Factorial Experimental Design to Study the Effects of Layers and Fiber Content on Concrete Flexural Behavior

Experimentation has come a long in helping researchers achieve breakthroughs in their different scientific areas and engineering happens to be one of those areas with the most impact from experimental advancement. The need for valid experimental results free from biases and confounding conclusions has prompted the development of new experimental techniques that takes consideration of all applicable factor and combinations in providing answers on a research topic, and the Factorial Experimental design credited to Sir Ronald Fisher is one technique yielding highly valid results. This paper uses the factorial design of experiments to research the flexural impact of polyvinyl acetate fiber and layered concrete in construction. The experiment considered two levels of fiber contents and two levels of layers, and prepared samples with all combinations of the variable factors. The samples were tested after 7 days from casting for flexural strength and an advance statistical analysis was performed on the flexural responses of the samples using R-program. The results from the analyses revealed the significance of the variables to the flexural strength of the samples, as well as their interactions. The experiment concluded that based on the number of layers and fiber content used for the experiment, casting concrete in layers does have a significant negative effect on the flexural strength of concrete, and the failure pattern of concrete members under flexural load in evidently influenced by the material composition of the concrete, and that it can be evidently influenced by casting the concrete in layers.

Preliminary Study on the Low Energy Ion Beam Mediated Parameters with Fractional Factorial Design Method

[Objective] The aim was to explore the biological effect of low energy ion beam mediated parameters with fractional factorial design method. [Method] The twin-embryos seed of autotetraploid rice DER10-04-01 was taken as the receptor material,and the Elymus dahuricus Turcz. was used as materials to provide DNA to carry out the ion beam mediated experiment. And the fractional factorial design method was used to study the parameters of low enery N＋ ion beam mediated foreign genes into rice. [Result] The implantation energy,dose,DNA concentrations and immersion time of DNA showed significant biological effects on the normal growth and development of DER10-04-01,in which the biological effects of implantation dose and DNA concentrations were relatively obvious. [Conclusion] The implantation energy,dose,DNA concentrations and immersion time of DNA were major factors showing important effects on the experimental result in ion beam mediated foreign genetic materials.

Removal of Copper Ions from Acid Mine Drainage Wastewater Using Ion Exchange Technique: Factorial Design Analysis

A factorial experimental design method was used to examine the “Cu2+” removal from acid mine drainage wastewater by ion exchange technique. Ion Exchange technique is preferred because of reduced sludge generation compared to conventional treatment techniques and better decontamination efficiency from highly diluted solutions. Factorial design of experiments is employed to study the effect of four factors pH (3, 5, and 6), flow rate (5, 10, 15 L/hr), resin bed height (20, 40 and 60 cm) and initial concentration of the metal (100, 150 and 200 mgl-1) at three levels. The efficiency of metal removal was determined after 100 min of treatment. Main effects and interaction effects of the four factors were analyzed using statistical techniques. A regression model was recommended and it was found to fit the experimental data very well. The results were analyzed statistically using the Student’s t-test, analysis of variance, F-test and lack of fit to define most important process variables affecting the percentage “Cu2+” removal. In this study , pH was thus found to be the most important variable.

Lightweight design of 45000r/min spindle using full factorial design and extreme vertices design methods

Factors for determining the spindle size are the shaft diameter, positions of bearing and motor, and entire length of the spindle. Then, it is important to find the assembling of the optimal design variables, which satisfy the stiffimss and rotational speed required to the spindle. A general full factorial design method was used to verify some factors that affect the natural frequency of a spindle. It is verified that the shorter shaft length and bearing span length represent the higher natural frequency, and there are some effects according to the change in the levels of factors. The detailed spindle dimension is determined by applying an EVD method, which can define the optimal bearing position through considering the limiting condition. Based on the estimated regression model, the optimal spindle size and bearing distance that can improve the primary natural frequency are obtained, and the influence of design factors on the natural frequency is also analyzed.

