel slag (SS), fly ash (FA), and calcium carbide residue (CCR) as binding agents. The primary emphasis lies in the evaluation of the macro unconfined compression strength of stabilized sludge over a seven-day curing period, facilitated by a quadratic polynomial response surface model to determine the optimal composite stabilizer (WZ01) proportions. Furthermore, an array of meticulous microstructural analyses encompassing X-ray diffraction, X-ray fluorescence, scanning electron microscopy, and energy-dispersive spectroscopy were undertaken to elucidate the development of internal cementitious products and the intrinsic mechanisms underpinning sludge stabilization in tandem with WZ01. The findings ascertain that the optimum WZ01 composition stands at SS: FA: CCR = 32:28:40. Prominent mineralogical constituents within the stabilized sludge encompass amorphous calcium silicate hydrate, calcium aluminate hydrate, and crystalline ettringite. The amelioration in stabilized sludge properties stems from intricate processes involving ion exchange, hydration reactions, and pozzolanic activities. Significantly, the WZ01 curing agent demonstrates heightened cost-effectiveness and environmental merits compared to conventional Portland cement.

Modeling stream baseflow nitrate concentration in an agricultural watershed using neural network and bootstrap method

The evaluation of water resource vulnerability to nonpoint source pollution in the presence of uncertainty remains a crucial concern. To enhance the accuracy of the assessment and pinpoint the key factors that affect watershed water quality, the integration of an artificial neural network (ANN) into the evaluation process is imperative. The research involved the collection of streams baseflow samples from thirty-eight sites between 1994 and 1999 in the Tomorrow-Waupaca River Watershed in central Wisconsin, USA, with a focus on examining the relationship between nitrate concentrations and a range of environmental and land use variables extracted from the watershed GIS database. This study utilized ANN methodology, combined with a bootstrap technique that employed a random resampling approach from a single input dataset, to simulate monthly stream baseflow nitrate concentrations. The effectiveness and predictive ability of the ANN model were assessed by comparing it to conventional multivariate regression methods. Through the use of ANN, more precise outcomes can be achieved while taking into account the uncertainty associated with the analysis. The findings demonstrated that the ANN outperformed both the multivariate linear regression and nonlinear quadratic response surface models in explaining the variance of stream nitrate and in external prediction consistency. This study also highlighted several key variables, such as the areal percentage of agricultural land and grassland, stream order, and the average slope of the groundwater flow path, that significantly impacted the stream baseflow nitrate concentrations in this watershed that was dominated by dairy farming and groundwater. Of these variables, the percentage of agricultural land emerged as the most significant factor.

Structural parameters of venturi injector for periodic air recovery based on response surface methodology

This work is devoted to the study of the structural parameters of a venturi injector for periodic air recovery. Using a push chain concrete spraying machine as a case, a numerical simulation study was conducted on the venturi injector under different structural parameter combinations. The venturi injector structure parameters diameter ratio of the throat to pipe a, convergent angle α, throat length to diameter ratio b, and diffusional angle β are designed and combined by the response surface method. The numerical simulation results and the prediction model obtained by the response surface method were verified by experiments, and the simulation results and prediction model were in good agreement with the experimental results. The results show that the residual air recovery of the push chain concrete spraying machine is best when a, α, b, and β are 0.8, 25°, 2.5, and 10°, respectively. In addition, the quadratic polynomial response surface model of the venturi injector pressure variation coefficient Cv and pressure drop Pd concerning the structural parameters was established, and the influence rules of each structural parameter on the Cv and Pd were obtained. The variation patterns of turbulent kinetic energy in the venturi at different times and stable sections at the back end are revealed. This paper can provide help for the design of venturi structures used for periodic air recovery in other chemical fields.

Study on Multi-factor Optimization of Adjacent Underground Layered Salt Rock Gas Storage Based on RSM

To study the significance of different factors on adjacent underground laminated salt rock storage, 15 groups of simulation tests are designed by using the response surface methodology (RSM), the quadratic response surface model with the midpoint displacement and medial waist stress of the interlayer as the response values is constructed. By analyzing the main effect and interaction of the regression model, the influence of the interaction between pillar width, interlayer thickness, and the location of a single interlayer on the midpoint displacement of the interlayer and the internal waist stress of the adjacent ellipsoidal cavity is studied. The results show that the interlayer thickness is the main effect factor of the midpoint displacement of the interlayer. And the pillar width is the main effect factor of the medial waist stress. When the adjacent storage is designed with as 2.5D pillar width, 2 m interlayer thickness, and the midpoint of the interlayer is located at 0.3H above the cavity, the displacement and stress of the test model are relatively small. The above conclusions can provide a certain reference value for the mechanical analysis of adjacent underground layered salt rock gas storage.

