Second-order Response Surface Research Articles

Multi-objective optimization of a Stairmand cyclone separator using response surface methodology and computational fluid dynamics

The performance of a cyclone is generally assessed using the pressure drop and the collection efficiency of the cyclone. In the present paper, a multi-objective optimization of a classic Stairmand cyclone separator is executed using the response surface methodology (RSM), combined with computational fluid dynamics (CFD) techniques for minimizing the pressure drop and maximizing the collection efficiency. Ten cyclone geometrical factors are considered in this work. Three of them are studied using the RSM according to the results of the preceding screening experiments. The second-order response surface models for each response are successfully carried out using the central composite design (CCD) in the RSM. The desirability function approach is used to optimize the geometrical factors of the cyclone. In comparison to the reference model, the optimal cyclone model decreases the pressure drop by 20.70% and the cut-off size by 75.38%. The accuracies of the response surface models are confirmed and the correctness of the optimal cyclone model is also validated using CFD; the results indicate excellent performance and reliability of the response surface model and the RSM optimization result. According to the analyses of the obtained flow fields, there are several reasons why decreases in the cut-off size with a lower pressure drop are found in the optimal model. The primary reasons for improvements are optimized values of relevant geometrical factors, the production of a distinct, undisturbed downward flow, an increase in the tangential velocity at the near wall region, and a decrease in the peak tangential velocity.

Optimization of high pressure processing parameters of Indian white prawn (Fenneropenaeus indicus)

ABSTRACTThe effect of pressure (150, 250 and 350 MPa), ramp rate (200, 400 and 600 MPa/min) and holding time (3, 6 and 9 min) on the quality indices (dependent variable) of Indian white prawn (Fenneropenaeus indicus) was optimized using response surface methodology. Box–Behnken response surface design was used with 15 runs. Second-order response surface model was fitted to the experimental data and the model adequacy was measured by R2 value. The linear and quadratic effect of pressure, ramp rate and holding time was significant for tri-methylamine, total volatile base nitrogen and total plate count. Based on the ridge analysis and response surface plots, the optimum combination obtained was 250 MPa pressure, 400 MPa/min ramp rate and 6 min holding time for high pressure (HP) processing of Indian white prawn. Validation of the experiment indicated that the developed model was appropriate to predict quality indices in Indian white prawn processed by HP processing.

Configuration optimization of shell-and-tube heat exchangers with helical baffles using multi-objective genetic algorithm based on fluid-structure interaction

The configuration parameters of helical angle and overlapped degree of shell-and-tube heat exchangers with helical baffles have been discussed for the thermal-structural comprehensive performance. Based on fluid-structure interaction theory, a method on configuration optimization of shell-and-tube heat exchangers with helical baffles is introduced using second-order polynomial regression response surface combined with Multi-objective Genetic Algorithm. The results show that the heat transfer coefficient per unit pressure drop of shell-and-tube heat exchangers with helical baffles increases firstly and then decreases with the increase of helical angle, and decreases with the increase of overlapped degree under certain shell-inlet velocity. And the performance of flow and heat transfer is more sensitive to helical angle compared with overlapped degree. The maximum shear stress increases with helical angle, but it is almost unaffected by overlapped degree for mechanical properties of helical baffles. The objectives of optimization are the heat transfer coefficient per unit pressure drop maximizing and maximum shear stress minimizing with scope of allowable stress, and three optimal structures are obtained. The optimal results indicate that the heat transfer coefficient per unit pressure drop increases averagely by 14.1%, the maximum shear stress decreases averagely by 4.1%, which provides theoretical guidance for industrial design of shell-and-tube heat exchangers with helical baffles.

Effective Surface Preparation Technique for Cementitious Samples in Nanoindentation Testing

Abstract The nanomechanical properties of cementitious materials determined by nanoindentation largely depend on the surface roughness and intrinsic material porosity of the samples. Studies have shown that high surface roughness causes an overall reduction in the measured indentation modulus and hardness. Therefore, it is important to reduce the surface roughness to a desirable value by means of polishing. However, polishing causes damage to the cement matrix. Thus, the most challenging task is to obtain a reasonable surface roughness with minimum disturbance to the microstructure of the samples. This paper discusses an effective surface preparation technique that would meet the roughness criteria for nanoindentation. With the application of Taguchi method, the optimum parameter combinations and relative contributions of various controlling factors such as force, speed, and time of polishing were determined. A second-order response surface model was developed based on signal to noise ratio to establish the relationship between the controlling factors and surface roughness. Finally, the predicted surface roughness values from both Taguchi method and response surface model were compared with the experimental values of the optimized confirmation runs and a good agreement was achieved.

