Second-order Response Surface Research Articles

Multi-objective lightweight and crashworthiness collaborative optimisation of commercial vehicle cab

A collaborative optimisation method for the lightweight and crashworthiness of the cab structure is proposed using mixed variable screening, approximate models, multi-objective optimisation and ideal point methods. First, modal and stiffness analyses of the cab model are built. Three impact simulation model of cab are established and verified via ECE R29-02 regulation tests. Subsequently, front impact, front pillar impact, and roof strength model are established following ECE R29-03, which is more stringent than the ECE R29-02. However, the result of the front pillar impact of the cab does not meet the requirements of the ECE R29-03. Several improved A-pillar structures are proposed, among which reinforced rib structure can effectively enhance the occupant’s living space. Then, 18 thickness and 4 material variables are selected as design variables based on the mixed variable screening method. Different approximate models are established for performance responses. The results show that the second-order response surface model has high fitting accuracy in the cab modal and bending and torsional stiffness performance, while the Kriging model has high fitting accuracy in the crashworthiness indicators of the cab. Finally, the multi-objective lightweight and crashworthiness collaborative optimisation of the cab are conducted. Compared with the initial model, the crashworthiness of the optimal cab model is improved and the mass is reduced by 27.1 kg.

Modelling and optimization of process parameters for production of desiccated Chhana-murki (Indian cottage cheese-based dessert).

In the present study, process parameters were optimized for the production of desiccated chhana-murki (Indian cottage cheese-based dessert). Response Surface Methodology (RSM)was employed to explore the mutual effects of coagulation temperature (CT) of milk (70-90°C), % fat level in milk (3.5%-5.5%), and sugar-to-paneer cube (SP) ratio (0.6-0.9) on instrumental hardness (N), water activity (aw), yield (%), sensory sweetness and overall acceptability (on 100-point intensity scale) of chhana-murki. The resulted responses were evaluated by analysis of variance (ANOVA), and the second-order polynomial response surface equations were fitted using multiple regression analysis. Determination coefficients (R 2) were equal to 80% or higher for individual responses stated that the developed models were well fitted to the experimental results. The optimized product was prepared using CT 79.22°C, milk fat 4.8%, and SP ratio 0.7. Confirmatory experiment values for instrument hardness, water activity (aw), yield (%), sensory sweetness and overall acceptability were 105.05N, 0.85, 115.2%, 61.2 and 78.8, respectively.

Robust parametric optimization for investment casting process of a turbine vane

Investment casting technology is an important manufacturing technology for the turbine guide vanes of the aero-engine, which directly affects the performance of the engine. However, most of the researches on the investment casting process of the vane is mainly based on the development of the materials, while the process parameters are less researched. The purpose of this paper is to perform a robust optimization for the process parameters of the investment casting of a typical vane. Firstly, a three-dimensional casting simulation model is established based on the ProCAST® software. Five key process parameters are chosen and their uncertainties are specified. A set of desired parameters are firstly obtained by conducting a deterministic optimization using a design of experiment (DOE) method. Next, a second-order response surface model (RSM) is built with Box-Behnken design based on the initial optimization results. Finally, an RSM-based robust parametric optimization with AMGA algorithm is proposed, deriving several Pareto solutions. By comparing and analyzing every solution, an optimal parameter scheme is developed by considering high quality of the casting and robustness of the casting process.

Multi-fidelity response surfaces for uncertainty quantification in beams using coarse and fine finite element discretizations

This paper discusses a benchmark problem to understand the response surface based multi-fidelity model and uncertainty quantification in the context of beam vibrations. A multi-fidelity model for the beam is constructed by blending a low-fidelity finite element model (coarse discretization) and a high-fidelity finite element model (fine discretization). The natural frequencies of the beam are the desired responses. A second-order correction response surface constructed based on high and low-fidelity simulations, is used to correct the low-fidelity response surface model. It is shown that the multi-fidelity model is accurate and ranks much better than the high-fidelity model in terms of computational effort.

