Second-order Response Surface Model Research Articles

Optimization of FDM 3D Printer Process Parameters to Minimize Dimensional Errors with PLA Material Using Response Surface Methodology

This paper presents a response surface methodology to fit a second-order response surface model aimed to finding process parameters to minimize length error (LE) and diameter error of the cylindrical shafts (DE) in fused deposition modeling (FDM) using polylactic acid (PLA) material. The process parameters in this study included layer height (LH), which varied from 0.1 to 0.4 mm, and print speed (PS), which ranged from 20 to 60 mm/s, while other parameters were set to constant values. The results showed that optimal process parameters obtained in this study significantly lower dimensional errors than the initial parameterization recommended by UltiMaker Cura software.

Optimization of enzymatic-assisted extraction of polyphenol from cashew nut testa by using cellulase and pectinase

A significant amount of cashew nut testa is removed during the processing of cashew kernels, resulting in many negative environmental impacts. The objective of this study was to valorize the cashew nut testa by enzymatic-assisted extraction of polyphenol using a mixture of cellulase and pectinase. A central composite design was employed to analyze the effects of extraction temperature from 41.6°C to 58.4°C, extraction pH from pH 3.2 to pH 4.8, and enzyme concentration from 0.03% to 0.37% (v/w) on extraction efficiency. A second-order response surface model was constructed to elucidate the effects of these independent variables on the response values of total phenolic content (TPC) and free radical scavenging activities [2,2-diphenyl-1-picrylhydrazyl (DPPH) and 2,2'-azinobis-3- ethylbenzothiazoline-6-sulfonic acid (ABTS) assays]. Regression analysis results showed that 91%, 88%, and 92% variations of the response variables of TPC, DPPH and ABTS scavenging activities can be explained by the models, respectively. Under optimal conditions, the predicted value for TPC was 164.26 (mg GAE/g DW), and the free radical scavenging activities according to DPPH and ABTS assays were 936.52 (µmol TE/g DW) and 1591.47 (µmol TE/g DW), respectively. The experimental results were consistent with the predicted values, demonstrating the suitability of the quadratic model and the success of the response surface method for optimizing the polyphenol extraction from cashew nut testa by using the enzyme mixture.

Comparison of the Three Types of Central Composite Designs Over Subsets of Reduced Models by Design Optimality Criteria

The purpose of this article is to compare the 3 important types of central composite designs (CCDs) consisting of central composite circumscribed design (CCCD), central composite inscribed design (CCID), and central composite face-centroid design (CCFD) in response surface methodology (RSM). The difference among these designs is the distance from the center design to the axial points. The comparison was performed across the full second-order response surface model and across a set of reduced models for 3, 4, and 5 design factors ( 3, 4, and 5) including 1, 3, and 5 center runs ( 1, 3, and 5). This study used D-, A-, and G- optimality criteria to evaluate the performance of CCDs by presenting the design optimality criteria comparison ranking throughout the reduced-model subsets of 43, 224, and 839 models for 3, 4, and 5 design variables, respectively. The results showed that CCCD was superior to CCID and CCFD according to A- and D- optimality criteria, while CCCD and CCID performed better than CCFD based on G- optimality criterion over a set of reduced models for 3, 4, and 5 design factors. It was observed that D-, A-, and G- optimality efficiencies were robust to changes in the linear and cross-product terms and sensitive to deviation in the square terms. The study will provide recommendations to assist the experimenters in the choice of the best design among the candidate designs for practice applications when some model effects may be insignificant. HIGHLIGHTS Comparison of 3 classifications of CCD. Assessment by using D-, A-, and G- optimality criteria over the reduced-model subsets for the full second-order response surface model. Generated the reduced models by using weak heredity. CCCD was superior to CCID and CCFD according to A- and D- optimality criteria, while CCCD and CCID performed better than CCFD based on G- optimality criterion over a set of reduced models for 3, 4, and 5 design factors. GRAPHICAL ABSTRACT

Laser-induced oxidation of Cf/SiC composites: Oxidation behavior analysis and parameter optimization

