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Research Papers: Gas Turbines: Turbomachinery

Research on Metamodel-Based Global Design Optimization and Data Mining Methods

[+] Author and Article Information
Liming Song

Institute of Turbomachinery,
Xi’an Jiaotong University,
No. 28 Xianning West Road,
Xi'an 710049, China
e-mail: songlm@mail.xjtu.edu.cn

Zhendong Guo

Institute of Turbomachinery,
Xi'an Jiaotong University,
No. 28 Xianning West Road,
Xi'an 710049, China
e-mail: ericzhendong@stu.xjtu.edu.cn

Jun Li

Professor
Institute of Turbomachinery,
Xi'an Jiaotong University,
No. 28 Xianning West Road,
Xi'an 710049, China
e-mail: junli@mail.xjtu.edu.cn

Zhenping Feng

Institute of Turbomachinery,
Xi'an Jiaotong University,
No. 28 Xianning West Road,
Xi'an 710049, China
e-mail: zpfeng@mail.xjtu.edu.cn

1Corresponding author.

Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received December 15, 2015; final manuscript received December 20, 2015; published online March 22, 2016. Editor: David Wisler.

J. Eng. Gas Turbines Power 138(9), 092604 (Mar 22, 2016) (14 pages) Paper No: GTP-15-1568; doi: 10.1115/1.4032653 History: Received December 15, 2015; Revised December 20, 2015

The turbomachinery cascades design is a typical high dimensional computationally expensive and black box problem, thus a metamodel-based design optimization and data mining method is proposed and programed in this work, which is intended to gain knowledge of design space except for optimal solutions. The method combines a Kriging-based global algorithm with data mining techniques of self-organizing map (SOM), analysis of variance (ANOVA), and parallel axis. NACA Rotor 37, a typical axial transonic rotor blade, is selected for the research. Through SOM analysis, the overall changing trend of performance indicators like isentropic efficiency, total pressure ratio, and so on for the rotor blade is nearly consistent; therefore, a single-objective design for maximizing isentropic efficiency of the rotor blade with constraints prescribed on total pressure ratio and mass flow rate is carried out. The computational fluid dynamics (CFD) evaluations needed for the Kriging-based optimization process amount to only 1/5 of that required when employing a modified differential evolution (DE) algorithm as the optimizer. The isentropic efficiency of related optimal solution is 1.74% higher than the reference design. Then, the interactions among design variables and critical performance indicators as well as common features of better solutions are analyzed via ANOVA and parallel axis. Particularly, an ANOVA-based optimization is tried, which can validate the detected significant variables and gain knowledge of subspace with minimum cost. By integrating data mining results with practical knowledge of aerodynamics, it is confirmed that the shock wave has the most significant influence on the aerodynamic performance of transonic rotor blades. The sweep in tip section is found to be responsible for slight tradeoff relation between isentropic efficiency and total pressure ratio. The combinations of forward lean, thinner section profile near the blade leading edge, and compound sweep are favorable to get better aerodynamic performance, which is validated by the configuration of optimal solution obtained by MBGO algorithm.