Use of Wavelet and Bootstrap Methods in Streamflow Prediction

Streamflow prediction is vital to control the effects of floods and mitigation. Physical prediction model often provides satisfactory results, but these models require massive computational work and hydrogeomorphological variables to develop a prediction system. At the same time, data-driven prediction models are quick to apply, easy to handle, and reliable. This study investigates a new hybrid model, the wavelet bootstrap quadratic response surface, for accurate streamflow prediction. Wavelet analysis is a well-known time-frequency joint analysis technique applied in various fields like biological signals, vibration signals, and hydrological signals. The wavelet analysis is used to denoise the time series data. Bootstrap is a nonparametric method for removing uncertainty that uses an intensive resampling methodology with replacement. The authors analyzed the results of the studied models with different statistical metrics, and it has been observed that the wavelet bootstrap quadratic response surface model provides the most efficient results.

Design and optimization of antisolvent crystallization of L-aspartic acid using response surface model: Focused beam reflectance measurements

In the present study, optimization of antisolvent crystallization of L-aspartic acid (L-ASP) was performed using response surface methodology (RSM) and a focused beam reflectance measurement (FBRM) tool. The main process parameters such as storage temperate, stirrer velocity, storage time and solvent ratio influencing the crystallization process were identified by RSM to achieve significant improvement in the yield and quality of the product while chord length distribution (CLD) data was obtained from FBRM. From the studies, it can be observed that 2-propanol was more effective antisolvent than methanol for L-aspartic acid crystallization. The temperature was found to have a critical effect on crystal formation. Crystals were formed between 298.15 and 303.15 K, whereas cohesion, disintegration, and conglomeration were noticed at other temperatures. ANOVA results revealed that all the studied variables have a significant impact on the yield and CLD. The optimum crystallization was obtained at 18 h, stirrer velocity of 200 rpm, distilled water-formic acid/IPA of 1:3(v/v), and storage temperature of 298.15 K. A quadratic response surface model described the crystallization of L-ASP satisfactorily with R2 of 0.99 and a deviation of 1.2%.

Process Optimization Using Response Surface Methodology for the Removal of Cu(II) and Co(II) from Aqueous Solution Using Gelatin-Cellulose Nanocrystals Hydrogel Membrane

The adsorption efficiency of gelatin-cellulose nanocrystals hydrogel membrane (GCHM) for the removal of Cu(II) and Co(II) from aqueous solution was studied in batch experiments. The interactive effect of independent variables such as pH, contact time, temperature, and ratio of gelatin and cellulose nanocrystals on Cu(II) and Co(II) adsorption were investigated. Analysis of variance (ANOVA) showed that the response surface quadratic model is highly impressive and can successfully predict the experimental results. The optimization results of the process variables by response surface methodology- central composition design (RSM-CCD) model was obtained at pH 6, temperature of 52.50 ℃, time of 67.50 min. and ration gelatin-CNCs of 3:1. The maximum removal percentage was 86.95% and 89.77% for Cu(II) and Co(II), respectively.

Recovery of Au and Cu from waste memory modules by electrolysis with hydrochloric acid-hydrogen peroxide system

E-waste is regarded as a special kind of solid waste, because its core components-waste memory modules (WMMs)-contain a large amount of high-value metal resources. However, there has been little research on the green recycling of key metals in WMMs. The difficulty lies in finding out how to reduce or eliminate the secondary pollution caused by the massive use of chemicals, and to improve the resource recovery rate. Therefore, this study constructed three systems based on an electrochemical method, to explore the leaching effects and principles of Au and Cu under different conditions (voltage, temperature, acid concentration and molar ratio). A response surface methodology called Box-Behnken Design was employed to optimize the parameters. The results showed that compared with other additives or without additives, H2O2 has the best effect on selective leaching of Au and Cu from WMMs. Meanwhile, HCl + H2O2 + direct current (DC) is the best system for selectively leaching Au and Cu compared to HCl + DC and HCl + H2O2. Appropriate increasing voltage, temperature and HCl concentration could effectively increase Au and Cu leaching rate, while the increase of mole ratio might inhibit Au and Cu leaching. The response surface quadratic model showed that the significance of Au response values was: voltage > n(HCl/H2O2) > temperature. Under the optimal conditions of 4.1 V DC constant voltage, 40 °C, 8.9 mol/L HCl concentration and 45 M ratio of acid to oxidant, the leaching rates of Au and Cu were 98.87 % and 92.10 %, respectively. It is worth noting that the electrolyte was composed of only HCl + H2O2, and electron was used as an oxidizing agent for potential controlling, which had the advantage of using less non-toxic and non-corrosive chemicals. The research results can provide a basis and technical support for e-waste recycling.

Milling of pharmaceutical powder carrier excipients: Application of central composite design

Pharmaceutical powder carriers are often used to prevent agglomeration of a micronized drug in the co-milling process. Twenty-four pharmaceutical excipients were subjected to preliminary mild milling conditions in this work. Ten of them showed acceptable milling properties with alginic acid, calcium alginate, microcrystalline cellulose (Avicel® 200), carrageenan, and hypromellose having the best particle size reduction without any aggregation while maintaining a narrow span. For the latter five substances, circumscribed central composite design (CCD) evaluating the effect of the factors milling speed and timeon the responses (particle size, particle size distribution) for three milling ball sizes was used to establish optimal milling conditions. For all ten possible factor combinations and each ball size, a quadratic response surface model was used to predict the response variable. For three substances out of five, the best results were achieved using 5-mm balls. Thermal characteristics showed the good stability of excipients under optimized milling conditions.