Some new three-level second-order response surface designs

In this paper, we use conference matrices and Plackett-Burman designs to construct some new three-level second-order response surface designs. The D-optimality values of the proposed designs are computed. These designs can fit the second-order response surface model with high efficiencies but with far fewer runs. Further, these designs are blocked orthogonally.

Comparison of fast elimination of Cr(VI) by alumina nanofiber and alumina nanoporous

The goal of this study is examination of the mixture between adsorption and permeation process for removing chromium (VI) from the water. Two types of supported membranes are developed: The first one which was made by sol–gel method is called nanoporous and the second one which was made by electrospinning is called nanofiber. The sorption capacity of nanoporous and nanofiber is examined in single batch experiments at various pH values, and it is found that maximum chromium removal is observed for both nanoporous and nanofiber at pH 3.5. Adsorption studies illustrated that the Cr(VI) adsorption onto alumina nanoporous and nanofiber is affected by changes in pH, contact time, dosage of adsorbent, concentration of chromium and solution volume. Langmuir and Freundlich isotherms can be used to explain the adsorption equilibria of Cr(VI) onto alumina nanoporous and nanofiber. It was found that balance adsorption data adequate Langmuir isotherm more than Freundlich model. Adsorption kinetics was found to be fitted to pseudo-second order and Weber and Morris model. The output of multiple linear regressions was run for the second-order response surface model implied that the linear agents of pH, sorbent dosage and Cr(VI) concentration are more significant factors. Manufacturing electrospun alumina nanofiber and sol–gel nanoporous with these cheap materials, renewable and fast methods are so important although the removal percentage is significant.

Construction of Weighted Second Order Rotatable Simplex Designs (Wrsd)

Response surface methodology is widely used for developing, improving, and optimizing processes in various fields. A rotatable simplex design is one of the new designs that have been suggested for fitting second-order response surface models. In this article, we present a method for constructing weighted second order rotatable simplex designs (WRSD) which are more efficient than the ordinary rotatable simplex designs (RSD). Using moment matrices based on the Simplex and Factorial Designs, and the General Equivalence Theorem (GET) for D- and A- optimality, weighted rotatable simplex designs (WRSDs) were obtained. A- and D- optimality criterion was then used to establish the efficiency of the designs.

Modeling the Effect of Temperature and Water Activity on the Thermal Resistance of Salmonella Enteritidis PT 30 in Wheat Flour

Salmonella continues to be a problem associated with low-moisture foods, particularly given enhanced thermal resistance at lower water activity (aw). However, there is a scarcity of thermal inactivation models accounting for the effect of aw. The objective of this study was to test multiple secondary models for the effect of product (wheat flour) aw on Salmonella enterica Enteritidis phage type 30 thermal resistance. A full-factorial experimental design included three temperatures (75, 80, and 85°C) and four aw values (~0.30, 0.45, 0.60, and 0.70). Prior to isothermal treatment, sample aw was achieved by equilibrating samples in a humidity-controlled conditioning chamber. Two primary models (log linear and Weibull type) and three secondary models (second-order response surface, modified Bigelow type, and combined effects) were evaluated using the corrected Akaike information criterion and root mean squared errors. Statistical analyses of the primary models favored the log-linear model. Incorporating the three secondary models into the log-linear primary model yielded root mean squared errors of 2.1, 0.78, and 0.96 log CFU/g and corrected Akaike information criterion values of 460, -145, and -19 for the response surface, modified Bigelow, and combined-effects models, respectively. The modified Bigelow-type model, which exponentially scaled both temperature and aw effects on thermal inactivation rates, predicted Salmonella lethality significantly better (P < 0.05) than did the other secondary models examined. Overall, aw is a critical factor affecting thermal inactivation of Salmonella in low-moisture products and should be appropriately included in thermal inactivation models for these types of systems.

