Second-order Response Surface Research Articles

Comprehensive Optimization of the Dispersion of Mixing Particles in an Inert-Particle Spouted-Bed Reactor (IPSBR) System

Effective gas dispersion and liquid mixing are significant parameters in the design of an inert-particle spouted-bed reactor (IPSBR) system. Solid particles can be used to ensure good mixing and an efficient rate of mass and heat transfer between the gas and liquid. In this study, computational fluid dynamics (CFD) coupled with the discrete phase model (DPM) were developed to investigate the effect of the feed gas velocity (0.5–1.5 m/s), orifice diameter (0.001–0.005 m), gas head (0.15–0.35 m), particle diameter (0.009–0.0225 m), and mixing-particle-to-reactor-volume fraction (2.0–10.0 vol.%) on the solid mass concentration, average solid velocity, and average solid volume fraction in the upper, middle, and conical regions of the reactor. Statistical analysis was performed using a second-order response surface methodology (RSM) with central composite design (CCD) to obtain the optimal operating conditions. Selected parameters were optimized to maximize the responses in the middle and upper regions, and minimize them in the conical region. Such conditions produced a high interfacial area and fewer dead zones owing to good particle dispersion. The optimal process variables were feed gas velocity of 1.5 m/s, orifice diameter of 0.001 m, gas head of 0.2025 m, a particle diameter of 0.01 m, and a particle load of 0.02 kg. The minimum average air velocity and maximum air volume fraction were observed under the same operating conditions. This confirmed the novelty of the reactor, which could work at a high feed gas velocity while maintaining a high residence time and gas volume fraction.

Prediction of Surface Roughness and Optimization of Process Parameters for Slow Tool Servo Turning

Surface roughness is an important index to evaluate the quality of a machined surface. In order to accurately predict the surface roughness for slow tool servo (STS) turning, taking toric surface as an example, response surface methodology (RSM) was used to perform the process test. The second-order response surface prediction model was established and the variance analysis and reliability test were carried out. The results showed that the average prediction error was 7.6%. In order to obtain the best process parameters, standard particle swarm optimization (PSO) was used. The results showed that the global optimization ability of standard PSO was poor. In order to solve the problem, compression factor was introduced and particle swarm optimization with compression factor (WCF-PSO) was constructed, which enhanced the convergence of PSO effectively. WCF-PSO was used to optimize the process parameters and the results obtained were Rt=0.87mm, af =0.01mm/r, ap=0.05mm, Δθ=8.70°, with a corresponding surface roughness of Ra=0.0486μm. The results of the verification test showed that the actual value was Ra=0.0520μm, and the error was only 7.0%, indi-cating that WCF-PSO had a better optimization effect.

Study the Surface and Chip Formation of Wood Materials by Milling Method

This paper discusses the experimental study and the mechanism of chip formation, sliding and cutting in processing wood milling surface. The main objective is to determine chip thickness upon the coefficient k and tool tip radius ρ. Technically, when analysing we use FCCCD's second-order response surfaces method and analysis of variance (ANOVA) for determining the coefficient k upon the factors of milling cutter diameter D, the feeding per tooth Sz and tool tip radius ρ. According to the obtained experimental results, we determined the value domain of the machine's working factors so that the cutter tool tip can slide or cut the chip on the milled surface of tropical wood materials. From the coefficient k, we can determine the slide length Lsl which gives reason for the abrasion phenomenon of the front or rear sides of the cutter. The results allow us to choose the geometrical parameters ​​for milling cutter, apart from the working parameters for processing the surface of wood materials with the highest quality as possible.

Optimized design of the power consumption test of mountain orchard transporters

In order to study the influence rule of various factors on the operation power consumption of the traction orchard transporter and realize the optimal design of the operation power consumption of the transporter, according to the traditional experience and the existing research foundation, the monorail transporter test bench was designed and built on the basis of the whole structure and operation characteristics of the transporter. Taking the motor frequency, track gradient and load as the investigation factors, and the driving shaft power, shaft power transmission and mechanical efficiency as the evaluation indices, the orthogonal test was conducted, and the range analysis of the influence effect was carried out according to the test results. The primary and secondary orders of the influence of various factors were obtained that motor frequency was greater than track gradient and track gradient was greater than load. According to the orthogonal test results, the second-order response surface method was used to establish the optimization model of the power consumption of the transporter, and the model was verified on the test bench. The results showed that the relative error between the model optimization value and the test value based on the response surface power optimization model was less than 10%, which indicated that the power optimization model had satisfactory performance. The research can provide a reference for the orchard conveyor to choose the parameter combination which can save power consumption and the motor that matches power consumption. Keywords: mountain orchard transporter, power consumption, orthogonal test, optimization model, analysis DOI: 10.25165/j.ijabe.20211405.6209 Citation: Li J X, Zhong M Y, Zhang Y L, Bao X L, Li S J, Liu M D, et al. Optimized design of the power consumption test of mountain orchard transporters. Int J Agric & Biol Eng, 2021; 14(5): 107–114.