Cf/SiC composite is widely utilized in aerospace and defense sectors owing to their outstanding high-temperature and mechanical performance. However, this material is a typical hard-to-machining material. Building upon prior research on the novel laser-induced oxidation-assisted milling technology, this paper conducted an in-depth study of the oxidation of Cf/SiC composite under laser induction. The study combined thermodynamic analysis with the detection of oxidation products to ascertain the oxidation reaction types of Cf/SiC composite. The oxidation process under the induction of lasers with different energy densities was investigated by combining the oxide layer morphology, element distribution, and high-speed photography results. And the oxidation mechanism was elucidated. A second-order response surface model for the oxide layer thickness with respect to the laser energy density, scanning speed, and scanning path spacing was established, and parameter optimization was performed based on this model. Experimental validation demonstrated the reliability of the model predictions.

Optimization and experiment research of the cylinder block of the roller piston pump

The roller piston pump is a new type of axial piston pump. The pump has the advantages of high limiting speed, low noise, and vibration compared to the traditional axial piston pump. However, the structure and flow channel of the cylinder block of the roller piston pump are more complicated. When the cylinder block is subjected to high hydraulic pressure, its radial compressive deformation is large, which will lead to wear of the cylinder block and distribution shaft. For this problem, the paper will optimize the structural parameters of the cylinder block. Eight key parameters of the cylinder block are selected as the design variables, and the maximum radial deformation and mass of the cylinder block are taken as the optimization objectives. The central composite design method is used to generate 81 sets of sample data, and the second-order response surface model is obtained by regression analysis. The optimal structural parameters of the cylinder block are obtained through multi-objective optimization, and the material of the cylinder block is optimized. Finally, an experiment bench was built for experimental validation, and the efficiency of the pump was further investigated. The optimization results show that the maximum compression deformation of the inner diameter surface of the cylinder block decreases from 15.865 to 4.903 µm, and the mass of the cylinder block increases from 434.951 to 489.892 g. The experimental results show that the load-bearing pressure of the optimized roller piston pump increases from less than 15 to 35 MPa, and compared with the traditional axial piston pump, there is an increase in both mechanical efficiency and volumetric efficiency.

Effect of nanosized titanium dioxide and zinc oxide as antimicrobial agents on early compressive strength of high-performance concrete

Incorporation of antimicrobial agents in concrete can enhance the resistance of the concrete to biodeterioration. However, there is lack of adequate knowledge on the effect of antimicrobial agents on performance measures of high-performance concrete (HPC), particularly during early strength development, when the hydration reaction is ongoing, is not well understood. Therefore, the effect of antimicrobial agents on early compressive strength (CS) of HPC was investigated. The cement in HPC samples was partially replaced with nanosized titanium dioxide (TiO2) and zinc oxide (ZnO) by up to 2% by weight of the cement. Using response surface methodology, 21 combinations of TiO2 and ZnO contents were generated. The combinations were adopted for preparation of the samples. Individual and combined effects of TiO2 and ZnO on 7-day CS of the samples were evaluated. The standard form of the second-order response surface model is adopted to develop a model to fit the strength data. Statistics of the data verify that the model can be employed to predict the 7-day CS of HPC that employs nanosized TiO2 and ZnO as antimicrobial agents.