Parameters studies for rail wear in high-speed railway turnouts by unreplicated saturated factorial design

Rail wear is one of the main reasons for reducing the service life of high-speed railway turnouts in China. The rail wear characteristics of high-speed railway turnouts are influenced by a large number of input parameters of the complex train-turnout system. To reproduce the actual operation conditions of railway turnouts, random distributions of these inputs need to be considered in rail wear simulation. For a given nominal layout of the high-speed railway turnout, 19 input parameters for rail wear simulation in high-speed railway turnouts are investigated based on orthogonal design of experiment. Three dynamic responses(wheel-rail friction work, normal contact force and size of contact patch) are defined as observed values and the significant factors(direction of passage, axle load, running speed, friction coefficient, and wheel and rail profiles) are determined by two unreplicated saturated factorial design methods, including the half-normal probability plot method and Dong 93 method. As part of the associated rail wear simulation, the influence of the wear models and the local elastic deformation on the rail wear was separately investigated. The calculation results for the wear models are quite different, especially for large creep mode. The local elastic deformation has a large effect on the sliding speed and rail wear and needs to be considered in the rail wear simulation.

Optimization of hydrothermal synthesis of H-ZSM-5 zeolite for dehydration of methanol to dimethyl ether using full factorial design

H-ZSM-5 zeolite was synthesized by hydrothermal method. The effects of different synthesis parameters, such as hydrothermal crystallization temperature （170-190 ℃） and Si/A1 molar ratio （100-150）, on the catalytic performance of the dehydration of methanol to dimethyl ether （DME） over the synthesized H-ZSM-5 zeolite were studied. The catalysts were characterized by N2 adsorption-desorption, XRD, NH3-TPD, TGA/DTA, and SEM techniques. The full factorial design of experiments was applied to the synthesis of H-ZSM-5 zeolite and the effects of synthesis conditions and their interaction on the yield of DME as the response variable were determined. Analysis of variance showed that two variables and their interaction significantly affected the response. According to the experimental results, the optimized catalyst prepared at 170℃ with the Si/A1 molar ratio of 100 showed the best catalytic performance among the tested H-ZSM-5 zeolite.

Evaluation of significant manufacturing parameters in lost foam casting of thin-wall Al-Si-Cu alloy using full factorial design of experiment

Controlling process parameters of lost foam casting （LFC） enables this process to produce defect-free complex shape castings. An experimental investigation on lost foam casting of an A1-Si-Cu cast alloy was carried out. The effects of pouting temperature, slurry viscosity, vibration time and sand size on surface finish, shrinkage porosity and eutectic silicon spacing of thin-wall casting were investigated. A full two-level factorial design of experimental technique was used to identify the significant manufacturing factors affecting the properties of casting. Pouring temperature was found as the most significant factor affecting A1-Si-Cu lost foam casting quality. It was shown that flask vibration time interacted with pouring temperature influenced euteetic silicon spacing and porosity percentage significantly. The results also revealed that the surface quality of the samples cast in fine sand moulds at higher pouring temperatures was almost unchanged, while those cast in coarse sand moulds possessed lower surface qualities. Furthermore, variation in slurry viscosity showed no significant effect on the evaluated properties compared to other parameters.

Methodology of factorial design deriving guidelines for simulation of growth curve and production of sugars by Spirulina (Arthrospira) maxima

It is practical, economic and sometimes essential to derive rules or conclusions by performing lesser runs of experiments. In this part, a methodology based on 2 f factorial design was brought up to derive guidelines to simulate growth curve and production of sugars by Spirulina (Arthrospira) maxima . The growth curve or accumulation process of sugars was idealized by sets of straight lines limited by phase transfers of growth or accumulation of sugars. Normal analyses of the critical values of the transfers were used to derive their linear relationships with the initial conditions of the experimental factors. These linear functions were called guidelines and were used to simulate the growth curve or accumulation of sugars. Generalization of the guideline technique was determined by the kinetic limitation of nutrient nitrogen or sulfur that was dependent upon their stoichiometric deficiency directly derived from their initial values in the medium. This method uses the initial conditions of culture and does not need measurements of concentrations of nitrate, sulfate and pigments during cultivation. It is a practical and useful alternative way to trace and predict approximately the growth curve and production of sugars by S. maxima .