Research on tool wear factors for milling wood-plastic composites based on response surface methodology

A high-speed milling experiment on wood-plastic composites was performed using cemented carbide tools, and the resulting wear pattern was studied. The influence of the cutting parameters, the cutting speed, feed speed, and axial cutting depth on the tool wear was studied via response surface methodology, and the influence of the interaction of the cutting parameters on tool wear was analyzed. Three-dimensional surface graphs and contour plots of the tool wear results were established. According to the experimental results, a mathematical model of the tool wear based on the second-order response surface methodology was established, and the model was utilized to verify its feasibility. The results show that the nose width (NW) increases with the increase of the cutting speed and axial cutting depth and decreases with the increase of feed speed. Among the factors affecting tool wear, the cutting speed had the greatest influence, followed by the feed rate, with the axial cutting depth affecting tool wear the least. According to the results of the interaction between the tool wear and the cutting parameters, a low feed speed and small axial cutting depth can be selected to ensure long tool life; for low-speed cutting, a high feed speed and large axial cutting depth can be adopted to ensure tool life while improving machining efficiency.

Frequency Response Function-Based Finite Element Model Updating Using Extreme Learning Machine Model

A frequency response function- (FRF-) based surrogate model for finite element model updating (FEMU) is presented in this paper. Extreme learning machine (ELM) is introduced as the surrogate model of the finite element model (FEM) to construct the relationship between updating parameters and structural responses. To further improve the generalization ability, the input weights and biases of ELM are optimized by Lévy flight trajectory-based whale optimization algorithm (LWOA). Then, LWOA is also applied to obtain the best updating results, where the objective function is defined by the difference between analytical FRF data and experimental data. Finally, a plane truss is used to demonstrate the performance of the proposed method. The results show that, compared with second-order response surface (RS), radial basis function (RBF), traditional ELM, and other optimized ELM, a LWOA-ELM model has higher prediction accuracy. After updating, the FRF data and frequencies have a significant match to the experimental model. The proposed FEMU method is feasible.

Force Prediction and Cutting-Parameter Optimization in Micro-Milling Al7075-T6 Based on Response Surface Method.

Optimization of cutting parameters in micro-milling is an important measure to improve surface quality and machining efficiency of the workpiece. Investigation of micro-milling forces prediction plays a positive role in improving machining capacity. To predict micro-milling forces and optimize micro-milling cutting parameters (per-feed tooth (fz), axial cutting depth (ap), spindle speed (n) and tool extended length (l)), a rotatable center composite experiment of micro-milling straight micro-groove in the workpiece of Al7075-T6 were designed, based on second-order response surface methods. According to the experiment results, the least square method was used to estimate the regression coefficient corresponding to the cutting parameters. Simultaneously, the response prediction model of micro-milling was established and successfully coincide the predicted values with the experiment values. The significance of the regression equation was tested by analysis of variance, and the influence of micro-milling cutting parameters on force and top burrs morphology was studied. The experiment results show that in a specific range of cutting parameters, ap and fz have a significant linear relation with the micro-milling force and the top burrs width. According to the optimal response value, the optimized cutting parameters for micro-milling obtained as: n is 11,393 r/min, fz is 6 µm/z, ap is 11 μm and l is 20.8 mm. The research results provide a useful reference for the selection of cutting parameters for micro-milling.

Standardization of seed and peel infused Syzygium cumini -wine fermentation using response surface methodology

Jamun known for its nutraceutical and therapeutic properties. However, due to its perishable nature with a short shelf life of 1–2 days, an efficient fermentative processing technology to produce local Jamun-wine is imminent. In the present study, a five-level three-factor Central Composite Rotatable design was used to optimize TSS, inoculum size and DAHP supplementation for total sugars, reducing sugars and ethanol response while seed powder and pulp powder concentrations were optimized for polyphenols and tannins response for the development of Jamun wine using Response surface methodology. A second-order polynomial response surface equation was generated which showed that the experimental variables significantly affected the ethanol production. The optimized fermentative parameters [Total soluble solids (TSS) 18°B, inoculum 5% (v/v) and Diammonium hydrogen orthophosphate (DAHP)100mg/100 ml] with and without supplements (seed powder and pulp powder @ 286.4 and 300mg/100 ml, respectively) were then validated to prepare Jamun-wine at 7L scale resulting in 9.93 and 10.14% (v/v) ethanol production, respectively that were stored for 90 days to determine the effect on sensory attributes. The sensory evaluation of these wines showed that both the wines were rated as “very liked”. The qualitative GCMS analysis revealed presence of seed and bark based volatiles in the jamun wine.

