Gluten-free products have some texture drawbacks compared with gluten products. The texture of gluten-free products is improved with the addition of hydrocolloids and pregelatinized starches. The effects of hydroxypropyl methylcellulose (HPMC), pregelatinized unripe banana flour (UBF-P) and water on the quality of gluten-free bread were studied. A composite central design and response surface methodology were used. The volume, specific volume, weight, and hardness were analyzed, and image analysis of the crumb was performed. The results showed that the volume and specific volume increased with the addition of HPMC and UBF-P, while the hardness decreased. The addition of UBF-P and water increased the number and size of alveoli and affected the distribution of alveoli in crumbs. The distribution and size of the alveoli affected the physical characteristics and texture of the bread. Unripe banana flour can be used as an alternative ingredient to prepare gluten-free bread that has good quality characteristics.
The statistical software package Design-Expert 8.0.4 (StatEase, Minneapolis, MN) was used for regression analysis of experimental data to obtain working parameters and to generate response surface graphs. ANOVA was used to estimate statistical parameters.
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To investigate the interaction among the variables and to determine the optimum concentration of each factor for maximum xylanase production by Cellulosimicrobium sp. CKMX1, the contour plot and three-dimensional response surfaces were plotted on the basis of the model equation. The effects of varying the concentration of yeast extract and one of the other variables are shown in Figs. 7 and 8, which demonstrates that the response surfaces for three combinations were similar to each other.
Three dimensional (3D) response surface plot of the CCD experiment for alkali-stable xylanase production by Cellulosimicrobium sp. CKMX1. The interactions between yeast extract and urea nitrogen (a), Urea nitrogen and CMC (b) and urea nitrogen and Tween 20 (c) are shown
Nowadays, there is growing acceptance of the use of statistical experimental designs in biotechnology to optimize culture medium components and conditions. Many studies have reported satisfactory optimization of xylanase production from microbial sources using a statistical approach (Wang et al. 2008). RSM and CCD was employed to optimize a fermentation medium for the production of xylanase by Cellulosimicrobium sp. CKMX1 at pH 8.0. The optimized medium resulted in a 1.6-fold increase in xylanase production. The application of statistical design for screening and optimization of culture conditions for the production of xylanolytic enzymes allows quick identification of the important factors, and the interactions between them. The RSM applied to the optimization of xylanase production in this investigation suggested the importance of a variety of factors at different levels. A high degree of similarity was observed between the predicted and experimental values, which reflected the accuracy and applicability of RSM to optimize the process for enzyme production. There have been reports on optimization of culture media using statistical approaches for a few bacterial xylanases processes but not for cellulase-free, alkali-stable xylanases in SSF of apple pomace. The statistical optimization approach is efficient and has been applied successfully to SSFs that have overcome the limitations of classical empirical methods (Yu et al. 1997). The results of CCD indicate the significance of yeast extract, urea nitrogen, Tween 20 and CMC on production of xylanase by Cellulosimicrobium sp. CKMX1. Despite some interactions, maximum interactions of different variables in the present investigation were found to be significant.
The Design Expert 8.0.6 software was used for the regression and graphical analysis of the data. The maximum values of JCB yield were taken as the response of the design experiment. The experimental data obtained by the above procedure was analyzed by the response surface regression using the following second-order polynomial: where is the response (JCB %), and are the linear and quadratic coefficients, respectively, is the regression co-efficient, and is the number of factors studied and optimized in the experiment. Statistical analysis of the model was carried out to evaluate the ANOVA. Confirmatory experiments were also carried out to validate the equation.
Featuring a substantial revision, the Fourth Edition of Response Surface Methodology: Process and Product Optimization Using Designed Experiments presents updated coverage on the underlying theory and applications of response surface methodology (RSM). Providing the assumptions and conditions necessary to successfully apply RSM in modern applications, the new edition covers classical and modern response surface designs in order to present a clear connection between the designs and analyses in RSM.