Optimizing efficiency of InGaP/GaAs dual-junction solar cells with double tunnel junction and bottom back surface field layers

Dual-junction solar cells have permitted to augment markedly efficiency of solar energy harvesting. This is because they involve a combination of III-V semiconductor materials with different band gaps which enables for better absorbance of the solar spectrum and consequently higher efficiency. In these last years, intensive research has been dedicated to develop reliable methods for performing structural optimization of these devices. This work proposes a new numerical procedure in order to achieve optimal design of a dual junction solar cell made of InGaP/GaAs tandem combination. This particular structure relies on the InGaP single junction solar cell, which is used as a front stack, and a back surface field. Optimization was conducted sequentially through post processing data results generated from large parametric simulations performed by using the 2D SILVACO-ATLAS software. The procedure encompasses using either a quadratic response surface model or an artificial neural network model at each stage of the optimization process to determine the actual optimal design of the solar cell. The obtained final optimal design has been shown to yield, under the AM1.5 spectrum, an efficiency of 35.15% at temperature 20°C which is higher than that of previous known results from literature.

Coconut Husk to Reducing Sugar Conversion Using Combined Ultrasound and Surfactant Aided Subcritical Water

The first purpose of this study was to investigate the effect of operating variables and surfactant concentration in subcritical water to after ultrasonic process on the sugar-producing yield from coconut husk. The second purpose was to obtain the optimum operating condition of the subcritical water process. The sonication before the subcritical water process was done by dispersing 40 mesh coconut husk powder in water at 60°C, and 35 kHz. The effect of sonication time was studied by comparing the material crystallinity and composition after being treated for 30 minutes. In this research, the optimization was done by using a Box-Behnken response surface methodology (RSM) experimental design with 3 factors (temperature, time, and surfactant concentration). The designed lower and upper levels were 130°C and 170°C, 40, and 80 minutes, as well as 1 and 3% (w). The results showed that the quadratic response surface model predicted the maximum reducing sugar yield to be 12.0%, which was achieved at the optimum condition of 170°C, 77.5 minutes, and 2.3% SDS surfactant addition. The experiment run at the obtained optimum condition resulted in a reducing sugar yield of 11.7%, which was close to that obtained from the model prediction.

Statistical Approach to Optimize Production of Biosurfactant by Achromobacter Xylos

This study aimed to optimize medium composition biosurfactant production of achromobacter xylos using response surface quadratic model . Lipoprotein and lipopeptides are used in many industries such as petroleum refining, pharmaceutical, mining, agriculture and bioprocess industries. The point of this assessment was to pull out and portray the biosurfactant passing on restriction of microorganisms from oil corrupted soil and considering their advancement energy at various temperatures and pH. The separation and growth study was directed in MSM medium using lamp fuel oil as sole carbon hotspot for bacterial turn of events. Confined strains were found to be Gram positive bacillus and in general Gram's positive minuscule life forms can convey lipopeptides type biosurfactants. The ideal conditions for achromobacteria xylos growth were discovered to be at pH seven (7) and temperature 30oC. Central composite design (CCD) was utilized to pick the following medium components (MgSO4, NaNO3, CaCl2, (NH4)2SO4, FeSO4, and KH2PO4). Central composite arrangement (CCD) of RSM was utilized to analyze the four parts at five stages, and biosurfactant fixation was evaluated as reaction. Backslide coefficients were directed by backslide examination, and the quadratic model condition was settled. R2 an impetus for bio-surfactant was endeavored to be 0.7527, showing that the quadratic model was basic with the exploratory outcomes. Confirmation of the numerical model was driven by playing out the assessment with the normal overhauled values, and bio-surfactant production was found to be 10.53 g/L. Underwriting of the normal quadratic model was 97.3% exact with the test results facilitated under the ideal conditions. CaCl2, (NH4)2SO4, FeSO4, and KH2PO4 were perceived as successful portions for bio-surfactant delivering 98% of achromobacter xylos microorganism.

A hybrid of surrogate model and MIGA method for optimization and compensation of steady-state flow force on water hydraulic HSV

In this research, a hybrid of surrogate model and Multi-island genetic algorithm (MIGA) is proposed for optimization and compensation of steady-state flow force on water hydraulic high-speed on-off valve (HSV) driven by voice coil motor. Firstly, a dynamic model on the spool of HSV is established, and the effects of spool displacement, spool half-cone angle, valve stem diameter and inlet pressure on the steady-state flow force of HSV are analyzed through the CFD simulation. Secondly, a quadratic response surface model is set up based on design of experiment (DOE) to analyze interactions of key parameters on steady-state flow force. MIGA is proposed to optimise the structural parameters of HSV, and the optimization results are analyzed and verified by CFD simulations. Simulation results demonstrate that the steady-state flow force is reduced significantly. Finally, the steady-state flow force in the optimized structure of HSV is also verified experimentally. The experiment results exhibit that the optimized spool can compensate about 71% for the steady-state flow force, then reduce about 15% the energy consumption of HSV. This research will provide the guide for the design and engineering application of HSV.