Multi-objective optimization of axial-flow-type gas-particle cyclone separator using response surface methodology and computational fluid dynamics

Pressure drop and separation efficiency are two critical performance parameters in the design of gas-particle separators. In this study, multi-objective optimization of an axial-flow-type gas-particle cyclone separator is conducted using the response surface methodology (RSM) and computational fluid dynamics (CFD) to minimize the pressure drop and maximize the separation efficiency. First, the accuracy of numerical simulation of airflow and particles predicted by the Reynolds stress model and discrete phase model is verified by experiments. Second, a screening experiment is set up to select the significant factors out of nine factors of interest. Four of the factors are studied using a central composite design in the RSM, and second-order response surface modeling is performed for two responses. A structural optimized design is obtained by the desirability function approach. Finally, the differences between the original and optimized designs are explained. Compared with the original design, the optimized design increases the removal efficiency for 8-μm particles by 100% and the static pressure drop by 69.32%. Based on the analysis of the flow field and the particle trajectory, the cause of performance change is explained. The optimized design is obtained based on a trade-off between static pressure drop and separation efficiency.

Wind Turbine Blade Optimal Design Considering Multi-Parameters and Response Surface Method

Within the framework of blade aerodynamic design, the maximum aerodynamic efficiency, power production, and minimum thrust force are the targets to obtain. This paper describes an improved optimization framework for blade aerodynamic design under realistic conditions, while considering multiple design parameters. The relationship between the objective function and the design parameters, such as the chord length, maximum chord, and twist angle, were obtained by using the second-order response surface methodology (RSM). Moreover, the identified parameters were organized to optimize the aerodynamic design of the blades. Furthermore, the initial and optimized blade geometries were compared and showed that the performance of the optimized blade improved significantly. In fact, the efficiency was increased by approximately 10%, although its thrust was not varied. In addition, to demonstrate the improvement in the resulting optimized blades, the annual energy production (AEP) was estimated when installed in a specific regional location. The result showed a significant improvement when compared to the baseline blades. This result will be extended to a new perspective approach for a more robust optimal design of a wind turbine blade.

Cavitating Flow Suppression in the Draft Tube of a Cryogenic Turbine Expander through Runner Optimization

The application of a cryogenic liquefied natural gas expander can reduce the production of flash steam and improve the efficiency of natural gas liquefaction. Like traditional hydraulic machinery, cavitation will occur during the operation of a liquefied natural gas expander, in particular, there is a strong vortex flow in the draft tube, and the cavitation phenomenon is serious. In this paper, the energy loss coefficient of the draft tube is used to describe the cavitation flow in the draft tube, and the goal of reducing the cavitation in the draft tube is achieved through the optimization design of the runner. Different runner models within the range of design parameters were obtained using the Latin hypercube test, and the relationship between design parameters and objective functions is constructed by a second-order response surface model. Finally, the optimized runners were obtained using a genetic algorithm. The effects of blade loading distribution and blade lean angles on the cavitation in the draft tube were studied. According to the optimization results, the blade loading distribution and blade lean angles are recommended in the end.

Estimation of opening discharge coefficient of naturally ventilated dairy buildings by response surface methodology

The discharge coefficient (Cd) is a characteristic parameter of an opening, which represents the effect of flow contraction and frictional losses when the flow goes across the opening. It is an important parameter for the ventilation rate determination when using the orifice equation method. The objectives of this study were to investigate the relationship between Cd and its potential influencing factors, i.e. opening ratio (r), building length to width ratio (α), wind speed (U), and wind direction (θ), and to evaluate the sensitivity of each factor on the Cd for naturally ventilated dairy buildings (NVDBs). The investigations were performed using the response surface methodology together with Box-Behnken Design and Computational Fluid Dynamics simulation methods. A second-order polynomial response surface model for the estimation of the discharge coefficient was developed and verified. The results showed that the Cd was significantly affected by the individual factors of r and θ, with more sensitivity to r when r > 42.5%. By contrast, the effects from the individual factors of α and U on Cd were insignificant. In addition, the interaction effects between r and θ, and between α and θ on Cd were also identified. It was concluded that the effects from both individual factors and interactions are required to be considered in the estimation of the opening discharge coefficient for NVDBs.

