Abstract
This paper presents an integrated optimization design method in which uniform design, response surface methodology and genetic algorithm are used in combination. In detail, uniform design is used to select the experimental sampling points in the experimental domain and the system performance is evaluated by means of computational fluid dynamics to construct a database. After that, response surface methodology is employed to generate a surrogate mathematical model relating the optimization objective and the design variables. Subsequently, genetic algorithm is adopted and applied to the surrogate model to acquire the optimal solution in the case of satisfying some constraints. The method has been applied to the optimization design of an axisymmetric diverging duct, dealing with three design variables including one qualitative variable and two quantitative variables. The method of modeling and optimization design performs well in improving the duct aerodynamic performance and can be also applied to wider fields of mechanical design and seen as a useful tool for engineering designers, by reducing the design time and computation consumption.
Acknowledgment
The authors would like to gratefully acknowledge the support by the National Natural Science Foundation of China (Grant No. 51176005).
Nomenclature
- B
wall profile
specific heat at constant pressure
- D
inlet diameter
- F
the objective function
- f
friction coefficient
- k
specific heat ratio
- L
axial length of diverging duct
mass flow rate
- Ma
Mach number
- P
static pressure
total pressure
- R
gas constant
coefficient of determination
- t
non-dimensional length based on L and D
- T
static temperature
- V
local velocity
- x
inlet Mach number
- y
value of response
estimated value of σ
- z
numeralization of variable B
- Greek Symbols
density of gas flow
shear stress
- Subscripts
- w
wall
References
1. Engelund WC, Stanley DO, Lepsch RA, McMillian MM. Aerodynamic configuration design using response surface methodology analysis. AIAA Paper No. AIAA 93–3967. 1993.Search in Google Scholar
2. Wang GG. Adaptive response surface method using inherited Latin hypercube design points. ASME J Mech Des 2003;125:210–20.10.1115/1.1561044Search in Google Scholar
3. Zhu CY, Qin GL. Design technology of centrifugal fan impeller based on response surface methodology. ASME Paper No. FEDSM-ICNMM 2010–30002. 2010.10.1115/FEDSM-ICNMM2010-30002Search in Google Scholar
4. Kim JH, Kim KY. Analysis and optimization of a vaned diffuser in a mixed flow pump to improve hydrodynamic performance. ASME J Fluids Eng 2012;134: 071104.10.1115/1.4006820Search in Google Scholar
5. Kim JH, Kim JW, Kim JY. Axial-flow ventilation fan design through multi-objective optimization to enhance aerodynamic performance. ASME J Fluids Eng 2011;133:101101.10.1115/1.4004906Search in Google Scholar
6. Fang KT, Lin DKJ, Winker P, Zhang Y. Uniform design: theory and application. Technomet 2000;42:237–48.10.1080/00401706.2000.10486045Search in Google Scholar
7. Fang KT. Uniform design and uniform design tables. Beijing, China: Science Press, 1994 Chapter. 1, 2, 3 (in Chinese).Search in Google Scholar
8. Fang KT, Li RZ, Sudjianto A. Design and modeling for computer experiments.Taylor & Francis Group LLC, 2006:45–103.10.1201/9781420034899Search in Google Scholar
9. Hickernell FJ. Goodness-of-fit statistics, discrepancies and robust designs. Statist Probab Lett 1999;44:73–8.10.1016/S0167-7152(98)00293-4Search in Google Scholar
10. Hickernell FJ, Liu MQ. Uniform designs limit aliasing. Biometrika 2002; 89:893–904.10.1093/biomet/89.4.893Search in Google Scholar
11. Fang KT, Liu QM, Zhou YD. Design and modeling of experiments. Beijing, China: Higher Education Press, 2011 (in Chinese).Search in Google Scholar
12. Bas D, Boyac IH. Modeling and optimization I: usability of response surface methodology. J Food Eng 2007;78:836–45.10.1016/j.jfoodeng.2005.11.024Search in Google Scholar
13. Gallagher K, Sambridge M. Genetic algorithms: a powerful tool for large-scale nonlinear optimization problems. Comput Geosci 1994;20:1229–36.10.1016/0098-3004(94)90072-8Search in Google Scholar
14. Zhou M, Sun SD. Genetic algorithms: theory and applications. Beijing, China: National Defence Industrial Press, 1999:18–65 (in Chinese).Search in Google Scholar
15. David JC, Birk AM. Numerically optimizing an annular diffuser using a genetic algorithm with three objectives. ASME Paper No. GT 2012–68205. 2012.Search in Google Scholar
16. Wang J, Chen BL, Rao XZ, Huang J, Li M. Optimization of culturing conditions of Porphyridium cruentum using uniform design. World J Microbiol Biotechnol 2007;23:1345–50.10.1007/s11274-007-9369-8Search in Google Scholar
17. Li WH, Liu LJ, Gong WG. Multi-objective uniform design as a SVM model selection tool for face recognition. Expert Syst Appl 2011;38:6689–95.10.1016/j.eswa.2010.11.066Search in Google Scholar
18. Liang YZ, Fang KT, Xu QS. Uniform design and its applications in chemistry and chemical engineering. Chemometr Intell Lab 2001;58:43–57.10.1016/S0169-7439(01)00139-3Search in Google Scholar
19. Liu XM, Zhang WB. Two Schemes of Multi-Objective Aerodynamics Optimization for Centrifugal Impeller Using Response Surface Model and Genetic Algorithm. ASME Paper No. GT2010–23775. 2010.10.1115/GT2010-23775Search in Google Scholar
20. Luo DH. Optimization of total polysaccharide extraction from Dioscorea Nipponica Makino using response surface methodology and uniform design. Carbohyd Polym 2012;90:284–8.10.1016/j.carbpol.2012.05.036Search in Google Scholar PubMed
21. Devanathan S, Koch PN. Comparison of meta-modeling approaches for optimization. ASME Paper No. IMECE2011–65541. 2011.10.1115/IMECE2011-65541Search in Google Scholar
©2016 by De Gruyter
