Abstract

Evolution strategies belong to the class of evolutionary algorithms which are direct pseudo-stochastic search methods which mimic the principles of Neo-Darwinian evolution. They are known to be powerful optimisation techniques in particular for the solution of multi-modal, noisy and non-differentiable complex problems. For problems where a continuous representation is “natural”, like the geometry of gas turbine blades, evolution strategies are particularly suitable. Besides the choice of the search operators, the representation is one of the most crucial elements in optimisation. The advantages and disadvantages of different approaches are discussed in this work. Furthermore, to evaluate different geometric alternatives the fluid-dynamical properties of the blades have to be estimated. We propose a framework in which a Navier-Stokes solver and a neural network approximation model are combined. In this way, the computationally expensive evaluation of the fluid dynamics can be reduced while guaranteeing correct convergence of the optimisation algorithm. Finally, the optimisation results are discussed and the performance of the optimised and the original blades are compared both for the simulation method and for the transonic windtunnel experiment. In both results it can be seen, that a high performance increase is achieved.

References

1. (1) T. Arslan, E. Ozdemir, M. S. Bright, and D. H. Horrocks. Genetic synthesis techniques for low-power digital signal processing circuits. In Proceedings of the IEE Colloquium On Digital Synthesis, pages 7/1-7/5. IEE, London, UK, Feburuary 1996.
2. (2) R. S. Zebulum, M. A. Pacheco, and M. Vellasco. Synthesis of CMOS operational amplifiers through Genetic Algorithms. In Proceedings of the Brazilian Symposium on Integrated Circuits, SBCCI’98, pages 125-128, Rio de Janeiro, Brazil, September 1998. IEEE.
3. (3) M. S. Bright and T. Arslan. Multi-objective design strategies for high-level low-power design of DSP systems. IEEE International Symposium on Circuits and Systems, ISCAS 99, 1:80-83, May-June 1999.
4. (4) G.M. Robinson. Load cell shape optimisation using genetic algorithms and finite elements analysis. In Proceedings of the 14th IMEKO TC3 Conference, pages 167-172, Warsaw, Poland, 1995.
5. (5) A.J. Keane and S.M. Brown. The design of a satelite boom with enhanced vibration performance using genetic algorithm techniques. In I.C. Parmee, editor, Proceedings of the Conference on Adaptive Computing in Engineering Design and Control 96, pages 107-113, University of Plymouth, Plymouth, 1996.
6. (6) Xin Yao. Evolving artificial neural networks. Proceedings of the IEEE, 87(9):1423-1447, 1999.
7. (7) B. Sendhoff and M. Kreutz. Variable encoding of modular neural networks for time series prediction. In V.W. Porto, editor, Congress on Evolutionary Computation CEC, pages 259-266. IEEE Press, 1999.
8. (8) H. Furuta, K. Maeda, and W. Watanabe. Application of genetic algorithm to aestetic design of bridge structures. In Microcomputers in Civil Engineering, 10/6:415-421, 1995.
9. (9) S. Obayashi, Y. Yamaguchi, and T. Nakamura. Multiobjective genetic algorithm for multidisplinary design of transonic wing planform. Journal of Aircraft, 34(5):690-693, 1997.
10. (10) J Sobieszanski-Sobieski and R. T. Haftka. Multidisciplinary aerospace design optimization: Survery of recent development. In 34th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 1996. AIAA Paper 96-0711.
11. (11) A. Vicini and D. Quagliarella. Airfoil and wing design through hybrid optimization strategies. In 16th Applied Aerodynamics Conference. American Institute of Aeronautics and Astronautics, 1998. AIAA Paper 98-2729.