Partially orthogonal blocked three-level response surface designs

When fitting second-order response surface models in a hypercuboidal region of experimentation, the variance matrices of D-optimal continuous designs have a particularly attractive structure, as do many regular unblocked exact designs. Methods for constructing blocked exact designs which preserve this structure and are orthogonal, or nearly orthogonal, are developed. Partially orthogonal designs are built using a small irregular fraction of a two- or three-level design and a regular fractional factorial design as building blocks. Results are derived which relate the properties of the blocked design to these components. Moreover, it is shown how the designs can be augmented to ensure that the model can be fitted and a method for constructing designs with small blocks is presented. Examples illustrate that partially orthogonal designs can compete with more traditional designs in terms of both efficiency and overall size of the experiment.

Requirement of digestible calcium at different dietary concentrations of digestible phosphorus for broiler chickens. 1. Broiler starters (d 1 to 10 post-hatch)

An experiment was conducted to determine the digestible calcium (Ca) and digestible phosphorous (P) requirements of 10-day-old broiler chickens. Fifteen corn-soybean meal-based diets containing 3.3, 3.9, 4.4, 5.0, and 5.5 g/kg standardized ileal digestible (SID) Ca and 4.0, 5.0, and 6.0 g/kg SID P was fed to broilers from d 1 to 10. Each experimental diet was randomly allocated to 6 replicate cages (12 birds per cage). Body weight and feed intake were recorded at the start and end of the experiment and the feed conversion ratio was calculated. On d 10, birds were euthanized to collect ileal digesta, toes and tibia for the determination of digestible Ca and P, toe ash concentration and the concentrations of ash, Ca, and P in tibia. Titanium dioxide (5 g/kg) was included in all diets as an indigestible indicator for apparent ileal digestibility measurements. Total excreta were collected from d 1 to 10 for the measurement of total tract retention of Ca and P. Fixed effects of the experiment were dietary concentrations of SID Ca and SID P and their interaction. If the interaction or main effects were significant (P < 0.05), the parameter estimates for second-order response surface model were determined using General Linear Model procedure of SAS software. The growth performance, bone mineralization and mineral utilization of broiler starters were found to be optimized at 5 g/kg SID P concentration. Required SID Ca for maximum weight gain and bone mineralization was determined to be 3.32 and 4.36 to 4.78 g/kg, respectively, at 5 g/kg SID P concentration, which correspond to SID Ca to SID P ratios of 0.66 and 0.87 to 0.96, respectively. The estimated SID Ca requirement for weight gain is lower than the current Ca recommendation (9.6 g/kg total Ca or 4.4 g/kg SID Ca) for broiler starters. However, bone mineralization is maximized around the current total Ca recommendation at 8.9 to 9.8 g/kg (4.36–4.78 g/kg SID Ca) and indicates that bone mineralization requires more Ca than growth performance.

A Novel Sustainable Biosorbent (Ulocladium Consortiale) Proposal with Central Composite Design to Reduce Water Pollution

Biosorption is an efficient and environmental-friendly technology for the decontamination of dyes from industrial wastewater. These properties bio absorbent usage instead of commercial chemicals supports not only the “economic” dimension, but also “environment” and “social” dimensions of sustainability. As a novel bioadsorbent, methylene blue-resistant fungal strain Ulocladium consortiale was isolated from the Lake Tuz (Turkey). The effect of four independent variables pH (7–11), initial dye concentration (10–50 mg/L), biomass dosage (0.1–0.5 g/mL), and contact time (2.5–12.5 min) was studied on methylene biosorption by employing U. consortiale using batch mode. Optimum conditions were selected for maximum biosorption. Central Composite Design (CCD) of Response Surface Methodology (RSM) an ideal solution for fitting a second-order response surface model was performed to determine the optimum levels of parameters and to spot the correlation between the various parameters. The highest removal efficiency (R, %) of methylene blue was achieved with 92.69 % and U. consortiale showed the highest biosorption capacity (q, mg/g) 181.28 mg/g. This efficiency was obtained at 10 pH, 46 mg/L initial dye concentration, 0.2 g/mL biomass dosage, and 2.5 min contact time. The results of CCD of RSM show that Ulocladium consortiale is a suitable and sustainable novel biosorbent can be used in for methylene blue removal under optimal conditions.

