DOI QR코드

DOI QR Code

Global Function Approximations Using Wavelet Neural Networks

웨이블렛 신경망을 이용한 전역근사 메타모델의 성능비교

  • 신광호 (연세대학교 대학원 기계공학과) ;
  • 이종수 (연세대학교 기계공학부)
  • Published : 2009.08.01

Abstract

Feed-forward neural networks have been widely used as function approximation tools in the context of global approximate optimization. In the present study, a wavelet neural network (WNN) which is based on wavelet transform theory is suggested as an alternative to a traditional back-propagation neural network (BPN). The basic theory of wavelet neural network is briefly described, and approximation performance is tested using a nonlinear multimodal function and a composite rotor blade analysis problem. Laplacian of Gaussian function, Mexican function, and Morlet function are considered during the construction of WNN architectures. In addition, approximation results from WNN are compared with those from BPN.

Keywords

Global Function Approximation;Feed-Forward Neural Networks;Wavelet Neural Network;Wavelet Transform

References

  1. Gondal, Z. and Lee, J., 2008, 'Reliability Assessment Using Neural Network Based Approximations and Monte Carlo Simulation,' Proceedings of the 5th China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems, Jeju, Korea
  2. Chung, S., Min, S., Lee, T., Choi, D.-H., Lee, J., Volovoi, V. and Mavris, D., 2005, 'Metamodeling of High Dimensional Models Using Sequential Adaptive Radial Basis Function,' Proceedings of the 6th World Congress on Structural and Multidisciplinary Optimization, Rio de Janeiro, Brazil
  3. Lee, J. and Hajela, P., 1996, 'Parallel Genetic Algorithm Implementation in Multidisciplinary Rotor Blade Design,' Journal of Aircraft, Vol. 33, No. 5, pp. 962~969 https://doi.org/10.2514/3.47042
  4. Lee, J. and Kim, S., 2007, 'Optimal Design of Engine Mount Rubber Considering Stiffness and Fatigue Strength,' Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, Vol. 221, No. 7, pp. 823~835 https://doi.org/10.1243/09544070JAUTO433
  5. Lee, J., Jeong, H. and Kang, S., 2008, 'Derivative and GA Based Methods in Meta-Modeling of Back-Propagation Neural Networks for Constraint Approximate Optimization,' Structural and Multidisciplinary Optimization, Vol. 35, No. 1, pp. 29~40 https://doi.org/10.1007/s00158-007-0110-x
  6. Yacine, O. and Gerard, D., 2000, 'Initialization by Selection for Wavelet Network Training,' Neurocomputing, Vol. 34, pp.131~143. https://doi.org/10.1016/S0925-2312(00)00295-2
  7. Zhang, Q. and Benveniste, A., 1992, 'Wavelet Networks,' IEEE Transactions on Neural Networks, Vol. 3, No. 6, pp. 889~898 https://doi.org/10.1109/72.165591
  8. Zhou, B., Shi, A, Cai, F. and Zhang, Y., 2004, 'Wavelet Neural Networks for Nonlinear Time Series Analysis,' ISNN 2004, Vol. 3174, pp. 430~435
  9. Yu, W., Hodges, D. H., Volovoi, V. V. and Cesnik, C. E. S., 2002, 'On Timoshenko Like Modeling of Initially Curved and Twisted Composite Beams,' International Journal of Solids and Structures, Vol. 39, No. 7, pp. 5185~5203 https://doi.org/10.1016/S0020-7683(02)00399-2
  10. Lee, J., Jeong, H., Choi, D.-H., Volovoi, V. and Mavris, D., 2007, 'An Enhancement of Constraint Feasibility in BPN Based Approximate Optimization,' Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issues 17-20, pp. 2147~2160 https://doi.org/10.1016/j.cma.2006.11.005
  11. Hornik, K., Stinchcombe, M. and White, H., 1990, 'Universal Approximation of an Unknown Mapping and Its Derivatives Using Multilayer Feed-forward Networks,' Neural Networks, Vol. 3, pp. 551~560 https://doi.org/10.1016/0893-6080(90)90005-6
  12. Lee, J. and Kim, D., 2006, 'A Method of Genetic Algorithm Based Multiobjective Optimization via Cooperative Coevolution,' Journal of Mechanical Science and Technology, Vol. 20, No. 12, pp. 2141~2149 https://doi.org/10.1007/BF02916328
  13. Lee, J. and Kang, S., 2007, 'GA Based Meta- Modeling of BPN Architecture for Constrained Approximate Optimization,' International Journal of Solids and Structures, Vol. 44, No. 18~19, pp. 5980~5993 https://doi.org/10.1016/j.ijsolstr.2007.02.008
  14. Cesnik, C. E. S. and Hodges, D. H., 1997, 'A New Concept for Composite Rotor Blade Cross-Sectional Modeling,' Journal of American Helicopter Society, Vol. 42, No. 1., pp.27~38 https://doi.org/10.4050/JAHS.42.27
  15. Oussar, Y. and Rivals, I., 1998, 'Training Wavelet Networks for Nonlinear Dynamic Input-Output Modeling,' Neurocomputing, Vol. 20, pp.173~188 https://doi.org/10.1016/S0925-2312(98)00010-1

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