Artificial Neural Network and Full Factorial Design Assisted AT-MRAM on Fe Oxides, Organic Materials, and Fe/Mn Oxides in Surficial Sediments

Artificial neural network（ANN） and full factorial design assisted atrazine（AT） multiple regression adsorption model（AT-MRAM） were developed to analyze the adsorption capability of the main components in the surficial sediments（SSs）. Artificial neural network was used to build a model（the determination coefficient square r2 is 0.9977） to describe the process of atrazine adsorption onto SSs, and then to predict responses of the full factorial design. Based on the results of the full factorial design, the interactions of the main components in SSs on AT adsorption were investigated through the analysis of variance（ANOVA）, F-test and t-test. The adsorption capability of the main components in SSs for AT was calculated via a multiple regression adsorption model（MRAM）. The results show that the greatest contribution to the adsorption of AT on a molar basis was attributed to Fe/Mn（–1.993 μmol/mol）. Organic materials（OMs） and Fe oxides in SSs are the important adsorption sites for AT, and the adsorption capabilities are 1.944 and 0.418 μmol/mol, respectively. The interaction among the non-residual components（Fe, Mn oxides and OMs） in SSs interferes in the adsorption of AT that shouldn’t be neglected, revealing the significant contribution of the interaction among non-residual components to controlling the behavior of AT in aquatic environments.

Systematic Analysis of Carbon Dioxide Activation of Waste Tire by Factorial Design

In this study, waste tire was used as raw material for the production of activated carbons through pyrolysis. ＇Fire char was first produced by carbomzation at 550℃ under nitrogen. A two tactortal design was used to optimize the production of activated carbon from tire char. The effects of several factors controlling the activation process, such as temperature （.830-930℃）, time （2-6h） and percentage ot carbon dioxide （70%-100%） were investigated. The production was described mathematically as a function of these three factors. First order modeling equations were developed for surface area, yield and mesopore volume. It was concluded that the yield, BET surface area and mesopore volume of activated carbon were most sensitive to activation temperature and time while percentage of carbon dioxide in the activation gas was a less significant factor.

Optimization of Biosurfactant Production from Glycerol by Pseudomonas Aeruginosa EQ 109 Using Factorial Design 2^3

One possible application for the excess of glycerol, which is an exceeding byproduct in biodiesel industry, was used as carbon and energy sources for bioproducts synthesis. This work aims to evaluate biosurfactant production from glycerol by Pseudomonas aeruginosa EQ 109 isolated from crude oil-contaminated soil. Factorial design 2^3 was utilized to optimize the amount of biosurfactant produced, by using pH （A）, initial biomass concentration （B）, and initial glycerol concentration （C） as independent factors. The experiments were carried out in flasks containing 100 mL of mineral medium. Biosurfactant production was monitored by increase of the emulsification of aviation kerosene （E24） and surface tension reduction （STr）. The results have shown that, at pH = 7.0, in order to increase E24, variables as B and C are the most influential, leading to a maximum value of E24 = 79%, as well as for an increase of GC （GCmax = 49%）. STR was the variable with the best correlation factor for the proposed linear model （R2=0.96） and its maximum value was 48%. Xfwas not significant to the model, although it was influenced by pH and C, with C = 40g/L （Xfmax = 4.56 g/L）.

Abrasive resistance of metastable V–Cr–Mn–Ni spheroidal carbide cast irons using the factorial design method

Full factorial design was used to evaluate the two-body abrasive resistance of 3wt%C–4wt%Mn–1.5wt%Ni spheroidal carbide cast irons with varying vanadium（5.0wt%–10.0wt%） and chromium（up to 9.0wt%） contents. The alloys were quenched at 920℃. The regression equation of wear rate as a function of V and Cr contents was proposed. This regression equation shows that the wear rate decreases with increasing V content because of the growth of spheroidal VC carbide amount. Cr influences the overall response in a complex manner both by reducing the wear rate owing to eutectic carbides（M7C3） and by increasing the wear rate though stabilizing austenite to deformation-induced martensite transformation. This transformation is recognized as an important factor in increasing the abrasive response of the alloys. By analyzing the regression equation, the optimal content ranges are found to be 7.5wt%–10.0wt% for V and 2.5wt%–4.5wt% for Cr, which corresponds to the alloys containing 9vol%–15vol% spheroidal VC carbides, 8vol%–16vol% M7C3, and a metastable austenite/martensite matrix. The wear resistance is 1.9–2.3 times that of the traditional 12wt% V–13wt% Mn spheroidal carbide cast iron.

