Least Squares Support Vector Machine-based Advance Monte Carlo Methods for Reliability Analysis of Structures

Document Type : Research Note

Authors

Yazd University

Abstract

The failure probability of structures are rather small and therefore calculation of structural reliability generally has a high computational cost. In order to reduce computational costs, this articles proposes a hybrid approach based on combination of the least squares support vector regression and two advanced Monte Carlo methods: importance sampling and Latin hypercube sampling. Two frames and one truss example are used to evaluate the performance of the proposed algorithm. Results demonstrate that proposed method provides an accurate estimation of failure probability and that the computational costs are lower than those of other methods

Keywords


1. Nowak, A.S., Collins, K.R., "Reliability of Structures", McGraw-Hill., Boston, pp. 1-6, (2000).
2. Hurtado, J.E., "An Examination of Methods for Approximating Implicit Limit State Functions From the Viewpoint of Statistical Learning Theory", Structural Safety, Vol. 26, pp. 271-293, (2004).
3. Zhang, H., Robert, L., Muhanna, R., and Almgren, R., " Interval Monte Carlo Methods for Structural Reliability", Structural Safety, Vol. 32, pp. 183–190, (2010).
4. Rackwitz, R., "Response Surfaces in Structural Reliability", Berichte Zur Zuverl Assign Keits Theorie der Bauwerke, Heft 67 Munchen, (1982).
5. Deng, J., Gu, D., Li, X. and Yue, Z.Q., "Structural Reliability Analysis for Implicit Performance Functions Using Artificial Neural Network", Structural Safety, Vol. 27, pp. 25–48, (2005).
6. Gomes, H.M., Awruch, A.M., "Comparison of Response Surface and Neural Network With Other Methods for Structural Reliability Analysis", Structural Safety, Vol. 26, pp. 49–67, (2004).
7. Cheng, J., "Hybrid Genetic Algorithms for Structural Reliability Analysis", Computers and Structures, Vol. 85, pp. 1524–1533, (2007).
8. Kaymaz, I., "Application of Kriging Method to Structural Reliability Problems", Structural Safety, Vol. 27, pp. 133–151, (2005).
9. Vapnik V. "Statistical Learning Theory", John, Wiley and Sons., New York, (1998).
10. Zhiwei, G., Guangchen, B., "Application of Least Squares Support Vector Machine for Regression to Reliability Analysis", Chinese Journal of Aeronautics, Vol. 22, pp. 160-166, (2009).
11. Li, H.S. And Lu, Z.Z., "Support Vector Regression for Structural Reliability Analysis", Applied Mathematics and Mechanics, Vol. 27(10), pp. 1295–1303, (2006).
12. Zhao, W., Qiu, Z., "An efficient response surface method and its application to structural reliability and reliability-based optimization", Finite Elements in Analysis and Design, Vol. 67, pp. 34–42, (2013).
13. Deng, J. "Structural Reliability Analysis for Implicit Performance Function using Radial Basis Function Network", International Journal of Solids and Structures, Vol. 43, pp. 3255-3291 (2006).
14. Tang, C.X., Jin, W.L. and Chen, J., "Importance Sampling Method based on SVM", J Yangtze River Scientific Res Inst, Vol. 24(6), pp. 62–5, (2007).
15. Bucher, C.G., Bourgund, U., "A fast and Efficient Response Surface Approach for Structural Reliability Problems", Structural Safety, Vol. 7(1), pp. 57–66, (1990).
16. McKay, M.D., Beckman, R.J., "A comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code", Technometrics, Vol. 42(1), pp. 239–45, (2000).
CAPTCHA Image