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Publishing Language: Chinese

Robust optimization method based on adaptive sparse polynomial chaos

Zhendong GUO1, Haojie LI1, Liming SONG1( ), Hualiang ZHANG2, Zhao YIN2
School of Energy and Power, Xi'an Jiaotong University, Xi'an 710049, China
Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China
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Abstract

Traditional polynomial chaos is faced with “curse of dimensionality”, and relies on practical tasks and experience to artificially determine the order of orthogonal polynomial expansion. In this paper, an Uncertainty Quantification (UQ) method based on Adaptive Sparse Polynomial Chaos (ASPC) is developed by using relevance vector machine regression to solve the sparse solution of the expansion coefficient and combining with the cross-validation method. The results of the functional example test show that the proposed method requires fewer samples, and is more accurate than the traditional regression method of polynomial chaos. In addition, a Robust Design Optimization (RDO) framework is established by combining the UQ method based on ASPC, the NSGA-II algorithm and the Kriging model. Considering the influence of manufacturing error uncertainty, the aerodynamic RDO of a power turbine cascade is completed with the objective functions of minimising the mean and the variance of the total pressure loss coefficient of cascade. The optimization results in a reduction in the mean of total pressure loss coefficient and a significant reduction in the degree of sensitivity to manufacturing error uncertainty. The mean and variance of the two representative optimized design individuals decrease by 16.41% and 98.57%, respectively, and the total pressure loss coefficient decreases by 13.43% and 2.82%, respectively. Finally, the flow field is analyzed, and the reasons for improved aerodynamic performance of the optimized design are revealed.

Keywords

uncertainty quantificationrobust design optimizationpolynomial chaossurrogate modelpower turbinemanufacturing error
CLC number: V232.4 Document code: A Article ID: 1000-6893(2024)19-630273-15

