Quadratic Polynomial Regression Equation Research Articles

The Pulse Electrolysis Treatment of Waste Emulsion Orthogonal Experimental Study

This mechanical processing waste emulsion for the study, handled by pulse electrolysis. Arrangements by orthogonal testing, experimental study on plate distance (d), current density (i), the pH value and the pulse width (tP) impact on COD removal efficiency, very poor analysis of test data to determine various factors affecting the COD removal efficiency of primary and secondary sort: pH value > current density > pulse width > plate distance, optimal operating conditions. Orthogonal experimental data derived from regression analysis, determination of cross of quadratic polynomial regression equations, mathematical model. Tests confirmed that pulse electrochemical method for treatment of waste emulsion with low energy consumption, short response time, and other advantages, strong applicability of wastewater, building mathematical models, providing theoretical basis for subsequent design.

The multi-objective optimization of the horizontal-axis marine current turbine based on NSGA-II algorithm

The present paper describes a hydrodynamic optimization technique for horizontal-axial marine current turbine. The pitch angle distribution is important to marine current turbine. In this paper, the pitch angle distribution curve is parameterized as four control points by Bezier curve method. The coordinates of the four control points are chosen as optimization variables, and the sample space are structured according to the Box-Behnken experimental design method (BBD). Then the power capture coefficient and axial thrust coefficient in design tip-speed ratio is obtained for all the elements in the sample space by CFD numerical simulation. The power capture coefficient and axial thrust are chosen as objective function, and quadratic polynomial regression equations are constructed to fit the relationship between the optimization variables and each objective function according to response surface model. With the obtained quadratic polynomial regression equations as performance prediction model, the marine current turbine is optimized using the NSGA-II multi-objective genetic algorithm, which finally offers an improved marine current turbine.

Medium optimization for exopolysaccharide production in liquid culture of endophytic fungus Berkleasmium sp. Dzf12.

Berkleasmium sp. Dzf12, an endophytic fungus from Dioscorea zingiberensis, is a high producer of spirobisnaphthalenes with various bioactivities. The exopolysaccharide (EPS) produced by this fungus also shows excellent antioxidant activity. In this study, the experimental designs based on statistics were employed to evaluate and optimize the medium for EPS production in liquid culture of Berkleasmium sp. Dzf12. For increasing EPS yield, the concentrations of glucose, peptone, KH2PO4, MgSO4·7H2O and FeSO4·7H2O in medium were optimized using response surface methodology (RSM). Both the fractional factorial design (FFD) and central composite design (CCD) were applied to optimize the main factors which significantly affected EPS production. The concentrations of glucose, peptone and MgSO4·7H2O were found to be the main effective factors for EPS production by FFD experimental analysis. Based on the further CCD optimization and RSM analysis, a quadratic polynomial regression equation was derived from the EPS yield and three variables. Statistical analysis showed the polynomial regression model was in good agreement with the experimental results with the determination coefficient (adj-R2) as 0.9434. By solving the quadratic regression equation, the optimal concentrations of glucose, peptone and MgSO4·7H2O for EPS production were determined as 63.80, 20.76 and 2.74 g/L, respectively. Under the optimum conditions, the predicted EPS yield reached the maximum (13.22 g/L). Verification experiment confirmed the validity with the actual EPS yield as 13.97 g/L, which was 6.29-fold in comparison with that (2.22 g/L) in the original basal medium. The results provide the support data for EPS production in large scale and also speed up the application of Berkleasmium sp. Dzf12.

Bacterial Cellulose Synthesis in Kombucha by <i>Gluconacetobacter</i> sp and <i>Saccharomyces</i> sp

Strain Gluconacetobacter hansenii CGMCC1671 and Saccharomyces cerevisiae CGMCC1670 were applied to make traditional Kombucha with pure cultures to search for the optimum parameters of major factors affecting the yields and productivities of Bacterial cellulose (BC) in the beverage. Three culture factors were examined. The yields and productivities of BC and sugar consumed were measured after cultured statically for 22 days. After single factor test factors affecting the yields and productivities of BC have been optimized by response surface methodology (RSM). The quadratic polynomial regression equation reflecting BC yield and affecting factors was build up with Box-Behnken design principle. The optimal values of 10.37% inoculum, initial pH 4.96 and medium volume 77.13 mL in 250 mL flask were obtained with theoretical BC yield 300.093mg/g. BC yield of 279.579 mg/g was obtained with 6.84% deviation by validation test with the optimal parameters. The co-culture of pure strains of traditional Kombucha technique can be used to provide both high quality and high yield of BC in addition to producing high quality Kombucha beverage.