48 Evaluation of Branched-Chain Amino Acid Interactions in 13 to 23 kg Nursery Pigs Using a Central Composite Design

Abstract Two groups of 240 pigs (PIC 337 X 1050, PIC Genus, Hendersonville, TN) with initial body weight (BW) 13.20 ± 3.05 kg were used to investigate interactions between the branched-chain amino acids (BCAA). At weaning, pigs were placed into 40 pens with three barrows and three gilts per pen and fed a common diet for 3 weeks. On day 21 post-weaning, pens were randomly assigned to 1 of 15 dietary treatments arranged in a rotatable central composite design. Experimental diets were formulated to various levels of standardized ileal digestible (SID) leucine, isoleucine, and valine by replacing corn starch and glycine with L-leucine, L-isoleucine, and L-valine in the base diet. Levels of BCAA were expressed as ratios to SID lysine and ranged from 98 to 180 for Leu, 46 to 64 for Ile, and 51 to 78 for Val. Diets were formulated to be sub-limiting in lysine at 1.19% SID Lys and exceed all other essential amino acid requirements. Additionally, diets were formulated to be isocaloric and isonitrogenous and met or exceeded NRC (2012) vitamin and mineral requirements. Pen weights and feed intake were measured for the 21-day experiment to calculate daily gain (ADG), average daily feed intake (ADFI), and feed efficiency (G:F). Data were fit as a second-order response surface model according to the central composite design in R version 4.2.1 (R Core Team, 2022). The model included linear and quadratic effects of Leu, Ile, and Val, and their cross-products. Pen was the experimental unit, and variables were considered significant at P ≤ 0.10. Valine linearly and quadratically impacted ADG and G:F, regardless of Leu and Ile levels. There was an interaction between Leu and Ile for ADG (P = 0.079) and G:F (P = 0.031), where, at increasing levels of Leu, decreasing Ile improved ADG and G:F. Conversely, ADG and G:F decreased as both Leu and Ile increased. Isoleucine did not impact ADFI (P ≥ 0.458); however, there was an interaction between Leu and Val (P = 0.088), where Leu negatively impacted ADFI at low levels of Val, but did not influence ADFI at greater levels of Val. In conclusion, the response of nursery pig ADG and G:F to Val is independent of Leu and Ile levels, while ADG and G:F are reduced at greater levels of Leu and Ile, which is resolved as either Leu or Ile are reduced. Furthermore, at deficient levels of Val, ADFI is negatively impacted by increased Leu; however, the negative impacts of increasing Leu on ADFI are negated when Val is adequate or above requirement. This experiment emphasizes the complexity of amino acid metabolism in nursery pigs and the importance of understanding potential interactions among amino acids when conducting research.

Box–Behnken design to determine optimal fermentation conditions for apple-fortified mulberry wine using Saccharomyces bayanus

Wine is a fermented product of fruit juice. Mulberry and apple juice can also be used to produce wine. Several factors influence the alcoholic fermentation of the must; therefore, the optimization of the mulberry wine fermentation conditions with the dry yeast strain Saccharomyces bayanus (concentration varied from 0.15 to 0.25 g/L), fermentation conditions as pH value (from 3.5 to 4.5), and total soluble solid (TSS) content (24–28°Brix) were performed in this study. To evaluate the influence of these factors, a Box–Behnken design was used to minimize the number of factor combinations required, which allows the determination of optimal fermentation conditions (pH, TSS content, and dry yeast concentration) to produce wines with high alcohol and bioactive compounds (total anthocyanin (TAC) and polyphenol content (TPC)). Based on the analysis of experimental data, the second-order response surface models were developed to describe the relationship between initial pH value, TSS, and dry yeast concentration on wine quality acquisition (ethanol content and bioactive compounds). The results of the analysis of variance (ANOVA) showed that the model setup by response surface quadratic regression was suitable for predicting the wine quality. It was observed that the quality of the apple-fortified mulberry wine was significantly affected by all variables. The optimal contents of ethanol, total anthocyanin, and total polyphenol were achieved at 12.97% (v/v), 171.85 mg/L, and 87.17 mgGAE/L, respectively, when fermented in juice medium with optimal values of pH, TSS, and yeast concentration of 3.9, 26°Brix, and 0.22 g/L, respectively.

Heat Transfer Analysis and Structural Optimization for Spiral Channel Regenerative Cooling Thrust Chamber

There is currently a lack of efficient heat transfer analysis methodologies for spiral channel regenerative cooling that has been increasingly applied in liquid rocket engines. To figure out the heat transfer characteristics of the spiral channel regenerative cooling thrust chamber, a simple 1D method based on the traditional semi-empirical formula after correcting the flow velocity is proposed. The accuracy of this approach is verified by the 3D numerical simulation. The verified method is further used to analyze the distribution of inner wall temperature in the test case and optimize the channel’s parameters. The research shows that the maximum inner wall temperature cooled by the spiral channel is 8.5% lower than that of the straight channel under the same channel size and boundary condition, indicating that the application of the spiral channel significantly improves the cooling effect. In addition, the 1D model combined with the second-order response surface model is employed to optimize the channel width, channel height, pitch, and inner wall thickness aiming for the best cooling effect. The calculated maximum temperature of the inner wall after the structure optimization is 586.6 K, which is 29.8% lower than the initial structure before optimization.

