This paper is concerned with robust aerodynamic design of compressor blades against erosion. The proposed approach combines a multiobjective genetic algorithm with geometry modeling methods, high-fidelity computational fluid dynamics, and surrogate models to arrive at robust designs on a limited computational budget. The multiobjective formulation used here allows explicit trade-off between the mean and variance of the performance to be carried out. Detailed numerical studies are presented for robust geometric design of a typical compressor fan blade section to illustrate the proposed methodology. The performance of a selected robust optimal solution on the Pareto front is compared to a deterministic optimal solution to demonstrate that significant improvements in the mean shift and variance can be achieved.
Issue Section:
Research Papers
Keywords:
design engineering,
aerodynamics,
genetic algorithms,
computational fluid dynamics,
compressors,
fans,
blades,
robust design,
multiobjective optimization,
surrogate modeling,
compressor blades,
erosion
Topics:
Blades,
Compressors,
Computational fluid dynamics,
Design,
Erosion,
Modeling,
Pressure,
Geometry
1.
Metwally
, M.
, Tabakoff
, W.
, and Hamed
, A.
, 1995, “Blade Erosion in Automotive Gas Turbine Engine
,” J. Eng. Gas Turbines Power
0742-4795, 117
, pp. 213
–219
.2.
Hamed
, A.
, Tabakoff
, W.
, and Sing
, D.
, 1998, “Modeling of Compressor Performance Deterioration Due to Erosion
,” Int. J. Rotating Mach.
1023-621X, 4
, pp. 243
–248
.3.
Roberts
, W. B.
, 1984, “Axial Compressor Performance Restoration by Blade Profile Control
,” AIAA-84-GT-232, ASME.4.
Kumar
, A.
, Nair
, P. B.
, Keane
, A. J.
, and Shahpar
, S.
, 2005, “Probabilistic Performance Analysis of Eroded Compressor Fan Blades
,” ASME Power PWR2005-50070.5.
Zang
, T. A.
, Hemsch
, M. J.
, Hilburger
, M. W.
, Kenny
, S. P.
, Luckring
, J. M.
, Maghami
, P.
, Padula
, S. L.
, and Stroud
, W. F.
, 2002, “Needs and Opportunities for Uncertainty-Based Multidisciplinary Design Methods for Aerospace Vehicles
,” Technical Report NASA/TM-2002-211462, NASA Langley Research Center
, Hampton, VA.6.
Phadke
, M. S.
, 1989, Quality Engineering using Robust Design
, Prentice Hall
, Englewood Cliffs, NJ
.7.
Taguchi
, G.
, and Wu
, Y.
, 1980, Introduction to Off-Line Quality Control
, Central Japan Quality Control Association
, Nagoya, Japan
.8.
Taguchi
, G.
, 1986, Introduction to Quality Engineering
, UNIPUB/Krauss International
, New York
.9.
Nair
, V. N.
, 1992, “Taguchi’s Parameter Design: A Panel Discussion
,” Technometrics
0040-1706, 34
, pp. 127
–161
.10.
Trosset
, M. W.
, 1996, “Taguchi and Robust Design
,” Technical Report No. 96–31, Houston, TX.11.
Box
, G. E. P.
, 1988, “Signal-to-Noise Ratios, Performance Criteria, and Transformations (with discussions)
,” Technometrics
0040-1706, 30
(1
), pp. 1
–17
.12.
Trosset
, M. W.
, Alexandrov
, N. M.
, and Watson
, L. T.
, 2003, “New Methods for Robust Design Using Computer Simulations
,” American Statistical Association, 2003, Proceedings of the Section on Physical and Engineering Science
.13.
Welch
, W. J.
, Yu
, T. K.
, Kang
, S. M.
, and Sacks
, J.
, 1990, “Computer Experiments for Quality Control
,” J. Quality Technol.
0022-4065, 22
, pp. 15
–22
.14.
Welch
, W. J.
, and Sacks
, J.
, 1991, “A System for Quality Improvement via Computer Experiments
,” Commun. Stat: Theory Meth.
0361-0926, 20
, pp. 477
–495
.15.
Ben-Tal
, A.
, and Nemirovski
, A.
, 1997, “Robust Truss Topology Design via Semidefinite Programming
,” SIAM J. Optim.
1052-6234, 7
, pp. 991
–1016
.16.
Gunawan
, S.
, and Azarm
, S.
, 2004, “Non-gradient Based Parameter Sensitivity Estimation of Single Objective Robust Design Optimization
,” ASME J. Mech. Des.
1050-0472, 126
, pp. 395
–402
.17.