Visualization and Feature Extraction of the Surface Morphology of the Abdomen of Red Swamp Crayfish

This paper demonstrates a method for visual reconstruction and feature analysis of the surface morphology of red swamp crayfish in CATIA (Computer Aided Three Dimensional Interactive Application) and Microsoft Excel. Red swamp crayfish, Procambarus clarkii, with efficient burrowing activities and coupling propel pattern of abdomen with tail, was selected to study the feasible methods in the visual reconstruction and feature analysis of the surface morphology of living things. The digital measurements of surface of the red swamp crayfish were carried out using a three-dimensional laser scanner. Point clouds, the scanning digital data of the surface of the red swamp crayfish, were processed by deleting unwanted data, reconstructing surface in CATIA. There was a perfectly shape character similarity between the digital picture of the abdomen with corresponding point clouds shown in CATIA, and transverse curves which shown the surface morphology of abdomen in the cross section along the red swamp crayfish were obtained and saved as files of ASCII format in CATIA. Feature analysis of the abdomen of red swamp crayfish were carried out after files of single transverse curve were imported into Microsoft Excel, results shown that, the first row in file of single transverse curve was the number of rows after it, and those other rows stored coordinate values of measured points of the abdomen in the preset three-dimensional coordinate system, shapes of the abdomen in different cross sections were similar, and quadratic polynomial regression equation was able to effectively express surface morphology of the abdomen of red swamp crayfish. Methods and results presented in this paper prove to be potentially useful for analyzing the feature of biological prototype, optimizing the mathematical model and affording deformable physical model to bionic engineering, those works would have great implications to the research of biological coupling theory and technological creation in bionic engineering. Key words: Visual reconstruction; Feature analysis; Surface morphology; Red swamp crayfish

Optimization of fermentation technology of hawthorn-pear wine by uniform design and response surface design

Uniform design methodology and response surface methodology were used to determine the optimum conditions for hawthorn-Yali pear wine. By using uniform design, the effects of fermentation temperature, sugar content, the ratio of hawthorn to pear, soaking time of hawthorn, additional volume of SO2, and yeast dosage on sensory quality were investigated, which indicated that the first three aspects were of great significance to the sensory quality. By using three-factor, three-level response surface methodology, a prediction model was established in the form of quadratic polynomial regression equation, with the best processing conditions hereby determined under the conditions of fermentation temperature (25.18°C), sugar content (22.00%), the ratio of hawthorn to pear (21.19:100), and the alcohol degree (11.05 (V/V %)).

Extraction performance of chromium (VI) with emulsion liquid membrane by Cyanex 923 as carrier using response surface methodology

Cr (VI) being a toxic and carcinogenic pollutant should be removed from industrial effluents. In the present investigation, Cr (VI) was transported selectively with Cyanex 923 carrier from bulk feed phase to internal stripping phase using emulsion liquid membrane technique. The liquid membrane was prepared by loading with Cyanex 923 as the carrier, Span 80 as the surfactant, kerosene as the solvent and sodium hydroxide as the stripping agent and their effect on the process parameters such as concentration of the surfactant, the ratio of organic phase to internal phase in the membrane and membrane to external phase ratio were studied using Box–Behnken design and response surface method. A quadratic polynomial regression equation was used to analyze the experimental data. The experimental and predicted values were in good agreement. The experimental results showed that chromium ion was extracted within 5 min. The chromium ion concentration was measured using inductively coupled plasma mass spectrometry (ICP-MS).