References

[1]
FU S L. Numerical research of variable-speed power turbine and optimization design[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2020: 29-41(in Chinese).
[2]
LI X Y, JIANG D P, ZHAO J M, et al. Aerodynamic analysis and optimization design of a power turbine[J]. Turbine Technology, 2021, 63(5): 330-332, 361(in Chinese).
Google Scholar
[3]
CHEN C, LI W. Optimization of blade profile of highly-loaded power turbine[J]. Modern Machinery, 2022(1): 1-5(in Chinese).
Google Scholar
[4]
LI X Y, HUO Y X, XU H C, et al. Aerodynamic design and optimization of power turbine for marine gas turbine[J]. Journal of Propulsion Technology, 2023, 44(2): 143-151(in Chinese).
Google Scholar
[5]
BAMMERT K, STOBBE H. Results of experiments for determining the influence of blade profile changes and manufacturing tolerances on the efficiency, the enthalpy drop, and the mass flow of multi-stage axial turbines[C]//Proceedings of ASME 1970 Winter Annual Meeting. New York: ASME, 2015.
Crossref
[6]
BAMMERT K, SANDSTEDE H. Influences of manufacturing tolerances and surface roughness of blades on the performance of turbines[J]. Journal of Engineering for Power, 1976, 98(1): 29-36.
Crossref Google Scholar
[7]
KANG J S, LEE T Y, LEE D Y. Robust optimization for engineering design[J]. Engineering Optimization, 2012, 44(2): 175-194.
Crossref Google Scholar
[8]
DING T, LIU S Y, YUAN W, et al. A two-stage robust reactive power optimization considering uncertain wind power integration in active distribution networks[J]. IEEE Transactions on Sustainable Energy, 2016, 7(1): 301-311.
Crossref Google Scholar
[9]
PAIVA R M, CRAWFORD C, SULEMAN A. Robust and reliability-based design optimization framework for wing design[J]. AIAA Journal, 2014, 52(4): 711-724.
Crossref Google Scholar
[10]
BENTAL A, NEMIROVSKI A. Robust optimization – methodology and applications[J]. Mathematical Programming, 2002, 92(3): 453-480.
Crossref Google Scholar
[11]
KUMAR A, KEANE A J, NAIR P B, et al. Robust design of compressor blades against manufacturing variations[C]//Proceedings of ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. New York: ASME, 2008: 1105-1118.
Crossref
[12]
VINOGRADOV K A, KRETININ G V, OTRYAHINA K V, et al. Robust optimization of the HPT blade cooling and aerodynamic efficiency[C]//Proceedings of ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. New York: ASME, 2016.
Crossref
[13]
REIS C J B, MANZANARES-FILHO N, DE LIMA A M G. Robust optimization of aerodynamic loadings for airfoil inverse designs[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2019, 41(5): 207.
Crossref Google Scholar
[14]
TAO Z, GUO Z D, LI C X, et al. Research on kriging-based uncertainty quantification and robust design optimization[J]. Journal of Engineering Thermophysics, 2019, 40(3): 537-542(in Chinese).
Google Scholar
[15]
XIA Z H, LUO J Q. Robust design optimization of a turbine cascade considering the uncertain changes of inlet flow angle[J]. Journal of Engineering Thermophysics, 2021, 42(1): 121-129(in Chinese).
Google Scholar
[16]
ZHAO H, GAO Z H, XIA L. Efficient robust aerodynamic design optimization method for high-speed NLF airfoil[J]. Acta Aeronautica et Astronautica Sinica, 2022, 43(1): 124894(in Chinese).
Google Scholar
[17]
LUO J Q, CHEN Z S, ZENG X. Robust aerodynamic design optimization of turbine cascades considering uncertainty of geometric design parameters[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(10): 123826(in Chinese).
Google Scholar
[18]
GARZON V E, DARMOFAL D L. Impact of geometric variability on axial compressor performance[J]. Journal of Turbomachinery, 2003, 125(4): 692-703.
Crossref Google Scholar
[19]
SCHNELL R, LENGYEL-KAMPMANN T, NICKE E. On the impact of geometric variability on fan aerodynamic performance, unsteady blade row interaction, and its mechanical characteristics[J]. Journal of Turbomachinery, 2014, 136(9): 091005.
Crossref Google Scholar
[20]
GIEBMANNS A, BACKHAUS J, FREY C, et al. Compressor leading edge sensitivities and analysis with an adjoint flow solver[C]//Proceedings of ASME Turbo Expo 2013: Turbine Technical Conference and Exposition. New York: ASME, 2013.
Crossref
[21]
LI Y, CHU W L, JI T Y. Uncertainty research of effects of blade stagger angle deviation on the performance of rotor[J]. Journal of Xi'an Jiaotong University, 2023, 57(4): 49-59(in Chinese).
Google Scholar
[22]
HAO M Y, BAI B, LI Y Y, et al. Uncertainty quantification on the cooling performance of a transonic turbine vane with upstream endwall misalignment[J]. Journal of Turbomachinery, 2022, 144(12): 121004.
Crossref Google Scholar
[23]
HUANG M, LI Z G, LI J, et al. Efficient uncertainty quantification and sensitivity analysis on the aerothermal performance of turbine blade squealer tip[J]. Journal of Turbomachinery, 2022, 144(5): 051014.
Crossref Google Scholar
[24]
XIU D B, KARNIADAKIS G E. The wiener-askey polynomial chaos for stochastic differential equations[J]. SIAM Journal on Scientific Computing, 2002, 24(2): 619-644.
Crossref Google Scholar
[25]
ZHANG G, BAI J J, WANG L X, et al. Uncertainty analysis of arbitrary probability distribution based on Stieltjes Process[C]//2017 IEEE 21st Workshop on Signal and Power Integrity (SPI). Piscataway: IEEE Press, 2017: 1-3.
Crossref
[26]
TIPPING M E. Sparse Bayesian learning and the relevance vector machine[J]. Journal of Machine Learning Research, 2001, 1: 211-244.
Google Scholar
[27]
MARREL A, IOOSS B, LAURENT B, et al. Calculations of Sobol indices for the Gaussian process metamodel[J]. Reliability Engineering & System Safety, 2009, 94(3): 742-751.
Crossref Google Scholar
[28]
OAKLEY J E, O'HAGAN A. Probabilistic sensitivity analysis of complex models: A Bayesian approach[J]. Journal of the Royal Statistical Society Series B: Statistical Methodology, 2004, 66(3): 751-769.
Crossref Google Scholar
[29]
YANG Y F. Experimental study on aerodynamic characteristics of wide operating condition power turbine and design optimization of low loss blade[D]. Xi'an: Xi'an Jiaotong University, 2023: 29-33(in Chinese).
[30]
SONG L M. Aerodynamic optimization system of axial turbomachinery blades using evolution algorithms[D]. Xi'an: Xi'an Jiaotong University, 2006: 14-24(in Chinese).
[31]
LI B, SONG L M, LI J, et al. Multidisciplinary and multiobjective optimization design of long blade turbine stage[J]. Journal of Xi'an Jiaotong University, 2014, 48(1): 1-6(in Chinese).
Google Scholar
[32]
SONG L M, LI J, FENG Z P. Study on aerodynamic optimization design of transonic turbine twist blade[J]. Journal of Xi'an Jiaotong University, 2005, 39(11): 1277-1281(in Chinese).
Google Scholar
[33]
CHEN Y, SONG L M, WANG L, et al. Application of automatic optimization technology in turbine design[J]. Aeroengine, 2021, 47(4): 59-66(in Chinese).
Google Scholar
[34]
YAN Y, ZHU P Y, SONG L M, et al. Uncertainty quantification of cascade manufacturing error based non-stationary Gaussian process[J]. Journal of Propulsion Technology, 2017, 38(8): 1767-1775(in Chinese).
Google Scholar
[35]
LIU K Y, WU C L, GUO Z T, et al. Uncertainty analysis of effects of manufacturing errors on aerodynamic performance of supersonic cascades[J/OL]. Journal of Aerospace Power, (2022-12-27)[2023-12-29]. https://doi.org/10.13224/j.cnki.jasp.20220791(in Chinese).
Google Scholar
[36]
BUNKER R S. The effects of manufacturing tolerances on gas turbine cooling[J]. Journal of Turbomachinery, 2009, 131(4): 041018.
Crossref Google Scholar
[37]
ALEXEEV R A, TISHCHENKO V A, GRIBIN V G, et al. Turbine blade profile design method based on Bezier curves[J]. Journal of Physics: Conference Series, 2017, 891: 012254.
Crossref Google Scholar
[38]
HAMAKHAN I A, KORAKIANITIS T. Aerodynamic performance effects of leading-edge geometry in gasturbine blades[J]. Applied Energy, 2010, 87(5): 1591-1601.
Crossref Google Scholar
Acta Aeronautica et Astronautica Sinica
Volume 45 Issue 19,
October 2024
DOI: 10.7527/S1000-6893.2024.30273
Cite this article:
GUO Z, LI H, SONG L, et al. Robust optimization method based on adaptive sparse polynomial chaos. Acta Aeronautica et Astronautica Sinica, 2024, 45(19). https://doi.org/10.7527/S1000-6893.2024.30273

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Received: 01 February 2024
Revised: 21 February 2024
Accepted: 15 March 2024
Published: 15 October 2024
© 2024 The Journal of Acta Aeronautica et Astronautica Sinica
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