Huyse
, L.
, and Lewis
, R.
, 2001, “Aerodynamic Shape Optimization of Two-Dimensional Airfoils Under Uncertain Operating Conditions
,” Technical Report NASA/CR-2001-210648, Langley Research Center
, Hampton, VA.18.
Li
, W.
, Huyse
, L.
, and Padula
, S.
, 2002, “Robust Airfoil Optimization to Achieve Drag Reduction Over a Range of Mach Numbers
,” Struct. Multidiscip. Optim.
1615-147X, 24
, pp. 38
–50
.19.
Tsutsui
, S.
, and Ghosh
, A.
, 1997, “Genetic Algorithms with a Robust Solution Searching Scheme
,” IEEE Trans. Evol. Comput.
1089-778X, 1
, pp. 201
–208
.20.
Tsutsui
, S.
, Ghosh
, A.
, and Fujimoto
, Y.
, 1996, “A Robust Solution Searching Scheme in Genetic Search
,” in Proceedings of Parallel Problem Solving in Nature
, pp. 543
–552
.21.
Huyse
, L.
, 2001, “Solving Problems of Optimization Under Uncertainty as Statistical Decision Problem
,” AIAA Pap.
0146-3705, 2001
–1519
.22.
Parkinson
, D. B.
, 1997, “Robust Design by Variability Optimization
,” Qual. Reliab. Eng. Int
0748-8017, 13
, pp. 97
–102
.23.
Al-Widyan
, K.
, and Angeles
, J.
, 2005, “A Model-Based Formulation of Robust Design
,” ASME J. Mech. Des.
1050-0472, 127
, pp. 388
–396
.24.
Jin
, Y.
, and Branke
, J.
, 2005, “Evolutionary Optimization in Uncertain Environments: A Survey
,” IEEE Trans. Evol. Comput.
1089-778X, 9
(3
), pp. 303
–317
.25.
Garzon
, V. E.
, 2003, “Probabilistic Aerothermal Design of Compressor Airfoils
,” Ph.D. thesis, Massachusetts Institute of Technology.26.
Das
, I.
, 2000, “Robustness Optimization for Constrained Nonlinear Programming Problems
,” Eng. Optimiz.
0305-215X, 32
(5
), pp. 585
–618
.27.
Jin
, Y.
, and Branke
, J.
, 2003, “Tradeoff Between Performance and Robustness: An Evolutionary Multiobjective Approach
,” Evolutionary Multi-Criterion Optimization
, Springer
, Berlin
, LNCS 2632.28.
Chen
, W.
, Allen
, J. K.
, Tsui
, K.-L.
, and Mistree
, F.
, 1996, “A Procedure for Robust Design: Minimizing Variations Caused by Noise Factors and Control Factors
,” ASME J. Mech. Des.
1050-0472, 118
, pp. 478
–485
.29.
Scott
, M. J.
, and Antonsson
, E. K.
, 2005, “Compensation and Weights for Trade-Offs in Engineering Design: Beyond the Weighted Sum
,” ASME J. Mech. Des.
1050-0472, 127
, pp. 1045
–1055
.30.
Das
, I.
, and Dennis
, J. E.
, 1997, “A Closer Look at Drawbacks of Minimizing Weighted Sum of Objectives for Pareto Set Generation in Multicriteria Optimization Problems
,” Struct. Optim.
0934-4373, 14
, pp. 63
–69
.31.
Chen
, W.
, Wiecek
, M. M.
, and Zhang
, J.
, 1998, “Quality Utility: A Compromise Programming Approach to Robust Design
,” ASME DETC98/DAC5601.32.
Fonseca
, C. M.
, and Fleming
, P. J.
, 1993, “Genetic Algorithm for Multi-Objective Optimization: Formulation, Discussion and Generalization
,” Proceedings of the Fifth International Conference on Genetic Algorithms
, S.
Forrest
, ed., San Mateo, CA
.33.
Horn
, J.
, Nafploitis
, N.
, and Goldberg
, D. E.
, 1994, “A Niched Pareto Genetic Algorithm for Multi-Objective Optimization
,” Proceedings of the First IEEE Conference on Evolutionary Computation
, Z.
Michalewicz
, ed., Piscataway, NJ
.34.
Zitler
, E.
, and Thiele
, L.
, 1999, “Multiobjective Evolutionary Algorithms: A Comparitive Case Study and the Strength Pareto Approach
,” IEEE Trans. Evol. Comput.
1089-778X, 3
, pp. 257
–271
.35.
Fieldsend
, J. E.
