A Least Square Support Vector Machine Approach Based on Uniform Design Method for Structural Reliability Analysis

Abstract:

Since the performance functions of large complex structures can not be expressed explicitly in the process of reliability analysis, support vector machines (SVM) with good ability of generalization are used as the response surface function based on the small training samples. The uniform design method was adopted in selecting the training data. The least support vector machines (LS-SVM) were used to find the support vectors. The limit state function was expressed by the LS-SVM regression. Reliability analysis was then performed by the usual reliability method (e.g., the first-order reliability method, the second-order reliability method or Monte Carlo) on the response surface. The results of calculations of numerical examples and a typical cable-stayed bridge show that LS-SVM using the uniform design method can well approximate the real response of complex structures which has a good efficiency and accuracy and can be applied in complex structures.

• Periodical: Advanced Materials Research (Volumes 163-167)
• Pages: 3348-3353
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.163-167.3348
• Online since: December 2010
• Authors: Xiao Lin Yu, Heng Bin Zheng, Quan Sheng Yan, Wei Li
• Keywords: Cable-Stayed Bridge, Least Squares Support Vector Machines (Ls-SVM), Reliability, Response Surface Method (RSM), Uniform Design Method

References

[1] V. N. Vapnik: The Nature of Statistical Learning Theory (Springer-Verlag, New York, 1995).

[2] W.L. JIN, C.X. TANG and J. CHENG: Chinese Journal of Computational Mechanic, Vol. 24(2007), p.713 (In Chinese).

[3] W. ZHAO and J.K. LIU: Journal of Mechanical Strength, Vol. 30(2008), p.916 (In Chinese).

[4] W.L. JIN and X.X. YUAN: Journal of Zhejiang University, Vol. 41(2007), p.44 (In Chinese).

[5] J. A. K. Suykens and J. Vandewale: Neural Network Letters, Vol. 19(1999), p.293.

[6] N.Y. DENG and Y.J. TIAN. Support vector machine—theroy, algorithm and expand(Science Press, Beijing, 2009). (In Chinese).

[7] K.T. FANG and C.X. MA: Orthogonal and uniform experimental design(Science Press, Beijing, 2001). (In Chinese).

[8] X. L. Guan and R. E. Melchers: Structural Safety, Vol. 16(2001), p.229.

[9] A. Haldar and S. Mahadevan: Reliability assessment using stochastic element analysis(Wiley, New York, 2000).

[10] J. Deng, D. Gu and X. Li, et.: Structural Safety, Vol. 35(2005), p.459.

[11] J. Deng: International Journal of Solids and Structures, Vol. 48(2006), p.225.