DOI QR코드

DOI QR Code

Approximation of Green Warranty Function by Radon Radial Basis Function Network

Radon RBF Network에 의해 그린 보증 함수의 근사화

  • Received : 2012.05.10
  • Accepted : 2012.06.08
  • Published : 2012.06.30

Abstract

As the price of traditional fuels soar, the alternatives are becoming more viable. And manufacturers are promoting the growing viability of electric and biofuel-powered vehicles through longer warranties. Now, these longer green environment (emission)warranties, sometimes called extended warranties or "super warranties," have been adapted. The main result of this paper is to present a new method to approximate a bivariate warranty function by using Radial Basis Function Network with application of Radon Transform and its inverse which is used to reduce the dimension of the warranty space. This method consist of the following stages: First, by using the Radon Transform, the bivariate warranty function can be reduced to one dimensional function. Second, each of the one dimensional functions is approximated by using neural network technique into neural sub-networks. Third, these neural sub-networks are combined together to form the final approximation neural network. Four, by using the inverse of radon transform to this final approximation neural network we get the approximation to the given function. Also, we apply the above method to some green warranty data of automotive vehicle company.

오래 전부터 연료의 가격은 상승하고 있다. 제조업체는 보증을 통해 실용적인 대안을 찾고자 전기와 강력한 바이오 연료를 이용하여 차량의 성장가능을 연구하고 있다. 이제, 이러한 녹색 환경(emission) 관련된 보증은 보증기간이 확장되며, 이러한 보증을 "수퍼 보증" 이라 불린다. 본 논문의 주요 결과는 라돈 변환의 역행렬을 보증공간의 수치를 줄이기 위해 사용되며, 응용 프로그램 및 RBF 네트워크를 사용하여 대략적인 이변량의 보증 기능에 새로운 방법을 제시한다. 이 방법은 다음과 같은 단계로 구성되어 있다. 첫째, 라돈 변환을 이용하여, 이변량 보증 함수의 1차원 함수를 줄일 수 있다. 둘째, 1 차원 함수의 각 신경 서브 네트워크와 신경 네트워크 기법을 사용하여 근사할 수 있다. 셋째, 이러한 신경 sub-networks 형태로 최종 근사 신경망 함께 결합 된다. 넷째, 라 돈 변환의 역함수 값을 사용 하여 최종 근사 신경 네트워크에 우리가 주어진 함수 근사화를 얻을 수 있다. 또한, 우리는 자동차 회사의 일부 그린 보증 데이터를 가지고 위의 방법을 적용한다.

Keywords

References

  1. B. J. C. Baxter, N. Sivakumar and J. D. Ward. Regarding the p-norms of Radial basis interpolation matrices, Constructive Approximation, Vol. 10, No. 4, pp. 451-468 (1994) https://doi.org/10.1007/BF01303522
  2. K. Ciesielski, J. P. Sacha and K. J. Cios. Synthesis of Feed forward Networks in Supermom Error Bound, IEEE Transactions on Neural Networks, Vol. 11, No. 6, pp. 1213-1227 (2000) https://doi.org/10.1109/72.883398
  3. S. R. Deans The Radon Transform and some of its applications, Publisher by John Wiley and Sons (1983)
  4. S. W. Ellacot, Aspects of the numerical analysis of neural networks, Acta Numerica, Cambridge University Press, Vol. 3, pp. 145-202 (1994)
  5. S. H. Lee, S. J. Lee, and K. I. Moon, A Fuzzy Logic-Based Approach to Two-Dimensional Automobile Warranty System, Journal of Circuits, Systems, and Computers, Vol. 19, No. 1, pp.139-154 (2010) https://doi.org/10.1142/S0218126610005974
  6. S. H. Lee, E. C. Lee, and K. I. Moon, "Neural Network Approach for Greenery Warranty Systems." Advanced Intelligent Computing Theories and Applications - 6th International Conference on Intelligent Computing, ICIC 2010, Changsha, China, (2010) August 18-21.
  7. W. A. Light and E. W. Cheney, Interpolation by periodic Radial basis functions, Mathematical Analysis and Applications, Vol. 168, pp. 111-130 (1992) https://doi.org/10.1016/0022-247X(92)90193-H
  8. S. Lolas, O. A. Olatunbosun, D. Steward, and J. Buckingham, Fuzzy Logic Knowledge Base Construction for a Reliability Improvement Expert System, Proceedings of the World Congress on Engineering ( 2007) Vol I WCE.
  9. P. Niyogi, and F. Girosi On the relationship between generalization error, hypothesis complexity, and sample complexity for Radial basis functions, J. of Neural Computation, Vol. 8, pp. 819-842 (1996) https://doi.org/10.1162/neco.1996.8.4.819
  10. M. J. L. Orr, Introduction to Radial basis function networks, Center for Cognitive Science, University of Edinburgh, Scotland, (1996)
  11. J. Radon, On the determination of functions from their integrals along certain manifolds, Berichte Sächsische Akademie der Wissenschaften, Leipzig, Math-Phys. Kl, Vol. 69, pp. 262-267 (1917)
  12. B. Rai and N. Singh, Hazard rate estimation from incomplete and unclean warranty data, Reliability Engineering and System Safety, Vol. 81, pp. 79-92. (2003) https://doi.org/10.1016/S0951-8320(03)00083-8
  13. M. P. Sampat, G. J. Whitman, M. K. Markey and A. C. Bovik, Evidence Based Detection of Spiculated Masses and Architectural Distortions, Medical Imaging 2005: Image Processing 5747 (2005): pp. 26-37.