Optimization Method Based on Hybrid Surrogate Model for Pulse-Jet Cleaning Performance of Bag Filter

The pulse-jet cleaning process is a critical part of the bag filter workflow. The dust-cleaning effect has a significant impact on the operating stability of bag filters. Aiming at the multi-parameter optimization problem involved in the pulse-jet cleaning process of bag filters, the construction method of hybrid surrogate models based on second-order polynomial response surface models (PRSMs), radial basis functions (RBFs), and Kriging sub-surrogate models is investigated. With four sub-surrogate model hybrid modes, the corresponding hybrid surrogate models, namely PR-HSM, PK-HSM, RK-HSM, and PRK-HSM, are constructed for the multi-parameter optimization involved in the pulse-jet cleaning process of bag filters, and their objective function is the average pressure on the inner side wall of the filter bag at 1 m from the bag bottom. The genetic algorithm is applied to search for the optimal parameter combination of the pulse-jet cleaning process. The results of simulation experiments and optimization calculations show that compared with the sub-surrogate model PRSM, the evaluation indices RMSE, R2, and RAAE of the hybrid surrogate model RK-HSM are 9.91%, 4.41%, and 15.60% better, respectively, which greatly enhances the reliability and practicability of the hybrid surrogate model. After using the RK-HSM, the optimized average pressure F on the inner side wall of the filter bag at 1 m from the bag bottom is −1205.1605 Pa, which is 1321.4543 Pa higher than the average pressure value under the initial parameter condition set by experience, and 58.4012 Pa to 515.2836 Pa higher than using the three sub-surrogate models, verifying its usefulness.

Normative database of response surface method for human trunk extension in isometric mode.

Recent studies show that asymmetric movements are important Low Back Disorders risk factors. Measuring the trunk strength and identifying the coupling effects in different postures can provide an objective tool to assess one's task capacity. This paper estimates the maximum performance capacity for isometric trunk extension and accompanying torques. Thirty males performed maximum voluntary isometric extension in 33 trunk postures on Sharif Lumbar Isometric Strength Tester device. Corresponding moments and angular positions were collected. Second-order full response surface models (RSM) were exploited to formulate the relationship between strengths and three trunk angles. The results of correlation coefficient, percent of standard estimation error and lack of fit reflected the adequacy of models. In conclusion, the main torque was the extension, but at the same time lateral bending and rotation torques were observed. For predicting these three torques in a specific posture and injury prevention, the second order RSM is a useful tool. The presented models can be used in the fields of ergonomics, occupational biomechanics and sport.

Numerical Study on the Heating Effect of a Spring-Loaded Actuator—Part II: Optimization Design of Heater Parameters

Unfavorable temperatures and humidity will cause the failure of spring actuators. In order to ensure the safe operation of the actuator, it is necessary to optimize the design of the built-in heater system of the actuator itself. In this study, an experimental design and a response surface model were used to fit the empirical formulas for the minimum temperature, maximum humidity, and maximum temperature on the heater surface. On this basis, a genetic algorithm was used to establish the optimal size of the heater in the chamber of the spring actuator. The study results show that the air inside the actuator shows a trend of a decrease in temperature and an increase in relative humidity from top to bottom. The empirical equation obtained by fitting the second-order response surface model has high accuracy, and the maximum prediction errors for the minimum temperature, maximum relative humidity, and maximum temperature of the heater surface of the spring actuator are −0.5%, 11.7%, and 4.7%, respectively. When the environmental temperature reduces from 313 K to 233 K, the optimal heating power of the heater increases from 10 W to 490 W, the optimal relative length increases from 3.57 to 6, and the optimal relative width increases from 1 to 5.3. Therefore, the study can act as a reference for the temperature and humidity control system of future actuators.

