Papers by Keyword: Response Surface Model

Abstract: Design of experiment (DoE) is a set of practical recipes and theoretical assumptions leading to the optimization of the technological process and/or the stabilization of its output quality. Practically, all the DoE approaches assume the normality of a random noise and the quasi-linearity of models taken from the general linear model (GLM) class. It allows to use traditional least-square methodology to identification of a model parameters and their confidence intervals. It gives usually sufficient results but completely fails if the model is not from GLM class or a random noise has not a normal distribution. The solution for such problems is the bootstrap approach, a resampling method based on Monte Carlo strategies. This paper tries to answer a question how many repetitions should be made to estimate parameters of the prediction model with sufficient accuracy.

Abstract: Typical design of experiments (DoE) approach to the response surface problem applies the polynomials with at most the second order terms. It is correct due to the Taylor’s theorem when the variability of input variables is sufficiently small. Unfortunately, the variability bound of a designed experiment is planned with high uncertainty about the investigated object’s behavior. If the response of the object has a large curvature then model quality indicators (residuals normality, lack of fit, significance of terms) appear to be unacceptable. In such a case, polynomial terms with the order higher than second should be applied. The paper describes the RSM model with the fourth order terms identified for relationship between settings of a meat tumbler machine (input variables) and the Warner-Bratzler shear force (output variable).

Abstract: In this paper, the critical flux was applied to represent the tendency of membrane fouling. The response surface model was used to study different factors, such as sludge concentration, space between membranes and aeration rate, affecting membrane fouling of the upper and lower layer membrane module. It was found that the model is fitting and significant, moreover, the sludge concentration, space between membranes and aeration rate has a significant impact on the upper and lower membrane fouling. Meanwhile, it was also observed that the critical flux of both upper and lower layer membrane module sharply decreased with the increase of sludge concentration. However, the different variation tendency of membrane fouling between upper and lower layer membrane module was detected due to the change of space between membranes and aeration rate, when it was under different sludge concentrations. Finally, optimum operating parameters under different sludge concentration simulated by response surface model were successfully applied to the process of using flat-sheet membrane for four-stage sludge thickening.

Abstract: Modern CAE technology is widely used in modern automobile design, engine design and so on. But its computational expense and highly time cost reduce the efficiency of design. The paper studied a respond surface model-based technique for predictive design. Firstly, we study and compare the four kinds of polynomial orders of RSM technique. Then we use Latin Hypercube technique choose enough sample points for approximation. At last, we employed cross-validation error analysis for error analysis. The results of expensive benchmark functions of CEC 2014 tested our predictive methods.

Abstract: Design of experiment (DoE) is a methodology widely used in an industry and an academia. However the fundamentals of DoE are well known since first articles of R.A. Fisher, the uncertainty estimation is still the investigated issue due to the fact that non-linear outcome functions do not preserve the normal distribution. The analytical solutions are known only for a very limited number of transformation. Authors propose to involve a bootstrap approach to estimate the outcome uncertainty of the response surface model.

Abstract: The randomness of structural and material parameters needs to be considered in the reliability analysis of gun barrel ablation life. However, the traditional method, like Stochastic FEM sampling, results in huge computing workload and low efficiency. This paper proposed a modified response surface model for estimating the gun barrel ablation life. In which, the estimation error of the response surface model is the optimization goal. Gauss-Newton method (GNM) is used to get the optimal solution whose initial value is solved by Genetic-algorithm (GA). After that, ablation life can be calculated by the optimized response surface model. GA is effective in global solution space searching, while GNM is effective in local searching. The new method takes full advantages of both GA and GNM in parameters estimation. The simulation result shows that the combination of GA and GNM obtains a higher precision of ablation estimation and greatly improves the computational efficiency.

Abstract: To reduce the computational resources, experimental design and response surface method (RSM) were employed to investigate the aerodynamic drag coefficient (C_D) and lift coefficient (C_L) of airfoils by using CFD methods. The selection of sample points, development and validation of response surface model and the effects of different sample points on approximation model were discussed. The results indicates that the number and distribution of sample points have a significant impact on model accuracy and optimize results. Also this method can greatly reduce calculation amount.

Abstract: A double pivot suspension used for in-wheel motor electric vehicle was designed, and the virtual prototype model of the suspension assembly was build. The suspension parameters changed greatly during steering. In order to solve this problem, this paper proposed a non-linear response surface model to fit the relationship of suspension parameters and design variables. An optimization scheme was designed based on the response surface model. The suspension performance was improved significantly using optimized variables.

Abstract: Aerodynamic characteristic analysis of hypersonic cruise aircraft is more difficult than that of conventional aircraft, for the complex flow field simulation and inadequate amount of results under limited flight conditions. In this paper, numerical schemes applicable for hypersonic flow field are adopted to acquire a set of aerodynamic characteristics of a typical hypersonic cruise aircraft as sample data, based on which response surface models (RSM) are constructed to provide approximation of aerodynamic characteristics under any flight conditions within the design domain, finally the overall approximation performance of the response surface models are analyzed.

Abstract: For the development trend of advanced aircraft wind tunnel tests which require shorter cycle time and lower cost, a new wind tunnel testing process called Modern Design of Experiments (MDOE) is under development at NASA Langley Research Center. This paper presents a case study of application of Modern Design of Experiment methods in high speed wind tunnel tests based on the aerodynamic data of certain type of aircrafts. The full process including experiment design, execution, analysis of variance, and block design is described. Comparisons between MDOE predictions and OFAT measurements were made in the present study. The results show that the MDOE methods have well predictive capability to meet specific test objectives with less data volume, less cost and less time compared to the conventional OFAT methods, which means the MDOE approach established and used in this study is feasible enough to meet specific aerodynamic wind tunnel testing objectives in place of conventional OFAT methods.