Statistical medium optimization and biodegradative capacity of Ralstonia eutropha toward p-nitrophenol

The effect of p-nitrophenol (PNP) concentration with or without glucose and yeast extract on the growth and biodegradative capacity of Ralstonia eutropha was examined. The chemical constituents of the culture medium were modeled using a response surface methodology. The experiments were performed according to the central composite design arrangement considering PNP, glucose and yeast extract as the selected variables whose influences on the degradation was evaluated (shaking in reciprocal mode, temperature of 30 degrees C, pH 7 and test time of about 9 h). Quadratic polynomial regression equations were used to quantitatively explain variations between and within the models (responses: the biodegradation capacity and the biomass formation). The coefficient of determination was high (R(adjusted)(2) = 0.9783), indicating the constructed polynomial model for PNP biodegradative capacity explains the variation between the regressors fairly well. A PNP removal efficiency of 74.5% occurred within 9 h (15 mg/L as the initial concentration of PNP with use of yeast extract at 0.5 g/L).

Analysis and prediction of dimensions and cost of laser micro-machining internal channel fabrication process

This paper presents the utilisation of Response Surface Methodology (RSM) as the prediction tool for the laser micro-machining process. Laser internal micro- channels machined using pulsed Nd:YVO4 laser in polycarbonate were investigated. The experiments were carried out according to 3 3 factorial Design of Experiment (DoE). In this work the three input process set as control parameters were laser power, P; pulse repetition frequency, PRF; and sample translation speed, U. Measured responses were the channel width and the micro-machining operating cost per metre of produced micro- channels. The responses were sufficiently predicted within the set micro-machining parameters limits. Two factorial interaction (2FI) and quadratic polynomial regression equations for both responses were constructed. It is proposed that the developed prediction equations can be used to find locally optimal micro-machining process parameters under experimental and operational conditions.

Monitoring of bone regeneration process by means of texture analysis

An image analysis method is proposed for the monitoring of the regeneration of the tibial bone. For this purpose, 130 digitized radiographs of 13 patients, who had undergone tibial lengthening by the Ilizarov method, were studied. For each patient, 10 radiographs, taken at an equal number of postoperative successive time moments, were available. Employing available software, 3 Regions Of Interest (ROIs), corresponding to the: (a) upper, (b) central, and (c) lower aspect of the gap, where bone regeneration was expected to occur, were determined on each radiograph. Employing custom developed algorithms: (i) a number of textural features were generated from each of the ROIs, and (ii) a texture-feature based regression model was designed for the quantitative monitoring of the bone regeneration process. Statistically significant differences (p < 0.05) were derived for the initial and the final textural features values, generated from the first and the last postoperatively obtained radiographs, respectively. A quadratic polynomial regression equation fitted data adequately (r2 = 0.9, p < 0.001). The suggested method may contribute to the monitoring of the tibial bone regeneration process.

Estimating fiber for lechuguilla ( Agave lecheguilla Torr., Agavaceae), a traditional non-timber forest product in Mexico

Lechuguilla ( Agave lecheguilla) plants are amongst non-timber forest products that are an important source of income for the inhabitants of the arid and semiarid regions of Mexico. There are however, no management programs to promote and protect this resource. In the present study a reliable, non-destructive and easy-to-follow method to estimate yield of lechuguilla fiber in wild populations was developed. A table for estimation of dry fiber production per plant was generated selecting height of cogollo multiplied by its diameter as the independent variable, using a quadratic polynomial regression equation. Using this table in the field would allow a quick and reliable estimation of lechuguilla fiber yield in natural populations.

Performance of hubbard classic broiler parents and fit the regression models for their prediction

The present study was conducted on Hubbard classic broiler parents in the Bangladesh Rural Advancement Committee (BRAC) poultry farm in Chittagong, Bangladesh to know the productive, reproductive performance and for modelling the performances for their prediction. The average live weight and egg production of Hubbard classic broiler parent were obtained as 3412.48 ± 137.773 g/hen and 170.99 ± 1.012 eggs/hen/year, respectively. By using the parameters of linear regression and quadratic polynomial regression equation the yearly predicted egg production (number), live weight (g) and feed intake (g) were predicted. The R2 and CV fit statistics were used to compare the model performance and actual and predicted values. The actual and predicted value for live weight and feed intake was similar except yearly egg production (number). Key words: Broiler parent; Performance; Modelling; Fit statistic; Predicted yield DOI: http://dx.doi.org/10.3329/bjas.v39i1-2.9689 Bang. J. Anim. Sci. 2010, 39(1&amp;2): 156-162