Design optimization of guide vane for mitigating elbow erosion using computational fluid dynamics and response surface methodology

A 90° elbow equipped with guide vanes was developed with the intent of reducing elbow erosion. Numerical models were formed to predict the maximum erosion rate of elbow and Face-1, and the response surface methodology was used to study the relationship between the erosion rate and structural parameters of guide vane. A second-order response surface model was established to determine the relationship between R1 and variables, and a reduced cubic (RC) polynomial model was obtained to reveal the relationship between R2 and the three factors. The numerical results show that the low-speed region is expended and the maximum discrete particle matter (DPM) concentration is reduced after installing the guide vane. This internal component provides a shelter for the elbow from the direct impact of high-speed solids.

Optimal Design of Flexspline in New Modular Robotic Joints Considering Position Keeping Conditions

In order to improve the service life of modular joints and meet the requirements of compact structure, considering the position keeping conditions of modular joints, a multi-objective optimization design method for the maximum stress and tube length of the new modular joint flexspline was proposed. This method established a finite element analysis model based on a new modular joint structure, conducted a thermo-mechanical coupling analysis on the joint under the holding state, and obtained the stress distribution of the flexible wheel. Plackett-Burman factorial design was used to screen the significant factors that affect the maximum stress. Based on the Box-Behnken test method and the least square method, the second-order response surface approximate model of the maximum stress of the flexspline was established. Taking the geometric structure parameters of the harmonic drive components as the design variables, and the maximum stress and tube length of the flexspline as the design goals, the response surface approximate model is optimized through the multi-objective genetic algorithm. The optimization calculation example of the new modular joint shows that the method can reduce the maximum stress of the flexspline while reducing the tube length, achieving the purpose of reducing the joint volume and increasing the service life.

D-Optimal Designs for Second-Order Response Surface Models with Qualitative Factors

Central composite design (CCD) is widely applied in many fields to construct a second-order response surface model with quantitative factors to help to increase the precision of the estimated model. When an experiment also includes qualitative factors, the effects between the quantitative and qualitative factors should be taken into consideration. In the present paper, D-optimal designs are investigated for models where the qualitative factors interact with, respectively, the linear effects, or the linear effects and 2-factor interactions or quadratic effects of the quantitative factors. It is shown that, at each qualitative level, the corresponding D-optimal design also consists of three portions as CCD, i.e. the cube design, the axial design and center points, but with different weights. An example about a chemical study is used to demonstrate how the D-optimal design obtained here may help to design an experiment with both quantitative and qualitative factors more efficiently.

D-Optimal Designs for Second-order Response Surface Models with Qualitative Factors

Central composite design (CCD) is widely applied in many fields to construct a second-order response surface model with quantitative factors to help to increase the precision of the estimated model. When an experiment also includes qualitative factors, the effects between the quantitative and qualitative factors should be taken into consideration. In the present paper, D-optimal designs are investigated for models where the qualitative factors interact with, respectively, the linear effects, or the linear effects and 2-factor interactions or quadratic effects of the quantitative factors. It is shown that, at each qualitative level, the corresponding D-optimal design also consists of three portions as CCD, i.e. the cube design, the axial design and center points, but with different weights. An example about a chemical study is used to demonstrate how the D-optimal design obtained here may help to design an experiment with both quantitative and qualitative factors more efficiently.

Statistical optimization of cellulases by Talaromyces thermophilus utilizing Saccharum spontaneum, a novel substrate

Abstract Background At present, cellulases are the most important enzymes worldwide, and their demand has been increasing in the industrial sector owing to their notable hydrolysis capability. Results In the present study, contrary to conventional techniques, three physical parameters were statistically optimized for the production of cellulase by thermophilic fungi by using response surface methodology (RSM). Among all the tested thermophilic strains, the best cellulase producing fungus was identified as Talaromyces thermophilus – both morphologically and molecularly through 5.8S/ITS rDNA sequencing. The central composite design (CCD) was used to evaluate the interactive effect of the significant factors. The CCD was applied by considering incubation period, pH, and temperature as the model factors for the present investigation. A second-order quadratic model and response surface method revealed that the independent variables including pH 6, temperature 50 °C, and incubation period 72 h significantly influenced the production of cellulases. The analysis of variance (ANOVA) indicated that the established model was significant (P ≤ 0.05) and showed the high adequacy of the model. The actual and predicted values of CMCase and FPase activity showed good agreement with each other and also confirmed the validity of the designed model. Conclusions We believe the present findings to be the first report on cellulase production by exploiting Kans grass (Saccharum spontaneum) as a substrate through response surface methodology by using thermophilic fungus, Talaromyces thermophilus. How to cite: Abdullah R, Tahseen M, Nisar K et al. Statistical optimization of cellulases by Talaromyces thermophilus utilizing Saccharum spontaneum, a novel substrate. Electron J Biotechnol 2021;51. https://doi.org/10.1016/j.ejbt.2021.03.007.