Structural Modal Analysis and Optimization of SUV Door Based on Response Surface Method

Sensitivity analysis and response surface methods were employed to optimize the structural modal of SUV doors. A finite element numerical simulation model was established and was calibrated by restraint modal tests. To screen out highly sensitive panels, a sensitivity analysis for the thickness of door panels was proposed based on the fifth-order modal frequency of the door. Data points were obtained by a faced central composite design with the design variables from the thickness of the highly sensitive panels, and a second-order explicit response surface function of the fifth-order modal frequency of the vehicle door was established. An optimization model was established according to the response surface method. The final results demonstrate that the modal-frequency matching of the door and body in white was optimized after changing the thicknesses, with a 5.74% material reduction.

Design optimization of S-shaped compressor transition duct using particle swarm optimization algorithm

A high-bypass turbofan engine transfers air from low- to the high-pressure compressor through an S-shaped transition duct. Minimization of the total pressure loss and maximization of uniform flow are key factors to ensure the maximum performance of the S-shaped transition duct. The conventional design approach is time-consuming and does not guarantee an optimal solution. Hence, the present article is based on the application of optimization for the S-shaped compressor transition duct. The optimization is carried out on the basis of shape parameters to minimize objectives namely pressure loss coefficient and non-uniformity with the reduction of length of the S-shaped transition duct. The 2-D axisymmetric approach of computational fluid dynamics is used as a design tool for performance evaluation with optimization techniques. The simulation model is validated with the available experimental results of the literature. The correlation between the response and independent variables is established with the help of the second-order polynomial response surface methodology. Further, individual optimization is carried out for single-objective consideration using particle swarm optimization and gray wolf optimization algorithms. As the results of single-objective optimization depict the conflicts between both objectives, later optimization using multi-objective particle swarm optimization and multi-objective gray wolf optimization algorithms is carried out. The performance metrics are obtained and compared. The ‘TOPSIS’ method is applied to get best solution out of multiple solutions. The optimized duct reduced pressure loss coefficient and non-uniformity index by 28.14% and 43.33% with a reduction of 6.37% of length compared to baseline S-shaped duct.

Constructing response surface designs with orthogonal quadratic effects using cyclic generators

The central composite designs (CCDs [1]) and small composite designs (SCDs [2,3]) are designs for sequential experimentation for response surface optimization. The CCDs for fitting the second-order response surface require a 2-level factorial or a resolution V fraction at the first stage (screening stage). The SCDs developed for fitting the same model require many fewer runs at the first stage as they only require a resolution III* fraction. This paper introduces an algorithm which can augment a 2-level first-order design with additional 3-level runs to form a second-order design. This algorithm does not require the 2-level first-order design in stage I to be a resolution V or resolution III* fraction. These augmented runs are made up of circulant matrices. Since CCDs and SCDs are special cases of the designs constructed this way, we call the new designs generalized composite designs or GCDs. Like CCDs and SCDs, GCDs have orthogonal quadratic effects. GCDs can often be found with numbers of runs between those of SCDs and CCDs. This is useful because SCDs often have poorly estimated parameters and CCDs often require substantially more runs than required to fit a full quadratic model.

Multiobjective optimization research on the response time of a pneumatic pilot-operated high speed on/off valve

In order to solve the contradiction between the opening and closing time of the high speed on/off valve for space propulsion systems of the liquid rocket engine, a pneumatic pilot-operated high speed on/off valve is proposed and multiobjective optimization for the opening and closing time of the valve is carried out in this paper. Based on the analysis of the working mechanism of the valve, the mathematical models for the pilot valve and the main valves are established respectively. The Plackett-Burman design is used to select the optimization variables which influence the performance of the response time significantly. The central composite design is used to obtain the sample points and establish second-order response surface models of the response time. The NSGA-II is used to obtain the Pareto front of the optimization objectives. The optimized opening and closing time can be reduced by 17.7% and 37.4% respectively. A prototype based on the optimized parameters is manufactured and tested to verify the accuracy of the multiobjective optimization results. The test results verify the validity of the optimization approach for the proposed valve in this paper.