Optimization of surface appearance for wire and arc additive manufacturing of Bainite steel

The improvements of surface quality and dimensional accuracy are critical for Wire and Arc Additive Manufacturing (WAAM). This paper highlights a multi-objective optimization process for Bainite steel additive manufacturing. The welding design matrix for conducting the experiments was made by using the Box-Behnken design of response surface methodology (RSM). The input process parameters were varied at three levels which result in 46 experimental trials. The responses were measured during or after conducting the experiments. A second-order response surface model was developed and then multi-objective optimization was performed to obtain the desired surface appearance. The acceleration and staggered deposition processes were used to decrease the head dimension of single weld bead. The results show that the optimized sample surface appearance is smooth which has little spatters and no visible defects. Compared with the traditional processes which rely on overlapping rate adjustment but weaken the single weld bead morphology optimization, the process of this paper has comprehensive considerations of droplet transfer, heat input, and shaping coefficient. It enables the capacity of fabricating metal parts with high accuracy and lays a good foundation for Bainite steel additive manufacturing.

Fatigue life analysis based on six sigma robust optimization for pantograph collector head support

In this article, a new fatigue life analysis method based on six sigma robust optimization is proposed, which considers the random effects of material properties, external loads, and dimensions on the fatigue life of a pantograph collector head support. Some main random factors are identified through fatigue reliability sensitivity analysis, which are used as input variables during fatigue life analysis. The six sigma optimization model is derived using the second-order response surface method. The response surface is fitted by the Monte Carlo method, the samples are obtained by the Latin hypercube sampling technique, and the proposed model is optimized using the interior point algorithm. Through the optimization, the collector head support weight is reduced, the mean and the standard deviation of fatigue life have been decreased, and the effect of design parameter variation on the fatigue life is reduced greatly. The robustness of fatigue life prediction of collector head support is improved. The proposed method may be extended to fatigue life analysis of other components of electric multiple units.

Biosorption of Lead(II) by Arthrobacter sp. 25: Process Optimization and Mechanism.

In the present work, Arthrobacter sp. 25, a lead-tolerant bacterium, was assayed to remove lead(II) from aqueous solution. The biosorption process was optimized by response surface methodology (RSM) based on the Box-Behnken design. The relationships between dependent and independent variables were quantitatively determined by second-order polynomial equation and 3D response surface plots. The biosorption mechanism was explored by characterization of the biosorbent before and after biosorption using atomic force microscopy (AFM), scanning electron microscopy, energy dispersive X-ray spectroscopy, X-ray diffraction, and Fourier transform infrared spectroscopy. The results showed that the maximum adsorption capacity of 9.6 mg/g was obtained at the initial lead ion concentration of 108.79 mg/l, pH value of 5.75, and biosorbent dosage of 9.9 g/l (fresh weight), which was close to the theoretically expected value of 9.88 mg/g. Arthrobacter sp. 25 is an ellipsoidalshaped bacterium covered with extracellular polymeric substances. The biosorption mechanism involved physical adsorption and microprecipitation as well as ion exchange, and functional groups such as phosphoryl, hydroxyl, amino, amide, carbonyl, and phosphate groups played vital roles in adsorption. The results indicate that Arthrobacter sp. 25 may be potentially used as a biosorbent for low-concentration lead(II) removal from wastewater.

Xylanase production from Penicillium citrinum isolate HZN13 using response surface methodology and characterization of immobilized xylanase on glutaraldehyde-activated calcium-alginate beads.

The present study reports the production of high-level cellulase-free xylanase from Penicillium citrinum isolate HZN13. The variability in xylanase titers was assessed under both solid-state (SSF) and submerged (SmF) fermentation. SSF was initially optimized with different agro-waste residues, among them sweet sorghum bagasse was found to be the best substrate that favored maximum xylanase production (9643 U/g). Plackett–Burman and response surface methodology employing central composite design were used to optimize the process parameters for the production of xylanase under SSF. A second-order quadratic model and response surface method revealed the optimum conditions for xylanase production (sweet sorghum bagasse 25 g/50 ml; ammonium sulphate 0.36 %; yeast extract 0.6 %; pH 4; temperature 40 °C) yielding 30,144 U/g. Analysis of variance (ANOVA) showed a high correlation coefficient (R 2 = 97.63 %). Glutaraldehyde-activated calcium-alginate-immobilized purified xylanase showed recycling stability (87 %) up to seven cycles. Immobilized purified xylanase showed enhanced thermo-stability in comparison to immobilized crude xylanase. Immobilization kinetics of crude and purified xylanase revealed an increase in K m (12.5 and 11.11 mg/ml) and V max (12,500 and 10,000 U/mg), respectively. Immobilized (crude) enzymatic hydrolysis of sweet sorghum bagasse released 8.1 g/g (48 h) of reducing sugars. Xylose and other oligosaccharides produced during hydrolysis were detected by High-Performance Liquid Chromatography. The biomass was characterized by Scanning Electron Microscopy, Energy Dispersive X-ray and Fourier Transformation Infrared Spectroscopy. However, this is one of the few reports on high-level cellulase-free xylanase from P. citrinum isolate using sweet sorghum bagasse.Electronic supplementary materialThe online version of this article (doi:10.1007/s13205-016-0484-9) contains supplementary material, which is available to authorized users.

