한국항공우주학회지 (Journal of the Korean Society for Aeronautical & Space Sciences)

  • 제48권3호
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  • Pages.175-185
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  • 2020
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  • 1225-1348(pISSN)
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  • 2287-6871(eISSN)
한국항공우주학회 (The Korean Society for Aeronautical and Space Sciences)
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물리적 구배 정보를 이용한 공력계수 모형화를 위한 GE 크리깅의 적용

Application of Gradient-Enhanced Kriging to Aerodynamic Coefficients Modeling With Physical Gradient Information

  • Kang, Shinseong (Department of Aerospace Engineering, Pusan National University) ;
  • Lee, Kyunghoon (Department of Aerospace Engineering, Pusan National University)
  • 투고 : 2019.10.22
  • 심사 : 2020.01.15
  • 발행 : 2020.03.01
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초록

유도무기는 원통형 형상에서 기인한 기하학적 특성으로 6자유도 공력계수에 물리적 구배 조건을 내포하게 된다. 본 연구는 부가적으로 주어진 물리적 구배 정보를 공력계수 모형화에서 효과적으로 이용할 목적으로 구배 보강 가우스 과정을 사용하였다. 물리적 구배 정보를 활용한 공력계수 예측의 정확성을 살펴보기 위해, 가우스 과정에 기초한 공력계수 예측 모형을 구배 정보의 유무에 따라 각각 구성한 후 서로의 예측 정확도를 비교·분석하였다. 그 결과, 물리적 구배 정보를 고려한 공력계수 예측은 부여된 구배 조건을 정확히 만족하였을 뿐만 아니라 그렇지 않은 모형에 비해 예측 정확도가 더 우수함을 확인하였다. 다만, 구배 보강 가우스 과정으로는 물리적 구배 정보를 연속적으로 부여할 수 없으며 추가된 구배 정보로 인해 공력계수 예측 모형 구성에 요구되는 표본수가 증가하는 단점도 확인하였다.

The six-DOF aerodynamic coefficients of a missile entail inherent physical gradient constraints originated from the geometric characteristics of a cylindrical fuselage. To effectively adopt the freely available gradient information in aerodynamic coefficients modeling, this research employed gradient-enhanced (GE) Gaussian process. To investigate the accuracy of aerodynamic coefficients predicted with gradients information, we compared two Gaussian-process-based models: ordinary and GE Gaussian process models with and without gradient information, respectively. As a result, we found that GE Gaussian process models were able to comply with imposed gradient information and more accurate than ordinary Gaussian process models. However, we also found that GE Gaussian process modeling cannot handle gradient information continuously and ends up with more samples due to additional gradient information.

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참고문헌

  1. Forrester, A., Sobester, A., and Keane, A., Engineering Design via Surrogate Modelling: A Practical Guide, John Wiley & Sons, Chichester, UK, 2008, pp. 49-63.
  2. Forrester, A. I., and Keane, A. J., "Recent Advances in Surrogate-Based Optimization," Progress in Aerospace Sciences, Vol. 45, No. 1-3, 2009, pp. 50-79. https://doi.org/10.1016/j.paerosci.2008.11.001
  3. Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H. P., "Design and Analysis of Computer Experiments," Statistical Science, 1989, pp. 409-423.
  4. Myers, D. E., "Co-Kriging-New Developments," In Geostatistics for Natural Resources Characterization, Springer, Dordrecht, 1984, pp. 295-305.
  5. Myers, D. E., "Matrix Formulation of Co-Kriging," Journal of the International Association for Mathematical Geology, Vol. 14, No. 3, 1982, pp. 249-257. https://doi.org/10.1007/BF01032887
  6. Chung, H. S., and Alonso, J., "Design of a Low-Boom Supersonic Business Jet Using Cokriging Approximation Models," In 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, March 2002, pp. 5598-1-21.
  7. Yamazaki, W., Rumpfkeil, M., and Mavriplis, D., "Design Optimization Utilizing Gradient/Hessian Enhanced Surrogate Model," In 28th AIAA Applied Aerodynamics Conference, November 2010, pp. 4363-1-23.
  8. Joseph, V. R., Hung, Y., and Sudjianto, A., "Blind Kriging: A New Method for Developing Metamodels," Journal of Mechanical Design, Vol. 130, No. 3, 2008, pp. 031102-1-8. https://doi.org/10.1115/1.2829873
  9. Han, Z. H., and Gortz, S., "Hierarchical Kriging Model for Variable-Fidelity Surrogate Modeling," AIAA Journal, Vol. 50, No. 9, 2012, pp. 1885-1896. https://doi.org/10.2514/1.J051354
  10. Ha, H., Oh, S., and Yee, K., "Feasibility Study of Hierarchical Kriging Model in the Design Optimization Process," Journal of the Korean Society for Aeronautical and Space Sciences, Vol. 42, No. 2, 2014, pp. 108-118. https://doi.org/10.5139/JKSAS.2014.42.2.108
  11. Han, Z. H., Görtz, S., and Zimmermann, R., "Improving Variable-Fidelity Surrogate Modeling via Gradient-Enhanced Kriging and a Generalized Hybrid Bridge Function," Aerospace Science and Technology, Vol. 25, No. 1, 2013, pp. 177-189. https://doi.org/10.1016/j.ast.2012.01.006
  12. Jo, Y., and Choi, S., "Variable-Fidelity Aerodynamic Design Using Gradient-Enhanced Kriging Surrogate Model with Regression," In 52nd Aerospace Sciences Meeting, January 2014, pp. 0900-1-29.
  13. Yondo, R., Andres, E., and Valero, E., "A Review on Design of Experiments and Surrogate Models in Aircraft Real-Time and Many-Query Aerodynamic Analyses," Progress in Aerospace Sciences, Vol. 96, 2018, pp. 23-61. https://doi.org/10.1016/j.paerosci.2017.11.003
  14. Laurenceau, J., Meaux, M., Montagnac, M., and Sagaut, P., "Comparison of Gradient-Based and Gradient-Enhanced Response-Surface-Based Optimizers," AIAA Journal, Vol. 48, No. 5, 2010, pp. 981-994. https://doi.org/10.2514/1.45331
  15. Han, Z. H., Zhang, Y., Song, C. X., and Zhang, K. S., "Weighted Gradient-Enhanced Kriging for High-Dimensional Surrogate Modeling and Design Optimization," AIAA Journal, Vol. 55, No. 12, 2017, pp. 4330-4346. https://doi.org/10.2514/1.J055842
  16. Xuan, Y., Xiang, J., Zhang, W., and Zhang, Y., "Gradient-Based Kriging Approximate Model and Its Application Research to Optimization Design," Science in China Series E: Technological Sciences, Vol. 52, No. 4, 2009, pp. 1117-1124. https://doi.org/10.1007/s11431-009-0096-2
  17. Yamazaki, W., Rumpfkeil, M., and Mavriplis, D., "Design Optimization Utilizing Gradient/Hessian Enhanced Surrogate Model," In 28th AIAA Applied Aerodynamics Conference, November 2012, pp. 4363-1-23.
  18. Dwight, R. P., and Brezillon, J., "Effect of Various Approximations of the Discrete Adjoint on Gradient-Based Optimization," AIAA Journal, Vol. 44, No. 12, 2006, pp. 3022-3031. https://doi.org/10.2514/1.21744
  19. Go, B. Y., and Hur, K. H., "A Study on the Effects of Side Jets to the Longitudinal Aerodynamics of Subsonic Missile," Journal of the Korea Institute of Military Science and Technology, Vol. 30, No. 3, 2017, pp. 393-404.