Multi-objective lightweight and crashworthiness collaborative optimisation of commercial vehicle cab

A collaborative optimisation method for the lightweight and crashworthiness of the cab structure is proposed using mixed variable screening, approximate models, multi-objective optimisation and ideal point methods. First, modal and stiffness analyses of the cab model are built. Three impact simulation model of cab are established and verified via ECE R29-02 regulation tests. Subsequently, front impact, front pillar impact, and roof strength model are established following ECE R29-03, which is more stringent than the ECE R29-02. However, the result of the front pillar impact of the cab does not meet the requirements of the ECE R29-03. Several improved A-pillar structures are proposed, among which reinforced rib structure can effectively enhance the occupant’s living space. Then, 18 thickness and 4 material variables are selected as design variables based on the mixed variable screening method. Different approximate models are established for performance responses. The results show that the second-order response surface model has high fitting accuracy in the cab modal and bending and torsional stiffness performance, while the Kriging model has high fitting accuracy in the crashworthiness indicators of the cab. Finally, the multi-objective lightweight and crashworthiness collaborative optimisation of the cab are conducted. Compared with the initial model, the crashworthiness of the optimal cab model is improved and the mass is reduced by 27.1 kg.

Modelling and optimization of process parameters for production of desiccated Chhana-murki (Indian cottage cheese-based dessert).

In the present study, process parameters were optimized for the production of desiccated chhana-murki (Indian cottage cheese-based dessert). Response Surface Methodology (RSM)was employed to explore the mutual effects of coagulation temperature (CT) of milk (70-90°C), % fat level in milk (3.5%-5.5%), and sugar-to-paneer cube (SP) ratio (0.6-0.9) on instrumental hardness (N), water activity (aw), yield (%), sensory sweetness and overall acceptability (on 100-point intensity scale) of chhana-murki. The resulted responses were evaluated by analysis of variance (ANOVA), and the second-order polynomial response surface equations were fitted using multiple regression analysis. Determination coefficients (R 2) were equal to 80% or higher for individual responses stated that the developed models were well fitted to the experimental results. The optimized product was prepared using CT 79.22°C, milk fat 4.8%, and SP ratio 0.7. Confirmatory experiment values for instrument hardness, water activity (aw), yield (%), sensory sweetness and overall acceptability were 105.05N, 0.85, 115.2%, 61.2 and 78.8, respectively.

Robust parametric optimization for investment casting process of a turbine vane

Investment casting technology is an important manufacturing technology for the turbine guide vanes of the aero-engine, which directly affects the performance of the engine. However, most of the researches on the investment casting process of the vane is mainly based on the development of the materials, while the process parameters are less researched. The purpose of this paper is to perform a robust optimization for the process parameters of the investment casting of a typical vane. Firstly, a three-dimensional casting simulation model is established based on the ProCAST® software. Five key process parameters are chosen and their uncertainties are specified. A set of desired parameters are firstly obtained by conducting a deterministic optimization using a design of experiment (DOE) method. Next, a second-order response surface model (RSM) is built with Box-Behnken design based on the initial optimization results. Finally, an RSM-based robust parametric optimization with AMGA algorithm is proposed, deriving several Pareto solutions. By comparing and analyzing every solution, an optimal parameter scheme is developed by considering high quality of the casting and robustness of the casting process.

Multi-fidelity response surfaces for uncertainty quantification in beams using coarse and fine finite element discretizations

This paper discusses a benchmark problem to understand the response surface based multi-fidelity model and uncertainty quantification in the context of beam vibrations. A multi-fidelity model for the beam is constructed by blending a low-fidelity finite element model (coarse discretization) and a high-fidelity finite element model (fine discretization). The natural frequencies of the beam are the desired responses. A second-order correction response surface constructed based on high and low-fidelity simulations, is used to correct the low-fidelity response surface model. It is shown that the multi-fidelity model is accurate and ranks much better than the high-fidelity model in terms of computational effort.