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References

Luo, J. , Xiong, J. , Liu, F. , and McBean, I. , 2011, “ Three-Dimensional Aerodynamic Design Optimization of a Turbine Blade by Using an Adjoint Method,” ASME J. Turbomach., 133(1), p. 011026. [CrossRef]
Benini, E ., 2004, “ Three-Dimensional Multi-Objective Design Optimization of a Transonic Compressor Rotor,” J. Propul. Power, 20(3), pp. 559–565. [CrossRef]
Luo, C. , Song, L. , Li, J. , and Feng, Z. , 2012, “ A Study on Multidisciplinary Optimization of an Axial Compressor Blade Based on Evolutionary Algorithms,” ASME J. Turbomach., 134(5), p. 054501. [CrossRef]
Song, L. , Luo, C. , Li, J. , and Feng, Z. , 2012, “ Automated Multi-Objective and Multidisciplinary Design Optimization of a Transonic Turbine Stages,” Proc. Inst. Mech. Eng., Part A, 226(2), pp. 262–276. [CrossRef]
Guo, Z. , Song, L. , Zhou, Z. , Li, J. , and Feng, Z. , 2015, “ Multi-Objective Aerodynamic Optimization Design and Data Mining of a Highly Pressure Ratio Centrifugal Impeller,” ASME J. Eng. Gas Turbines Power, 137(9), p. 092602. [CrossRef]
Oyama, A. , Liou, M. S. , and Obayashi, S. , 2004, “ Transonic Axial Flow Blade Optimization: Evolutionary Algorithms/Three Dimensional Navier–Stokes Solver,” J. Propul. Power, 20(4), pp. 612–619. [CrossRef]
Jin, Y ., 2011, “ Surrogate-Assisted Evolutionary Computation: Recent Advances and Future Challenges,” Swarm Evol. Comput., 1(2), pp. 61–70. [CrossRef]
Forrester, A. I. J. , and Keane, A. J. , 2009, “ Recent Advances in Surrogate-Based Optimization,” Prog. Aerosp. Sci., 45(1), pp. 50–79. [CrossRef]
OKui, H. , Verstrate, T. , Van den Braembussche, R. A. , and Alsalihi, Z. , 2013, “ Three-Dimensional Design and Optimization of a Transonic Rotor in Axial Flow Compressors,” ASME J. Turbomach., 135(2), p. 031009. [CrossRef]
Samad, A. , Kim, K. Y. , Goel, T. , Haftka, R. T. , and Shyy, W. , 2008, “ Multiple Surrogate Modeling for Axial Compressor Blade Shape Optimization,” J. Propul. Power, 24(2), pp. 301–310. [CrossRef]
Wang, G. G. , and Shan, S. , 2007, “ Review of Metamodeling Techniques in Support of Engineering Design Optimization,” ASME J. Mech. Des., 129(4), pp. 370–380. [CrossRef]
Jones, D. R. , Schonlau, M. , and Welch, W. J. , 1998, “ Efficient Global Optimization of Expensive Black-Box Functions,” J. Global Optim., 13(4), pp. 455–492. [CrossRef]
Jeong, S. , Murayama, M. , and Yamamoto, K. , 2005, “ Efficient Optimization Design Method Using Kriging Model,” J. Aircr., 42(2), pp. 413–420. [CrossRef]
Huang, D. , Allen, T. T. , Notz, W. I. , and Zeng, N. , 2006, “ Global Optimization of Stochastic Black-Box Systems Via Sequential Kriging Meta-Models,” J. Global Optim., 34(3), pp. 441–466. [CrossRef]
Aulich, M. , and Siller, U. , 2011, “ High-Dimensional Constrained Multiobjective Optimization of a Fan Stage,” ASME Paper No. GT2011-45618.
Bagshaw, D. , Ingram, G. , Gregory-Smith, D. , Stokes, M. , and Harvey, N. , 2008, “ The Design of Three-Dimensional Turbine Blades Combined With Profiled Endwalls,” Proc. Inst. Mech. Eng., Part A, 222(1), pp. 93–102. [CrossRef]
Shan, S. , and Wang, G. G. , 2010, “ Survey of Modeling and Optimization Strategies to Solve High-Dimensional Design Problems With Computationally-Expensive Black-Box Functions,” Struct. Multidiscip. Optim., 41(2), pp. 219–241. [CrossRef]
Viana, F. A. C. , Simpson, T. W. , Balabanov, V. , and Toropov, V. , 2014, “ Metamodeling in Multidisciplinary Design Optimization: How Far Have We Really Come?” AIAA J., 52(4), pp. 670–690. [CrossRef]
Chiba, K. , and Obayashi, S. , 2008, “ Knowledge Discovery for Flyback-Booster Aerodynamic Wing Using Data Mining,” J. Spacecr. Rockets, 45(5), pp. 975–987. [CrossRef]
Chiba, K. , Oyama, A. , Obayashi, S. , and Nakahashi, K. , 2007, “ Multidisciplinary Design Optimization and Data Mining for Transonic Regional-Jet Wing,” J. Aircr., 44(4), pp. 1100–1112. [CrossRef]
Oyama, A. , Nonomura, T. , and Fujii, K. , 2010, “ Data Mining of Pareto-Optimal Transonic Airfoil Shapes Using Proper Orthogonal Decomposition,” J. Aircr., 47(5), pp. 1756–1762. [CrossRef]
German, B. J. , Feigh, K. M. , and Daskilewicz, M. J. , 2013, “ An Experimental Study of Continuous and Discrete Visualization Paradigms for Interactive Trade Space Exploration,” ASME J. Comput. Inf. Sci. Eng., 13(2), p. 021004. [CrossRef]
Miller, S. W. , Simpson, T. W. , Yukish, M. A. , Stump, G. , Mesmer, B. L. , Tibor, E. B. , Bloebaum, C. L. , and Winer, E. H. , 2014, “ Toward a Value-Driven Design Approach for Complex Engineered Systems Using Trade Space Exploration Tools,” ASME Paper No. DETC2014-34503.
Vesanto, J ., 1999, “ SOM-Based Data Visualization Methods,” Intell. Data Anal., 3(2), pp. 111–126. [CrossRef]
Schonlau, M. , and Welch, W. J. , 2006, Screening the Input Variables to a Computer Model via Analysis of Variance and Visualization Screening, Springer, New York, pp. 308–327.
Alhoniemi, E. , Himberg, J. , Parhankangas, J. , and Vesanto, J. , 2013, “ SOM Toolbox,” Laboratory of Computer and Information Science, Helsinki University of Technology, Helsinki, Finland, Last accessed June 20, 2014, http://www.cis.hut.fi/projects/somtoolbox/
Fang, K. T. , Lin, D. K. J. , Winker, P. , and Zhang, Y. , 2001, “ Uniform Design: Theory and Applications,” Technometrics, 42(3), pp. 237–248. [CrossRef]
Giunta, A. A. , Wojtkiewicz, S. F., Jr. , and Eldred, M. S. , 2003, “ Overview of Modern Design of Experiments Methods for Computational Simulations,” AIAA Paper No. 2003-0649.
Gutmann, H. M. , 2001, “ A Radial Basis Function Method for Global Optimization,” J. Global Optim., 19(3), pp. 201–227. [CrossRef]
Storn, R. , and Price, K. , 1997, “ Differential Evolution—A Simple and Efficient Heuristic for Global Optimization Over Continuous Spaces,” J. Global Optim., 11(4), pp. 341–359. [CrossRef]
Reid, L. , and Moore, R. D. , 1978, “ Design and Overall Performance of Four Highly Loaded, High-Speed Inlet Stages for an Advanced High-Pressure Ratio Core Compressor,” Paper No. NASA TP 1337.
Moore, R. D. , and Reid, L. , 1980, “ Performance of Single Axial Flow Transonic Compressor With Rotor and Stator Aspect Ratio of 1.19 and 1.26, Respectively, and With Design Pressure Ratio of 2.05,” Paper No. NASA TP 1659.
Gen, M. , and Cheng, R. , 1996, “ Optimal Design of System Reliability Using Interval Programming and Genetic Algorithms,” Comp. Ind. Eng., 31(1–2), pp. 237–240.
Song, L. , Luo, C. , Li, J. , and Feng, Z. , 2011, “ Aerodynamic Optimization of Axial Turbomachinery Blades Using Parallel Adaptive Range Differential Evolution and Reynolds-Averaged Navier–Stokes Solutions,” Int. J. Numer. Methods Biomed. Eng., 27(2), pp. 283–303. [CrossRef]
Benini, E. , and Biollo, R. , 2007, “ Aerodynamics of Swept and Leaned Transonic Compressor-Rotors,” Appl. Energy, 84(10), pp. 1012–1027. [CrossRef]
Daskilewicz, M. , and German, B. , 2015, “ RAVE,” Aerospace Systems Design Laboratory, Georgia Institute of Technology, Atlanta, GA, last accessed July 10, 2015, http://www.rave.gatech.edu/rave.shtml

