Neural Computing and Applications

, Volume 18, Issue 5, pp 477–484 | Cite as

A gradient-based sequential radial basis function neural network modeling method

ISNN 2008


Radial basis function neural network (RBFNN) is widely used in nonlinear function approximation. One of the key issues in RBFNN modeling is to improve the approximation ability with samples as few as possible, so as to limit the network’s complexity. To solve this problem, a gradient-based sequential RBFNN modeling method is proposed. This method can utilize the gradient information of the present model to expand the sample set and refine the model sequentially, so as to improve the approximation accuracy effectively. Two mathematical examples and one practical problem are tested to verify the efficiency of this method.


RBFNN Sequential modeling Gradient 


  1. 1.
    Park J, Sandberg W (1991) Universal approximation using radial basis function networks. Neural Comput 3(2):246–257. doi:10.1162/neco.1991.3.2.246 CrossRefGoogle Scholar
  2. 2.
    Fang H, Horstemeyer (2005) Metamodeling with radial basis functions. In: The 46th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conferrence, paper no. AIAA 2005-2059, AustinGoogle Scholar
  3. 3.
    Wu Z (1995) Compactly supported positive definite radial function. Adv Comput Math 4:283–292MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Wendland H (1999) On the smoothness of positive definite and radial functions. J Comput Appl Math 101:177–188. doi:10.1016/S0377-0427(98)00218-0 MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Chen S, Cowan CF, Grant PM (1991) Orthogonal least square algorithm for radial basis function networks. IEEE Trans Neural Netw 2:302–309. doi:10.1109/72.80341 CrossRefGoogle Scholar
  6. 6.
    Xiaofang Y, Yaonan W, Wei S, Huiqian Y (2005) A hybrid learning algorithm for RBF neural networks based on support vector machines and BP algorithms. J Hunan Univ 32(3):88–92 in Chinese. Natural SciencesGoogle Scholar
  7. 7.
    Lin Y, Mistree F, Allen JK, Tsui KL, Chen VCP (2004) Sequential metamodeling in engineering design. In: The 10th AIAA/ISSMO multidisciplinary analysis and optimization conference, paper no. AIAA 2004-4304, AlbanyGoogle Scholar
  8. 8.
    Lin Y (2004) An efficient robust concept exploration method and sequential exploratory experimental design. PhD dissertation, Philosophy in Mechanical Engineering, Georgia Institute of TechnologyGoogle Scholar
  9. 9.
    Krishnamurthy T (2003) Response surface approximation with augmented and compactly supported radial basis functions. In: The 44th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, paper no. AIAA 2003-1748. NorfolkGoogle Scholar
  10. 10.
    Jin R, Chen W, Sudjianto A (2002) On sequential sampling for global metamodeling in engineering design. In: ASME 2002 design engineering technical conferences and computer and information in engineering conference, paper no. DETC2002/DAC-34092, MontrealGoogle Scholar
  11. 11.
    Yao W (2007) Research on uncertainty multidisciplinary design optimization theory and application to satellite system design (in Chinese). Master of engineering dissertation, National University of Defense TechnologyGoogle Scholar
  12. 12.
    Giunta AA, Wojtkiewicz SF Jr, Eldred MS (2003) Overview of modern design of experiments methods for computational simulations. In: 41st aerospace sciences meeting and exhibit, paper no. AIAA 2003-649, RenoGoogle Scholar
  13. 13.
    Giunta AA, Watson LT (1998) A comparison of approximation modeling techniques: polynomial versus interpolating models. In: The 7th AIAA/USAF/NASA/ISSMO symposium on multidisciplinary analysis and optimization, paper no. AIAA 98-4758, LouisGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2009

Authors and Affiliations

  1. 1.Multidisciplinary Aerospace Design Optimization Research Center, College of Aerospace and Material EngineeringNational University of Defense TechnologyChangshaChina

Personalised recommendations