Influence of parental sample sizes on the estimating genetic parameters in cultured clam Meretrix meretrix based on factorial mating designs

The precise and accurate knowledge of genetic parameters is a prerequisite for making efficient selection strategies in breeding programs.A number of estimators of heritability about important economic traits in many marine mollusks are available in the literature,however very few research have evaluated about the accuracy of genetic parameters estimated with different family structures.Thus,in the present study,the effect of parent sample size for estimating the precision of genetic parameters of four growth traits in clam M.meretrix by factorial designs were analyzed through restricted maximum likelihood（REML） and Bayesian.The results showed that the average estimated heritabilities of growth traits obtained from REML were 0.23-0.32 for 9 and 16 full-sib families and 0.19-0.22 for 25 full-sib families.When using Bayesian inference,the average estimated heritabilities were0.11-0.12 for 9 and 16 full-sib families and 0.13-0.16 for 25 full-sib families.Compared with REML,Bayesian got lower heritabilities,but still remained at a medium level.When the number of parents increased from 6 to 10,the estimated heritabilities were more closed to 0.20 in REML and 0.12 in Bayesian inference.Genetic correlations among traits were positive and high and had no significant difference between different sizes of designs.The accuracies of estimated breeding values from the 9 and 16 families were less precise than those from 25 families.Our results provide a basic genetic evaluation for growth traits and should be useful for the design and operation of a practical selective breeding program in the clam M.meretrix.

Boron Removal by Electrocoagulation Using Full Factorial Design

Saline waters treatment has become increasingly important for drinking water supply in a greater part of the world. However, some serious limitations had recently been discovered during water treatment, among them the boron problem seems to have a critical meaning. According to the WHO regulations (2011), the boron concentration should be reduced to less than 2.4 mg/L for drinking water. The purpose of this study is to investigate the feasibility of electrocoagulation (EC) as a pretreatment process to remove boron from saline waters. To optimize the experimental conditions of boron removal, the effects of some parameters were studied such as inter-electrode distance (die), electrode connection mode, (S/V) ratio, pHi and initial conductivity of the solution (σi). Subsequently, an experimental design methodology was implemented to evaluate statistically the most significant operating parameters. The effects of current density, EC time and initial boron concentration and their mutual interaction were investigated using 23 full factorial design. At optimal conditions, boron removal from synthetic aqueous solutions containing initial boron concentrations of 5 and 50 mg/L reached 81% and 79%, respectively. Applied to boron removal from seawater samples, EC reduces boron concentration to less to 2.4 mg/L with excessive energy consumption under optimal parameters.

Modeling of biodiesel production: Performance comparison of Box–Behnken, face central composite and full factorial design

The performances of the response surface methodology(RSM)in connection with the Box–Behnken,face central composite or full factorial design(BBD,FCCD or FFD,respectively)were compared for the use in modeling of the NaOH-catalyzed sunflower oil ethanolysis.The influence of temperature,catalyst loading,and ethanol-to-oil molar ratio(EOMR)on fatty acid ethyl esters(FAEE)content was evaluated.All three multivariate strategies were efficient in the statistical modeling and optimization of the influential process variables but BBD and FCCD realization involved less number of experiments,generating smaller costs,requiring less work and consuming shorter time than the corresponding FFD.All three designs resulted in the same optimal catalyst loading(1.25%of oil)and EOMR(12:1).The reduced two-factorinteraction(2 FI)models based on the BBD and FCCD defined a range of optimal reaction temperature(25℃–75℃)and 25℃,respectively while the same model based on the 33 FFD appointed 75℃.The predicted FAEE content of about 97%–98.0%was close to the experimentally obtained FAEE content of about 97.0%–97.6%under the optimal reaction conditions.Therefore,the simpler BBD or FCCD might successfully be applied for statistical modeling of biodiesel production processes instead of the more extensive,more laborious and more expensive FFD.