Research on tool wear factors for milling wood-plastic composites based on response surface methodology

A high-speed milling experiment on wood-plastic composites was performed using cemented carbide tools, and the resulting wear pattern was studied. The influence of the cutting parameters, the cutting speed, feed speed, and axial cutting depth on the tool wear was studied via response surface methodology, and the influence of the interaction of the cutting parameters on tool wear was analyzed. Three-dimensional surface graphs and contour plots of the tool wear results were established. According to the experimental results, a mathematical model of the tool wear based on the second-order response surface methodology was established, and the model was utilized to verify its feasibility. The results show that the nose width (NW) increases with the increase of the cutting speed and axial cutting depth and decreases with the increase of feed speed. Among the factors affecting tool wear, the cutting speed had the greatest influence, followed by the feed rate, with the axial cutting depth affecting tool wear the least. According to the results of the interaction between the tool wear and the cutting parameters, a low feed speed and small axial cutting depth can be selected to ensure long tool life; for low-speed cutting, a high feed speed and large axial cutting depth can be adopted to ensure tool life while improving machining efficiency.

Frequency Response Function-Based Finite Element Model Updating Using Extreme Learning Machine Model

A frequency response function- (FRF-) based surrogate model for finite element model updating (FEMU) is presented in this paper. Extreme learning machine (ELM) is introduced as the surrogate model of the finite element model (FEM) to construct the relationship between updating parameters and structural responses. To further improve the generalization ability, the input weights and biases of ELM are optimized by Lévy flight trajectory-based whale optimization algorithm (LWOA). Then, LWOA is also applied to obtain the best updating results, where the objective function is defined by the difference between analytical FRF data and experimental data. Finally, a plane truss is used to demonstrate the performance of the proposed method. The results show that, compared with second-order response surface (RS), radial basis function (RBF), traditional ELM, and other optimized ELM, a LWOA-ELM model has higher prediction accuracy. After updating, the FRF data and frequencies have a significant match to the experimental model. The proposed FEMU method is feasible.

Force Prediction and Cutting-Parameter Optimization in Micro-Milling Al7075-T6 Based on Response Surface Method.

Optimization of cutting parameters in micro-milling is an important measure to improve surface quality and machining efficiency of the workpiece. Investigation of micro-milling forces prediction plays a positive role in improving machining capacity. To predict micro-milling forces and optimize micro-milling cutting parameters (per-feed tooth (fz), axial cutting depth (ap), spindle speed (n) and tool extended length (l)), a rotatable center composite experiment of micro-milling straight micro-groove in the workpiece of Al7075-T6 were designed, based on second-order response surface methods. According to the experiment results, the least square method was used to estimate the regression coefficient corresponding to the cutting parameters. Simultaneously, the response prediction model of micro-milling was established and successfully coincide the predicted values with the experiment values. The significance of the regression equation was tested by analysis of variance, and the influence of micro-milling cutting parameters on force and top burrs morphology was studied. The experiment results show that in a specific range of cutting parameters, ap and fz have a significant linear relation with the micro-milling force and the top burrs width. According to the optimal response value, the optimized cutting parameters for micro-milling obtained as: n is 11,393 r/min, fz is 6 µm/z, ap is 11 μm and l is 20.8 mm. The research results provide a useful reference for the selection of cutting parameters for micro-milling.

Standardization of seed and peel infused Syzygium cumini -wine fermentation using response surface methodology

Jamun known for its nutraceutical and therapeutic properties. However, due to its perishable nature with a short shelf life of 1–2 days, an efficient fermentative processing technology to produce local Jamun-wine is imminent. In the present study, a five-level three-factor Central Composite Rotatable design was used to optimize TSS, inoculum size and DAHP supplementation for total sugars, reducing sugars and ethanol response while seed powder and pulp powder concentrations were optimized for polyphenols and tannins response for the development of Jamun wine using Response surface methodology. A second-order polynomial response surface equation was generated which showed that the experimental variables significantly affected the ethanol production. The optimized fermentative parameters [Total soluble solids (TSS) 18°B, inoculum 5% (v/v) and Diammonium hydrogen orthophosphate (DAHP)100mg/100 ml] with and without supplements (seed powder and pulp powder @ 286.4 and 300mg/100 ml, respectively) were then validated to prepare Jamun-wine at 7L scale resulting in 9.93 and 10.14% (v/v) ethanol production, respectively that were stored for 90 days to determine the effect on sensory attributes. The sensory evaluation of these wines showed that both the wines were rated as “very liked”. The qualitative GCMS analysis revealed presence of seed and bark based volatiles in the jamun wine.