, Everson
, R. M.
, and Singh
, S.
, 2003, “Using Unconstrained Elite Archives for Multiobjective Optimization
,” IEEE Trans. Evol. Comput.
1089-778X, 7
, pp. 305
–323
.36.
Deb
, K.
, Pratap
, A.
, Agarwal
, S.
, and Meyarivan
, T.
, 2002, “A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II
,” IEEE Trans. Evol. Comput.
1089-778X, 6
, pp. 182
–197
.37.
Hicks
, R. M.
, and Henne
, P. A.
, 1998, “Wing Design by Numerical Optimisation
,” J. Aircr.
0021-8669, 15
(7
), pp. 407
–412
.38.
Wu
, H. Y.
, Yang
, S.
, and Liu
, F.
, 2003, “Comparison of Three Geometric Representation of Airfoils for Aerodynamic Optimization
,” AIAA Pap.
0146-3705, 2003
–4095
.39.
Shahpar
, S.
, and Lapworth
, L.
, 2003, “Parametric Design and Rapid Meshing Systems for Turbomachinery Optimisation
,” ASME-GT2003-38698.40.
Moinier
, P.
, 1999, “Algorithm Developments for an Unstructured Viscous Flow Solver
,” Ph.D. thesis, Oxford University, Oxford.41.
Moinier
, P.
, Muller
, J. D.
, and Giles
, M. B.
, 1999, “Edge-Based Multigrid and Preconditioning for Hybrid Grids
,” AIAA Pap.
0146-3705, 99
–3339
.42.
Keane
, A. J.
, and Nair
, P. B.
, 2005, Computational Approaches for Aerospace Design
, Wiley
, New York
.43.
Matheron
, G.
, 1963, “Principles of Geostatistics
,” Econ. Geol.
0361-0128, 58
, pp. 1246
–1266
.44.
Neal
, R. M.
, 1996, Bayesian Learning for Neural Networks
, Springer
, New York
.45.
MacKay
, D. J. C.
, 1997, “Gaussian Processes-A Replacement for Supervised Neural Networks
,” Tutorial lecture Notes for NIPS, at http://www.inference.phy.cam.ac.uk/mackay/abstracts/gp.htmlhttp://www.inference.phy.cam.ac.uk/mackay/abstracts/gp.html, 1997.46.
Jones
, D. R.
, Schonlau
, M.
, and Welch
, W. J.
, 1998, “Efficient Global Optimization of Expensive Black-Box Functions
,” J. Global Optim.
0925-5001, 13
(4
), pp. 455
–492
.47.
Nair
, P. B.
, Choudhary
, A.
, and Keane
, A. J.
, 2001, “A Bayesian Framework for Uncertainty Analysis Using Deterministic Black-Box Simulation Code
,” AIAA Pap.
0146-3705, 2001
–1676
.48.
Keane
, A. J.
, 2003, “Wing Optimization Using Design of Experiment, Response Surface, and Data Fusion Methods
,” J. Aircr.
0021-8669, 40
, pp. 741
–750
.49.
Sacks
, J.
, Welch
, W. J.
, Mitchell
, T. J.
, and Wynn
, H. P.
, 1989, “Design and Analysis of Computer Experiments
,” Stat. Sci.
0883-4237, 4
(4
), pp. 409
–435
.50.
Schonlau
, M.
, 1997, “Computer Experiments and Global Optimization
,” Ph.D. thesis, University of Waterloo.51.
Chen
, W.
, Jin
, R.
, and Sudjianto
, A.
, 2005, “Analytical Variance-Based Global Sensitivity Analysis in Simulation-Based Design Under Uncertainty
,” ASME J. Mech. Des.
1050-0472, 127
, pp. 875
–884
.52.
Sobol
, I. M.
, 1994, A Primer for the Monte Carlo Method
, CRC Press
, Boca Raton
.53.
Athan
, T. W.
, and Papalambros
, P. Y.
, 1996, “A Note on Weighted Criteria Methods for Compromise Solutions in Multi-Objective Optimization
,” Eng. Optimiz.
0305-215X, 27
(2
), pp. 155
–176
.54.
Koski
, J.
, 1985, “Defectiveness of Weighting Method in Multicriterion Optimization of Structures
,” Commun. Appl. Numer. Methods
0748-8025, 1
, pp. 333
–337
.55.
Deb
, K.
, 1999, “Multi-Objective Genetic Algorithms: Problem Difficulties and Construction of Test Functions
,” Evol. Comput.
1063-6560, 7
, pp. 205
–230
.Copyright © 2006
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