Synthesis of biodegradable Mg-Zn alloy by mechanical alloying: Statistical prediction of elastic modulus and mass loss using fractional factorial design

Biodegradable Mg-Zn alloy was synthesized using mechanical alloying where a statistical model was developed using fractional factorial design to predict elastic modulus and mass loss of the bulk alloy.The effects of mechanical alloying parameters(i.e.,milling time,milling speed,ball-to-powder mass ratio and Zn content)and their interactions were investigated involving 4 numerical factors with 2 replicates,thus 16 runs of two-level fractional factorial design.Results of analysis of variance(ANOVA),regression analysis and R2 test indicated good accuracy of the model.The statistical model determined that the elastic modulus of biodegradable Mg-Zn alloy was between 40.18 and 47.88 GPa,which was improved and resembled that of natural bone(30-57 GPa).Corrosion resistance(mass loss of pure Mg,33.74 mg)was enhanced with addition of 3%-10%Zn(between 9.32 and 15.38 mg).The most significant independent variable was Zn content,and only the interaction of milling time and ball-to-powder mass ratio was significant as P-value was less than 0.05.Interestingly,mechanical properties(represented by elastic modulus)and corrosion resistance(represented by mass loss)of biodegradable Mg-Zn alloy can be statistically predicted according to the developed models.

Characterization of Six Categories of Systematic 2^{<i>n</i>-(<i>n</i>-<i>k</i>)}Fractional Factorial Designs

Six categories of systematic 2n-(n-k) designs derivable from the full 2k factorial experiment by the interactions-main effects assignment are available for carrying out 2n-(n-k) factorial experiments sequentially run after the other such that main effects are protected against the linear/quadratic time trend and/or such that the number of factor level changes (i.e. cost) between the runs is minimal. Three of these six categories are of resolution at least III and three are of resolution at least IV. The three categories of designs within each resolution are: 1) minimum cost 2n-(n-k) designs, 2) minimum cost linear trend free 2n-(n-k) designs and 3) minimum cost linear and quadratic trend free 2n-(n-k) designs. This paper characterizes these six categories and documents their differences with regard to either time trend resistance of factor effects and/or the number of factor level changes. The paper introduces the last category of systematic 2n-(n-k) designs (i.e. the sixth) for the purpose of extending the design resolution from III into IV and also for raising the level of protection of main effects from the linear time trend into the quadratic, where a catalog of minimum cost linear and quadratic trend free 2n-(n-k) designs (of resolution at least IV) will be proposed. The paper provides for each design in any of the six categories: 1) the sequence of its runs in minimum number of factor level changes 2) the defining relation or its 2n-(n-k) alias structure and 3) the k independent generators needed for sequencing the 2n-(n-k) runs by the generalized foldover scheme. A comparison among these six categories of designs reveals that when the polynomial degree of the time trend increases from linear into quadratic and/or when the design’s resolution increases from III to IV, the number of factor level changes between the 2n-(n-k) runs increases. Also as the number of factors (i.e. n) increases, the design’s resolution decreases.

Prediction of Weld Bead Geometry in Plasma Arc Welding using Factorial Design Approach

The effect of various process parameters like welding current, torch height, welding speed and plasma gas flow rate on front melting width, back melting width and weld reinforcement of plasma arc welding on aluminum alloy is investigated by using factorial design approach. Variable polarity plasma arc welding is used for welding aluminum alloy. Trail experiments are conducted and the limits of the input process parameters are decided. Two levels and four input process parameters are chosen and experiments are conducted as per typical design matrix considering full factorial design. Total sixteen experiments are conducted and output responses are measured. The coefficients are calculated by using regression analysis and the mathematical models are constructed. By using the mathematical models the main and interaction effect of various process parameters on weld quality is studied.

Factorial study of moxibustion in treatment of diarrhea-predominant irritable bowel syndrome

AIM: To identify an appropriate therapeutic regimen for using aconite cake-separated moxibustion to treat diarrhea-predominant irritable bowel syndrome (D-IBS).