Process design for heat fusion of thermoplastic composites using molecular dynamics and a response surface method

This study investigates efficient optimization of heat fusion conditions between thermoplastics using molecular dynamics (MD) and a response surface method. The heat fusion process between polypropylene and polyethylene and the uniaxial elongation for evaluation of the interfacial bonding strength were modeled using coarse-grained MD simulation. To determine the optimal conditions of heat fusion, experimental points were selected on the basis of a central composite design, and a second-order polynomial response surface was created by setting temperature, pressure, and polymerization degree as explanatory variables and the strength of fused interface as the response. The obtained optimal solution under constrained conditions yielded the highest strength when compared with other experimental points and random points.

Optimal Design of IPM Motors With Different Cooling Systems and Winding Configurations

Performance improvement of permanent magnet (PM) motors through optimization techniques has been widely investigated in the literature. Oftentimes the practice of design optimization leads to derivation/interpretation of optimal scaling rules of PM motors for a particular loading condition. This paper demonstrates how these derivations vary with respect to the machine ampere loading and ferrous core saturation level. A parallel sensitivity analysis using a second-order response surface methodology followed by a large-scale design optimization based on evolutionary algorithms are pursued in order to establish the variation of the relationships between the main design parameters and the performance characteristics with respect to the ampere loading and magnetic core saturation levels prevalent in the naturally cooled, fan-cooled, and liquid-cooled machines. For this purpose, a finite-element-based platform with a full account of complex geometry, magnetic core nonlinearities, and stator and rotor losses is used. Four main performance metrics including active material cost, power losses, torque ripple, and rotor PM demagnetization are investigated for two generic industrial PM motors with distributed and concentrated windings with subsequent conclusions drawn based on the results.

Application of Response Surface Methodology for Design and Optimization of Reservoir-type Transdermal Patch of Simvastatin.

The objective of the present investigation was to develop and optimize reservoir-type of transdermal drug delivery system of Simvastatin using response surface methodology. A total of 17 experimental runs were conducted according to three-factor, three-level Box-Behnken design employing Design expert®2 software to determine the effect of independent variables (simvastatin concentration, percentage of poloxamer 407, and concentration of D-limonene) on cumulative amount of simvastatin permeation through human cadaver skin in 48 h (dependent variable). The experimental data was fitted to different response surface models using multiple regression analysis and observed quadratic model was the best fit model with significant p-value (p꞊0.0003) and coefficient of determination value of 0.9949. The second-order polynomial equation and response surface plots indicated the significant influence of concentration of simvastatin and D-limonene on the simvastatin permeation in 48 h. The highest simvastatin permeation value of 76.94 μg/cm2 was observed in case of experimental number 10 with 1.5% (w/w) of simvastatin, 25% (w/w) of poloxamer 407, and 10% (w/w) of D-limonene. Using Derringer's desirability functional tool for optimization, the highest simvastatin permeation value of 78.7684 μg/cm2 in 48 h was predicted under optimum condition of; simvastatin concentration of 1.4893% (w/w), poloxamer 407 percentage of 22.43% (w/w), and D-limonene concentration of 9.8541% (w/w) with optimum desirability value. The in-vivo hypolipidemic study conducted for 14 days in hyperlipidemia induced Sprague-Dawley rats revealed that the optimized patch exhibited significant lowering of blood lipid profile. Finally, histology study was performed on skin sample used in permeation study of optimized formulation and compared with untreated skin sample. The treated skin sample showed a significant distortion in stratum corneum, which supported the ex-vivo permeation result. Thus, the patch may serve as an alternative therapy to oral dosage form of simvastatin with outmost patient compliance.