A New Class of Second-Order Response Surface Designs

Response surface methodology (RSM) refers to experimental designs for optimizing or developing processes, initially in manufacturing. In this paper, a new method is presented and an algorithm is implemented that modifies the axial part in a central composite design to achieve a good D-value and efficiency. The new designs are suitable for sequential experimentation. In comparison with known designs in the same class, the new designs are tested and found to have better D-values on a range of factors. With this new approach, efficient orthogonal designs for response surface methodology were generated for a number of parameters that were previously impossible to construct. The new generated designs and their comparison with known designs from the literature are presented in tables for practitioners' use.

Development of low-cost production process for prototype components based on Wire and Arc Additive Manufacturing (WAAM)

Wire and Arc Additive Manufacturing is a fast-growing technology that allows to produce medium to large metal parts in both a material- and cost-efficient way. Because it is based on existing welding technology, it is certainly an affordable technology for small and medium sized companies. However, the integration of this technology for prototype manufacturing still needs certain difficulties to be solved, such as the determination of process parameters and deposition strategies, programming software to be used, postprocessing, etc. This paper focuses on the different steps to be taken to adapt the existing Gas Metal Arc Welding (GMAW) technology into an affordable and efficient WAAM technology. The technology developed has been integrated within a robotized platform. Experiments for the determination of bead geometry were conducted both for conventional GMAW (MAG welding) and Cold Metal Transfer (CMT) welding. A central composite rotatable design (CCD) was used for fitting second-order response surfaces, allowing to predict bead geometry corresponding to the welding parameters and to set the required information for generating the robot programs. Also, productivity of both processes was compared, highlighting significant dependency on part’s geometry and dimensions as also the quantity of parts simultaneously produced.

Adsorption of acid violet 7 (AV7) dye using RHA-CFA adsorbent: Modeling, process analysis, and optimization

ABSTRACT In this study, the factors affecting the performance of rice husk ash (RHA)-coal fly ash (CFA) adsorbent in removing acid violet 7 (AV7) dye were analyzed using response surface methodology (RSM). The experiment was run based on the 3-level factorial design in RSM. Modeling and optimization analyses were carried out using RSM and artificial neural network (ANN). Response surface plot suggested that higher adsorption efficiency can be achieved at higher ash ratio and additive concentration. RSM had the highest accuracy (R2 = 0.934) in predicting dye adsorption efficiency, while ANN modeling by Mathematical calculations (i.e., using predictor function) showed the lowest accuracy (R2 = 0.733). The optimum RHA-CFA adsorbent preparation condition with the highest AV7 dye adsorption efficiency was obtained through the numerical optimization of RSM model. Through RSM optimization study, maximum adsorption efficiency obtained was 45.1% at RHA/CFA ratio of 3.00 and 1.00 M of NaOH. This study demonstrated that the second-order response surface model (RSM) together with ANN models was used successfully to predict and optimize the AV7 dye adsorption efficiency of RHA-CFA adsorbent.

Optimization of A-TIG Welding Process Parameters for P92 (9Cr-0.5Mo-1.8W-VNb) Steel by Using Response Surface Methodology

Abstract Response surface methodology (RSM) is a mathematical and statistical technique useful for the modeling and optimization of processes in which a response of significance is influenced by a number of process parameters called input variables. The major concern faced by fabrication engineers during activated tungsten inert gas (A-TIG) welding is the selection of the optimum combination of input variables for achieving the desired weld bead geometry. In this research work, the optimization of A-TIG welding process parameters for P92 (9Cr-0.5Mo-1.8W-VNb) steel have been carried out using RSM. The design matrix for conducting experiments was generated using the central composite design of RSM. The four input process variables, such as welding current, torch speed, arc gap, and electrode tip angles, are varied at five levels. A-TIG bead-on-plate welds were made on a 10 mm-thick P92 steel plate as per the combination of input parameters given by the design matrix. Weld bead geometry, such as the depth of penetration, bead width, and width of the heat-affected zone, were measured and recorded as responses. Second-order response surface models were developed for predicting the response for the set of given input process parameters. Moreover, the response optimization was carried out for obtaining the maximum depth of penetration, minimum bead width, and target heat-affected zone width using the desirability approach. The validation experiments were carried out on the determined optimized process parameters, and it was found that there was good agreement between the predicted weld bead dimensions and actual values obtained during the experiments.