Optimization and Prediction of Process Parameters during Abrasive Water Jet Machining of Hybrid Rice Straw and Furcraea foetida Fiber Reinforced Polymer Composite

In the last few decades, natural composite materials have been considered one of the highly sustainable ecological alternatives for reducing the consumption of synthetic materials. Today, research on natural fiber composites is the main thrust for their use in various industrial applications. Further, continuous research works are being carried out to utilize natural composites as an alternative to synthetic materials. However, the inhomogeneity of composites, delamination, fiber pullout, higher surface roughness (SR) and dimensional inaccuracy under traditional machining have led the attention towards non-traditional machining, such as abrasive water jet machining, to achieve high-quality components. Hence, in this study, an experimental analysis based on the design of experiments is conducted on the machinability of a hybrid rice straw/Furcraea foetida composite under abrasive water jet machining (AWJM). Further, the concentration of the rice straw and the AWJ process parameters are varied, and their effects on the quality of machining is evaluated. The experimental trials are designed based on the Taguchi L27 orthogonal array, followed by an analysis of variance (ANOVA). From extensive experimentations, the concentration of rice straw is observed to be the most contributing (93.5%) factor to the SR. The traverse speed (TS) shows the highest percentage contributions of 93.13%, 55.50 and 55.70% to the material removal rate (MRR) and the top (TKW) and bottom kerf widths (BKW), respectively. However, the interaction between the fiber concentration and traverse speed gives the maximum contribution (35.04%) to the kerf taper (KT). A second-order response surface model is generated to study the effects of the process parameters on the SR, MRR, TKW, BKW and KT in any experimental domain. Finally, the microstructural characteristics of the machined surfaces, such as micro-cracks, debonding, and fiber pullout, are discussed.

Optimization Design and Fatigue Lifetime Analysis for Elastic Wheel of Low-floor Trams Using in Urban Rail Transit

Elastic wheel is an important component of the low floor tram using in urban rail transit, so it is of significance to optimize its structure and predict its service lifetime. Firstly, the fatigue characteristics of rubber material are studied based on the crack energy theory, and a finite element model of an elastic wheel for fatigue lifetime prediction is constructed. The numerical simulation results show that the fatigue lifetime of such a elastic wheel does not match with the expected one. Secondly, based on the orthogonal numerical test and the Sobol model, an improved sensitivity analysis method is proposed. Taking the minimum strain as an optimization objective, and selecting the structural parameters determined by the sensitivity analysis method as the design variables, the second-order response surface model is established, and the multi-island genetic algorithm is used to carry out the single objective and multi-factor optimization design of the rubber bodies of elastic wheel under the condition of stiffness constraint. The simulation results of the elastic wheel show that the fatigue lifetime of the optimized structure is 30% higher than that of the original one. Finally, the optimized elastic wheel is tested, and the results show that the stiffness coefficient, and the fatigue lifetime as well, are all satisfy with the design requirements.

Lightweight Optimization Design and Fatigue Lifetime Analysis for Anti-rolling Torsion Bar of Rail Vehicle

Based on the fatigue strength assessment method in the FKM standard, the lightweight design of a type of anti-rolling torsion bar is studied by using the finite element method. Firstly, the finite element model of the torsion bar structure is constructed by using the Creo software and the HyperMesh software, and then the finite element analysis is carried out by using the ABAQUS software. The numerical simulation results indicate that under the condition of ultimate load 29.2kN, the static strength, anti-rolling stiffness and fatigue strength of the torsion bar are all satisfy with the design requirements. Secondly, the orthogonal numerical test method is utilized to investigate the influence of geometric parameters on the anti-rolling stiffness and Factor of Strength (FOS) value of the torsion bar. Taking the structural geometric parameters as variables and the FOS value as the objective function, a second-order response surface model is established. The single objective and multi-factor optimization design for the torsion bar under the condition of stiffness constraint is conducted by using the Isight software and multi-island genetic algorithm. The results show that, comparing with the original structure, the weight of the optimized structure is reduced by 20.89%, and the static and dynamic strength, and anti-rolling stiffness of the optimized structure are match with the design requirements. Finally, the static and dynamic strength tests for the optimized torsion bar are individually operated at the ultimate load and under two-stage cyclic loading with amplitude 18.0kN and 29.2kN. the results show that the calculated stiffness coefficient is consistent with the test one, and the service lifetime of the torsion bar is satisfy with the design requirement.

