An Adaptive Response Surface Methodology Based on Active Subspaces for Mixed Random and Interval Uncertainties

2019 ◽  
Vol 4 (2) ◽  
Author(s):  
Xingzhi Hu ◽  
Yanhui Duan ◽  
Ruili Wang ◽  
Xiao Liang ◽  
Jiangtao Chen
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Estimation Error ◽  
Three Dimensional ◽  
Nonlinear Function ◽  
Response Analysis ◽  
Dynamic Correlation ◽  
Interval Uncertainties ◽  
Speed Reducer ◽  
Active Subspaces

Abstract The popular use of response surface methodology (RSM) accelerates the solutions of parameter identification and response analysis issues. However, accurate RSM models subject to aleatory and epistemic uncertainties are still challenging to construct, especially for multidimensional inputs, which is widely existed in real-world problems. In this study, an adaptive interval response surface methodology (AIRSM) based on extended active subspaces is proposed for mixed random and interval uncertainties. Based on the idea of subspace dimension reduction, extended active subspaces are given for mixed uncertainties, and interval active variable representation is derived for the construction of AIRSM. A weighted response surface strategy is introduced and tested for predicting the accurate boundary. Moreover, an interval dynamic correlation index is defined, and significance check and cross validation are reformulated in active subspaces to evaluate the AIRSM. The effectiveness of AIRSM is demonstrated on two test examples: three-dimensional nonlinear function and speed reducer design. They both possess a dominant one-dimensional active subspace with small estimation error, and the accuracy of AIRSM is verified by comparing with full-dimensional Monte Carlo simulates, thus providing a potential template for tackling high-dimensional problems involving mixed aleatory and interval uncertainties.

Application of response surface methodology for optimization of reactive black 5 removal by three dimensional electro-Fenton process

2018 ◽  
Vol 6 (2) ◽  
pp. 3418-3435 ◽  
Author(s):  
Faeze Iranpour ◽  
Hamidreza Pourzamani ◽  
Nezamaddin Mengelizadeh ◽  
Parisa Bahrami ◽  
Hamed Mohammadi
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Three Dimensional ◽  
Reactive Black 5 ◽  
Fenton Process

The optimization of prebiotic sucrose-free mango nectar by response surface methodology: The effect of stevia and inulin on physicochemical and rheological properties

2018 ◽  
Vol 25 (3) ◽  
pp. 243-251 ◽  
Author(s):  
Ainaz Alizadeh ◽  
Amin Seyedan Oskuyi ◽  
Sajed Amjadi
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Food Industry ◽  
Three Dimensional ◽  
Coefficient Of Determination ◽  
Sugar Consumption ◽  
Low Calorie ◽  
Independent Variables ◽  
Optimum Model ◽  
Optimum Sample

The reduction of sugar consumption is one of the major challenges for nutritionists and food industry. Therefore, it is significant to replace sucrose with other types of sweeteners, especially, natural ones. The aim of the present study is to produce low-calorie, sucrose-free mango nectar and to optimize the formulation by employing response surface methodology. The two independent variables were stevia, as a low-calorie sugar replacer (0, 1.5, and 3% w/w) and inulin as a prebiotic texturizer (0, 3, and 6% w/w) in order to compensate sugar elimination defect on viscosity and °Brix. The fitted models indicated a high coefficient of determination. The results revealed that stevia and inulin are as the independent variables which had significant effects on °Brix, viscosity, and sensory scores (p < 0.05). Also, pH was affected by stevia concentration. The rheological behavior of the sucrose-free mango nectar was non-Newtonian, shear thinning as Herschel–Bulkley model which was not different from the reported behavior for normal mango nectar-containing sucrose. The optimization of the variables, based on the response surface three-dimensional plots, demonstrated that utilizing 6% w/w inulin and 3% w/w stevia produced the optimum mango nectar with the desirability of 0.85 without undesirable changes in the physicochemical and organoleptic properties. The optimum sample was produced in triplicate to validate the optimum model as well.

scholarly journals Optimization of ultrasound-assisted extraction of polyphenolic compounds from coriander seeds using response surface methodology

2016 ◽  
pp. 249-263 ◽  
Author(s):  
Zoran Zekovic ◽  
Sasa Djurovic ◽  
Branimir Pavlic
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Three Dimensional ◽  
Extraction Process ◽  
Biologically Active ◽  
Ultrasonic Power ◽  
Ultrasound Assisted Extraction ◽  
Assisted Extraction ◽  
Order Polynomial ◽  
Predicted Values

Coriandrum sativum L. (coriander) seeds (CS) were used for preparation of extracts with high content of biologically active compounds. In order to optimize ultrasoundassisted extraction process, three levels and three variables of Box-Behnken experimental design (BBD) in combination with response surface methodology (RSM) were applied, yielding maximized total phenolics (TP) and flavonoids (TF) content and antioxidant activity (IC50 and EC50 values). Independent variables were temperature (40-80oC), extraction time (40-80 min) and ultrasonic power (96-216 W). Experimental results were fitted to a second-order polynomial model with multiple regression, while the analysis of variance (ANOVA) was employed to assess the model fitness and determine optimal conditions for TP (79.60oC, 49.20 min, 96.69 W), TF (79.40oC, 43.60 min, 216.00 W), IC50 (80.00oC, 60.40 min, 216.00 W) and EC50 (78.40oC, 68.60 min, 214.80 W). On the basis of the obtained mathematical models, three-dimensional surface plots were generated. The predicted values for TP, TF, IC50 and EC50 were: 382.68 mg GAE/100 g CS, 216 mg CE/100 g CS, 0.03764 mg/mL and 0.1425 mg/mL, respectively.

scholarly journals Densification and volumetric change during supersolidus liquid phase sintering of prealloyed brass Cu28Zn powder: Modeling and optimization

2014 ◽  
Vol 46 (1) ◽  
pp. 23-35 ◽  
Author(s):  
A. Mohammadzadeh ◽  
M. Azadbeh ◽  
Sabahi Namini
Keyword(s):  
Response Surface Methodology ◽  
Liquid Phase ◽  
Response Surface ◽  
Three Dimensional ◽  
Liquid Phase Sintering ◽  
Central Composite Rotatable Design ◽  
Volumetric Change ◽  
Short Period ◽  
Central Composite ◽  
Rotatable Design

An investigation has been made to use response surface methodology and central composite rotatable design for modeling and optimizing the effect of sintering variables on densification of prealloyed Cu28Zn brass powder during supersolidus liquid phase sintering. The mathematical equations were derived to predict sintered density, densification parameter, porosity percentage and volumetric change of samples using second order regression analysis. As well as the adequacy of models was evaluated by analysis of variance technique at 95% confidence level. Finally, the influence and interaction of sintering variables, on achieving any desired properties was demonstrated graphically in contour and three dimensional plots. In order to better analyze the samples, microstructure evaluation was carried out. It was concluded that response surface methodology based on central composite rotatable design, is an economical way to obtain arbitrary information with performing the fewest number of experiments in a short period of time.

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