12. (12) D.J. Doorly. Parallel genetic algorithms for optimization in cfd. In J. Périaux and G. Winter, editors, Genetic Algorithms in Engineering and Computer Science. Wiley, 1995.
13. (13) Brian R. Jones, William A. Crossley, and Anastasios S. Lyrintzis. Aerodynamic and aeroacoustic optimization of airfoils via a parallel genetic algorithm. In Proceedings of the 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, 1998. AIAA Paper 98-4811.
14. (14) D.B. Fogel. Evolutionary Computation. IEEE Press, 1995.
15. (15) H.-P. Schwefel. Evolution and Optimum Seeking. John Wiley & sons, New York, 1995.
16. (16) N. Hansen and A. Ostermeier. Completely derandomized self-adaptation in evolution strategies. Evolutionary Computation, 9(2):159-196, 2001.
17. (17) M. Olhofer, T. Arima, T. Sonoda, and B. Sendhoff. Optimization of a stator blade used in a transonic compressor cascade with evolution strategies. In I. Parmee, editor, Adaptive Computation in Design and Manufacture (ACDM), pages 45-54. Springer Verlag, 2000.
18. (18) T. Arima, T. Sonoda, M. Shirotori, A. Tamura, and K. Kikuchi. A numerical investigation of transonic axial compressor rotor flow using a low-Reynolds number k-e turbulence model. Journal of Turbomachinery, 121:44-58, 1999. Transactions of the ASME.
19. (19) K. Y. Chien. Predictions of channel and boundary-layer flows with a low reynolds number turbulence model. AIAA Journal, 20:33-38, 1982.
20. (20) T. H. Pulliam and D. S. Chaussee. A diagonal form of an implicit approximate factorization algorithm. Journal of Computational Physics, 39:347-363, 1981.
21. (21) S. R. Chakravarthy and S. Osher. A new class of high accuracy tvd schemes for hyperbolic conservation laws. In AIAA 23rd Aerospace Scinces Meeting. American Institute of Aeronautics and Astronautics, 1985. AIAA Paper 85-0363.
22. (22) C. M. Bishop. Neural Networks for Pattern Recognition. Oxford University Press, Oxford, UK, 1995.
23. (23) Y. Jin and B. Sendhoff. Knowledge incorporation into neural networks from fuzzy rules. Neural Processing Letters, 10(3):231-242, 1999.
24. (24) Y. Jin, M. Olhofer, and B. Sendhoff. On evolutionary optimization with approximate fitness functions. In Proceedings of the Genetic and Evolutionary Computation Conference, pages 786-792. Morgan Kaufmann, 2000.
25. (25) J. Redmond and G. Parker. Actuator placement based on reachable set optimization for expected disturbance. Journal Optimization Theory and Applications, 90(2):279-300, August 1996.
26. (26) A. Ratle. Optimal sampling strategies for learning a fitness model. In Proceedings of 1999 Congress on Evolutionary Computation, volume 3, pages 2078-2085, Washington D.C., July 1999.
27. (27) Y. Jin, M. Olhofer, and B. Sendhoff. Managing approximate models in evolutionary aerodynamic design optimization. In Congress on Evolutionary Computation (CEC), volume 2, pages 592-599, Seoul, Korea, May 2001.
28. (28) A. Geist, A. Beguellin, J. Dongarra, W. Jiang, R. Manchek, and V. Sunderam. Parallel Virtual Machine: A Guide to Networked and Parallel Computing. The MIT Press, 1994.
29. (29) M. Olhofer, Y. Jin, and B. Sendhoff. Adaptive encoding for aerodynamic shape optimization using evolution strategies. In Congress on Evolutionary Computation (CEC), volume 2, pages 576-583, Seoul, Korea, May 2001.

Author (organization or company)

• Markus OLHOFER（Honda R&D Europe (Germany) GmbH）
• Toshiyuki ARIMA（Wako Research Center）
• Yaochu JIN（Honda R&D Europe (Germany) GmbH）
• Toyotaka SONODA（Wako Research Center）
• Bernhard SENDHOFF（Wako Research Center）

Publication Information

Article of Honda R&D Technical Review Vol.14 No.1 (203 - 216)

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