Raymond H. Myers, PhD, is Professor Emeritus in the Department of Statistics at Virginia Polytechnic Institute and State University. He has more than 40 years of academic experience in the areas of experimental design and analysis, response surface analysis, and designs for nonlinear models. A Fellow of the American Statistical Association (ASA) and the American Society for Quality (ASQ), Dr. Myers has authored numerous journal articles and books, including Generalized Linear Models: with Applications in Engineering and the Sciences, Second Edition, also published by Wiley. Douglas C. Montgomery, PhD, is Regents' Professor of Industrial Engineering and Arizona State University Foundation Professor of Engineering. Dr. Montgomery has more than 30 years of academic and consulting experience and his research interest includes the design and analysis of experiments. He is a Fellow of the ASA and the Institute of Industrial Engineers, and an Honorary Member of the ASQ. He has authored numerous journal articles and books, including Design and Analysis of Experiments, Eighth Edition; Generalized Linear Models: with Applications in Engineering and the Sciences, Second Edition; Introduction to Introduction to Linear Regression Analysis, Fifth Edition; and Introduction to Time Series Analysis and Forecasting, Second Edition, all published by Wiley. Christine M. Anderson-Cook, PhD, is a Research Scientist and Project Leader in the Statistical Sciences Group at the Los Alamos National Laboratory, New Mexico. Dr. Anderson-Cook has over 20 years of academic and consulting experience, and has written numerous journal articles on the topics of design of experiments, response surface methodology and reliability. She is a Fellow of the ASA and the ASQ. Permissions Request permission to reuse content from this site
This paper presents a novel gradient-free trust region assisted adaptive response surface method for aircraft optimization problems with expensive functions. A gradient-free trust region sampling space approach is developed for design space reduction and sequential sampling, and response surface metamodel refitting enables the trust region assisted adaptive response surface method to possess higher optimization efficiency and better global convergence capability. Besides, an election sequential Latin hypercube sampling method is developed to improve the space-filling property and feasibility of the sequential samples. Moreover, the augmented Lagrangian method is employed to handle expensive constraints. The trust region assisted adaptive response surface method outperforms several adaptive response surface metamodel variants in the comparative study on a number of benchmark problems. Additionally, compared with several other well-known metamodel-based global optimization algorithms, the proposed algorithm also shows favorable performance in global convergence, efficiency, and robustness. Next, the trust region assisted adaptive response surface method is successfully applied to solve an airfoil aerodynamic optimization problem based on computational fluid dynamics simulation to demonstrate its effectiveness for real-world engineering problems. Finally, limitations of the proposed method and future work are discussed.
Response surface methodology (RSM) is a useful technique for analyzing interactions among various factors and exploring the relationships between the response and the independent variables [14]. It is a collection of statistical and mathematical techniques that has been used for developing, improving, and optimizing various processes [15,16]. As a powerful statistical tool, RSM has been successfully used in various fields of food chemistry such as in the optimization of anthocyanin hydrolysis from red wine and the optimization of the solvent extraction of phenolic compounds from beans and other plants [17,18,19].
Table 1 displays the results from regression and variance analysis. The statistical significance of response surface models was assessed according to regression analysis and the analysis of variance (ANOVA). The estimated regression coefficients for the response variable, along with the adjusted R2 (adj-R2), corresponding R2, p-value, and lack of fit, are shown in Table 1.
The results in Table 1 show that the linear effects of phosphatidylcholine-to-cholesterol ratio, ultrasound time, and magnetic stirring time were significant (p 0.05). Influence of the independent variables on lysozyme nanoliposomes is demonstrated in Figure 1. The interactive effects of independent variables on the responses were further investigated by constructing three-dimensional response surface graphs and two-dimensional contour plots [21]. In accordance with Figure 1A, the encapsulation efficiency was increased with the increasing phosphatidylcholine-to-cholesterol ratio. It might be due to the fact that cholesterol can change the order of mobility of lecithin in the lipid bilayer, thus reinforcing the membrane stability [22]. For another, increasing the magnetic stirring time could increase the encapsulation efficiency (EE), allowing more lysozyme to be encapsulated in the nanoliposomes. 2ff7e9595c
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