Alternative Second-Order N-Point Spherical Response Surface Methodology Design and Their Efficiencies

The equiradial designs are studied as alternative second-order N-point spherical Response Surface Methodology designs in two variables, for design radius ρ = 1.0. These designs are seen comparable with the standard second-order response surface methodology designs, namely the Central Composite Designs. The D-efficiencies of the equiradial designs are evaluated with respect to the spherical Central Composite Designs. Furthermore, D-efficiencies of the equiradial designs are evaluated with respect to the D-optimal exact designs defined on the design regions of the Circumscribed Central Composite Design, the Inscribed Central Composite Design and the Face-centered Central Composite Design. The D-efficiency values reveal that the alternative second-order N-point spherical equiradial designs are better than the Inscribed Central Composite Design though inferior to the Circumscribed Central Composite Design with efficiency values less than 50% in all cases studied. Also, D-efficiency values reveal that the alternative second-order N-point spherical equiradial designs are better than the N-point D-optimal exact designs defined on the design region supported by the design points of the Inscribed Central Composite Design. However, the N-point spherical equiradial designs are inferior to the N-point D-optimal exact designs defined on the design region supported by the design points of the Circumscribed Central Composite Design and those of the Face-centered Central Composite Design, with worse cases with respect to the design region of the Circumscribed Central Composite Design.

Efficient system reliability analysis of soil slopes using multivariate adaptive regression splines-based Monte Carlo simulation

System effects should be considered in the probabilistic analysis of a layered soil slope due to the potential existence of multiple failure modes. This paper presents a system reliability analysis approach for layered soil slopes based on multivariate adaptive regression splines (MARS) and Monte Carlo simulation (MCS). The proposed approach is achieved in a two-phase process. First, MARS is constructed based on a group of training samples that are generated by Latin hypercube sampling (LHS). MARS is validated by a specific number of testing samples which are randomly generated per the underlying distributions. Second, the established MARS is integrated with MCS to estimate the system failure probability of slopes. Two types of multi-layered soil slopes (cohesive slope and c–φ slope) are examined to assess the capability and validity of the proposed approach. Each type of slope includes two examples with different statistics and system failure probability levels. The proposed approach can provide an accurate estimation of the system failure probability of a soil slope. In addition, the proposed approach is more accurate than the quadratic response surface method (QRSM) and the second-order stochastic response surface method (SRSM) for slopes with highly nonlinear limit state functions (LSFs). The results show that the proposed MARS-based MCS is a favorable and useful tool for the system reliability analysis of soil slopes.

An optimum design on rollers containing the groove with changeable inner diameter based on response surface methodology

In order to realize the precision plastic forming of the revolving body component with changeable wall thickness, a kind of roller containing grooves with changeable inner diameter is put forward, as the forming mould of the technology of rolling-extrusion. Specifically, first, the arc length of the groove in the roller is designed according to the prediction on the forward slip value during the process of forming, to make accurate control of the actual length of the forming segments; then, to obtain better parameters of the roller structure, a second-order response surface model combining finite element numerical simulation and response surface methodology was put forward, taking the factor of forming uniformity as evaluation index. The result of the experiment shows that, for the formed component, not only the size can meet the needs but also each mechanical property index can be greatly improved, which verify the rationality of the forward slip model and the structural parameter of the optimum model based on the response surface methodology.

Approximated optimum condition of second order response surface model with correlated observations

In the present paper we establish an inference procedure for the eigenvalues of the model matrix of the second-order response surface model (RSM). In contrast to the classical treatment where the sample are assumed to be independently distributed, in this work we do not need such distributional simplification. The confidence region for the unknown vector of the eigenvalues is derived by means of delta method. The finite sample behavior of the convergence result is discussed by Monte Carlo Simulation. We get the approximated distribution of the pivotal quantity of the population eigenvalues as a chi-square distribution model. Next we attempt to apply the method to a real data provided by a mining industry. The data represents the percentage of cobalt (Co) observed over the exploration region.

Algorithmic construction of [formula omitted]-optimal designs for second-order response surface models

The R-optimality criterion introduced by Dette (1997) minimizes the volume of Bonferroni t-intervals. The present paper is devoted to the construction of R-optimal designs for second-order response surface models with k≥1 predictors. An equivalence theorem are given as an important tool for determining the R-optimal designs. The algorithms are given for constructing the R-optimal designs for second-order response surface models on the k-dimensional unit cube and ball, respectively. Numerical results of the R-optimal designs for 2≤k≤25 are obtained by using the proposed algorithms.