Optimization and Prediction of Thermal Conductivity and Electrical Conductivity of Vacuum Sintered Ti-6Al-4V-SiC(15 Wt.%) Using Soft Computing Techniques

Titanium silicon carbide (Ti3SiC2) is a novel composite material that has found a multitude of uses in the aerodynamics, automobile, and marine industries due to its excellent properties such as high strength and modulus, high thermal and electrical conductivity, high melting point, excellent corrosion resistance, and high-temperature oxidation resistance. These properties are strongly associated with physical properties and microstructural features. Due to difficulties in the synthesis of this material, there have been very few investigations on the relationship between microstructure and physical characteristics of titanium silicon carbide composites processed through powder metallurgical process. However, the importance of thermal conductivity and electrical conductivity of titanium silicon carbide composites in various potential applications has led to keen attention from several researchers. Hence, in this paper, optimization, and prediction of process input parameters during processing under vacuum sintering for achieving maximum electrical and thermal conductivity of Ti-6Al-4V-SiC(15 Wt.%) has been presented. Using Taguchi’s L9 Orthogonal Array, it has been observed that aging temperature (1150 °C), aging time (four hours), heating rate (25 °C/min), and cooling rate (5 °C/min) result in optimum input parameters for achieving the highest electrical conductivity values during the processing of Ti-6Al-4V-SiCp composites. Further, for maximum thermal conductivity values during the processing of Ti-6Al-4V-SiCp composites, aging temperature (1150 °C), aging time (four hours), heating rate (5 °C/min), and cooling rate (5 °C/min) are preferred. A second-order response surface model generated can be effectively used for predicting the electrical conductivity and thermal conductivity during the processing of Ti-6Al-4V-SiCp composites with an accuracy of 99.28% (electrical conductivity) and 99.14% (thermal conductivity). By comparing the experimental results along with the results of the mathematical model and the BPANN model results for nine trials, it was observed that the estimated value is accurate for all tests with an error of 0.39% (electrical conductivity) and 0.48% (thermal conductivity). Further, from X-ray diffraction studies and microstructural analysis, it has been observed that aging at 1150 °C for four hours resulted in the formation of a ternary carbide phase of titanium silicon carbide (Ti3SiC2), which resulted in maximum electrical conductivity (4,260,000 Ω−1 m−1) and thermal conductivity (36.42 W/m·K) of the Ti-6Al-4V-SiC (15 Wt.%) composite specimen.

System reliability-based design optimization of flexible pavements using adaptive meta-modelling techniques

Recognizing the need for sustainable and long-lasting structures, reliability-based designs have been gaining acceptance in the pavement engineering community. The Reliability Based Design Optimization (RBDO) is formulated to design cost-effective flexible pavements in the presence of uncertainties. Two meta-modelling approaches are considered in this study, the second-order adaptive Response Surface Model (RSM) and the adaptive Polynomial-Chaos based Kriging (PC-Kriging) meta-model. The study highlights the need for adaptive meta-modelling techniques in the reliability-based design of pavement structures, through the quantification of the epistemic uncertainty. For the numerical examples considered in this study, the model uncertainty was found to be around 1% for three-layer sections and below 2.5% for four-layer pavements. To address the correlation between the pavement failure modes, a System Reliability Based Design Optimization (SRBDO) approach is proposed in this paper. The SRBDO methodology is further adapted to design the optimum combination of pavement layer thicknesses and moduli, to meet the target levels of reliability, given the expected traffic demand and subgrade strength at a pavement site. Thus, the SRBDO formulation using adaptive meta-models, presented in this study, efficiently integrates the economic analysis of various pavement design alternatives with the Mechanistic-Empirical procedure in a system reliability framework.

Requirement of digestible calcium at different dietary concentrations of digestible phosphorus for broiler chickens 3. Broiler finishers (d 25 to 35 post-hatch)