Figures

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Fig. 1

Metamodel-based design optimization and data mining method

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Fig. 2

Schematic map of SOM: (a) two-dimensional projection and (b) component map

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Fig. 3

Component maps with 2000 neurons

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Fig. 5

Performance validation at off-design conditions

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Fig. 6

SOM component maps of critical parameters: (a) p2t/p1t, (b) m, (c) ηis, (d) c2, and (e) p2s/p1s

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Fig. 7

Three-dimensional blade parameterization of NACA Rotor 37: (a) control point, (b) 2D section profile, (c) spatial folding, and (d) 3D profile

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Fig. 8

Variable range of (a) section profiling, (b) sweep, and (c) compound lean

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Fig. 9

Relative Mach number contours at 90% span: (a) reference design and (b) optimal design

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Fig. 10

Limiting streamlines of the blade and the hub: (a) reference design and (b) optimal design

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Fig. 11

Overall performance of the blade along the span at optimization point

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Fig. 12

Overall performance at off-design conditions

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Fig. 13

Cross validation of Kriging response: (a) ηis, (b) p2t/p1t, and (c) m

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Fig. 14

Variance proportion of significant design variables: (a) ηis, (b) p2t/p1t, and (c) m

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Fig. 15

Main effects of critical performance indicators: (a) ηis, (b) p2t/p1t, and (c) m

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Fig. 16

Overall performance of optimal solutions at optimization point

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Fig. 17

Relative Mach number at 90% span of optimal solutions: (a) reference design, (b) FullOpt, (c) ANOVA_EO, (d) ANOVA_PRO, (e) SectionProfiling_Opt, (f) CompoundLean_Opt, (g) Sweep_EO, and (h) Sweep_PRO

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Fig. 18

Overall performance of optimal solutions for profiling techniques at off-design conditions

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Fig. 19

Interactions of design variables and performance indicators for profiling techniques: (a) compound lean, (b) sweep, (c) section profiling, and (d) full design

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Fig. 20

Variable distribution of optimized solutions

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Fig. 21

Two-dimensional section profile of reference and optimal design at different span: (a) root section, (b) middle section, and (c) tip section

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Fig. 22

Three-dimensional blade profile of (a) reference and (b) optimal designs

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