An experiment was conducted to determine the digestible calcium (Ca) and digestible phosphorous (P) requirements of 25 to 35-day-old broiler chickens. Fifteen corn-soybean meal-based diets containing 2.0, 2.5, 3.0, 3.5, and 4.0 g/kg standardized ileal digestible (SID) Ca and 2.5, 3.5, and 4.5 g/kg SID P were fed to broilers from d 25 to 35 post-hatch. Each experimental diet was randomly allocated to 6 replicate cages (8 birds per cage). Body weight and feed intake were recorded, and the feed conversion ratio was calculated. On d 35, birds were euthanized to collect the ileal digesta, tibia, and carcass for the determination of ileal Ca, and P digestibility, concentrations of ash, Ca, and P in tibia and the retention of Ca and P in the carcass. Titanium dioxide (5.0 g/kg) was included in all diets as an indigestible indicator for the ileal digestibility measurement. Feed intake and total excreta output were measured during the last 4 d of the experimental period for the measurement of apparent 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 (RSM) were determined using General Linear Model procedure of SAS. The maximum response was not predicted for most of the parameters (including growth performance and tibia) as the Ca effect was linear which indicated that the highest level of Ca employed in the study may have not been high enough. The requirement of dietary SID Ca for maximization of these parameters, therefore, depends on the dietary SID P concentration when the dietary SID Ca is within 2.0 to 4.0 g/kg. However, based on the factorial analysis, the highest weight gain was observed at 3.5 g/kg SID P and 3.5 g/kg SID Ca concentrations. Tibia ash was higher in birds fed 4.5 g/kg SID P and was unaffected by dietary SID Ca concentrations. However, based on overall findings, a combination of 3.5 g/kg SID P and 3.0-3.5 g/kg SID Ca may be recommended for the optimum tibia ash. The recommended SID Ca requirements (at 3.5 g/kg SID P) for weight gain (3.5 g/kg or 6.4 g/kg total Ca) and tibia ash (3.0-3.5 g/kg or 5.5-6.4 g/kg total Ca) are lower than the current Ca recommendations (7.8 g/kg total Ca equivalent to 4.25 g/kg SID Ca; Ross, 2019) for broiler finishers, suggesting possible excess of Ca in diets formulated based on the current recommendation.

Response Surface Methodology (RSM) Approach for Optimization of Parameters for Synthesis of Organic Compounds and Evaluation of Biological Activity with Molecular Docking

The triazolidine derivatives were synthesized by green and sustainable chemistry approach. The response surface methodology (RSM) was applied to optimize the reaction parameters during the synthesis. Reaction parameter which affect the yield of product were studied, which includes the temperature and time of the reaction. Various statistical RSM with different central composite designs (CCD) such as circumscribed (CCC), face-centered (CCF) and inscribed (CCI) were used to find the maximum yield of the product (%) of reaction at the given parameters and selected, which gave the maximum possible yield. The relationship between reaction parameters (temperature and time) and the yield of product modeled using second-order response surface model. The optimum reaction parameters given by CCI were 80.8 ºC reaction temperature and 15.03 min reaction time with yield of product is up to 94.57%. The adequacy and reliability of the predicted model was checked by ANOVA, R-square and adjusted R-square and revealed the good agreement between predicted model and actual experimental data. The study described here can be efficiently applied for the optimization of parameters in the synthesis of any organic compound. The molecular docking was carried out by using AutoDock vina 1.2.0 on (CYP51) [PDBID: 1EA1] and (DprE1) [PDBID: 4FDO] for target anti-tuberculosis activity while (FabH) [PDBID: 1HNJ] for target antimicrobial activity. There was better interaction within receptor amino acids compound 3d and 3b with FabH and CYP51 enzyme, respectively for anti-tuberculosis activity and compound 3d with DprE1 enzyme for antimicrobial activity observed very good docking score among all compounds.

Augmenting definitive screening designs: Going outside the box

Definitive screening designs (DSDs) have grown rapidly in popularity since their introduction by Jones and Nachtsheim (2011). Their appeal is that the second-order response surface (RS) model can be estimated in any subset of three factors, without having to perform a follow-up experiment. However, their usefulness as a one-step RS modeling strategy depends heavily on the sparsity of second-order effects and the dominance of first-order terms over pure quadratic terms. To address these limitations, we show how viewing a projection of the design region as spherical and augmenting the DSD with axial points in factors found to involve second-order effects remedies the deficiencies of a stand-alone DSD. We show that augmentation with a second design consisting of axial points is often the D s -optimal augmentation, as well as minimizing the average prediction variance. Supplemented by this strategy, DSDs are highly effective initial screening designs that support estimation of the second-order RS model in three or four factors.