- Volume 56 Issue 4
A first-order moment method (FORM) reliability analysis is commonly used for structural stability analysis. It requires the values and partial derivatives of the performance to function with respect to the random variables for the design. These calculations can be cumbersome when the performance functions are implicit. A Gaussian process (GP)-based response surface is adopted in this study to approximate the limit state function. By using a trained GP model, a large number of values and partial derivatives of the performance functions can be obtained for conventional reliability analysis with a FORM, thereby reducing the number of stability analysis calculations. This dynamic renewed knowledge source can provide great assistance in improving the predictive capacity of GP during the iterative process, particularly from the view of machine learning. An iterative algorithm is therefore proposed to improve the precision of GP approximation around the design point by constantly adding new design points to the initial training set. Examples are provided to illustrate the GP-based response surface for both structural and non-structural reliability analyses. The results show that the proposed approach is applicable to structural reliability analyses that involve implicit performance functions and structural response evaluations that entail time-consuming finite element analyses.
first-order moment method;structural reliability;response surface method;Gaussian process
- Bucher, C.G. and Bourgund, U. (1990), "A fast and efficient response surface approach for structural reliability problems", Struct. Saf., 7(1), 57-66. https://doi.org/10.1016/0167-4730(90)90012-E
- Chen, T., Morris, J. and Martin, E. (2007), "Gaussian process regression for multivariate spectroscopic calibration", Chemometr. Intell. Labs., 87(1), 59-71. https://doi.org/10.1016/j.chemolab.2006.09.004
- Cheng, J., Li, Q.S. and Xiao, R.C. (2008), "A new artificial neural network-based response surface method for structural reliability analysis", Probab. Eng. Mech., 23(1), 51-63. https://doi.org/10.1016/j.probengmech.2007.10.003
- Christian, B. and Thomas, M. (2008), "A comparison of approximate response functions in structural reliability analysis", Probab. Eng. Mech., 23(1), 154-163. https://doi.org/10.1016/j.probengmech.2007.12.022
- Das, P.K. and Zheng, Y. (2000), "Cumulative formation of response surface and its use in reliability analysis", Probab. Eng. Mech., 15(4), 309-315. https://doi.org/10.1016/S0266-8920(99)00030-2
- Deng, J., Gu, D.S., Li, X.B. and Yue, Z.Q. (2005), "Structural reliability analysis for implicit performance function using artificial neural network", Struct. Saf., 27(1), 25-48. https://doi.org/10.1016/j.strusafe.2004.03.004
- Gayton, N., Bourinet, J.M. and Lemaire, M. (2003), "CQ2RS: a new statistical approach to the response surface method for reliability analysis", Struct. Saf., 25(1), 99-121. https://doi.org/10.1016/S0167-4730(02)00045-0
- Guan, X.L. and Melchers, R.E. (2001), "Effect of response surface parameter variation on structural reliability estimates", Struct. Saf., 23(4), 429-444. https://doi.org/10.1016/S0167-4730(02)00013-9
- Hensman, J., Mills, R., Pierce, S.G., Worden, K. and Eaton, M. (2010), "Locating acoustic emission sources in complex structures using Gaussian processes", Mech. Syst. Signal Pr., 24(1), 211-223. https://doi.org/10.1016/j.ymssp.2009.05.018
- Herbert, M.G. and Armando, M.A. (2004), "Comparison of response surface and neural network with other methods for structural reliability analysis", Struct. Saf., 26(1), 49-67. https://doi.org/10.1016/S0167-4730(03)00022-5
- Hurtado, J.E. (2007), "Filtered importance sampling with support vector margin: a powerful method for structural reliability analysis", Struct. Saf., 29(1), 2-15. https://doi.org/10.1016/j.strusafe.2005.12.002
- Jiang, S.H., Li, D.Q., Zhou, C.B. and Zhang, L.M. (2014), "Capabilities of stochastic response surface method and response surface method in reliability analysis", Struct. Eng. Mech, 49(1), 111-128. https://doi.org/10.12989/sem.2014.49.1.111
- Kim, S.H. and Na, S.W. (1997), "Response surface method using vector projected sampling points", Struct. Saf., 19(1), 3-19. https://doi.org/10.1016/S0167-4730(96)00037-9
- Li, H.S., Lv, Z.Z. and Yue, Z.F. (2006), "Support vector machine for structural reliability analysis", Appl. Math. Mech., 27(10-11), 35-43.
- Luc, S. and Dionys, V.G. (2005), "Benefit of splines and neural networks in simulation based structural reliability analysis", Struct. Saf., 27(3), 246-261. https://doi.org/10.1016/j.strusafe.2004.11.001
- MacKay, D.J.C. (1998), Introduction to Gaussian processes, Technical report, Cambridge University, London, UK.
- Malur, R.R. and Bruce, R.E. (1993), "A new look at the response surface approach for reliability analysis", Struct. Saf., 12(3), 205-220. https://doi.org/10.1016/0167-4730(93)90003-J
- Rackwitz, R. and Fiessler, B. (1976), Note on discrete safety checking when using non-normal stochastic models for basic variable, Loads Project Working Session, MIT Press, London.
- Rasmusen, C.E. and Williams, C.K.I. (2006), Gaussian Processes for Machine Learning, MIT Press, London.
- Rocco, C.M. and Moreno, J.A. (2002), "Fast Monte Carlo reliability evaluation using support vector machine", Reliab. Eng. Syst. Saf., 76(2), 37-43.
- Su, G.S., Yan, L.B. and Song, Y.C. (2007), "Gaussian process for non-linear displacement time series prediction of landslide", J. China Univ. Geosci., 18, 212-219.
- Vapnik, V. (1998), Statistical learning theory, John Wiley and Sons, New York.
- Williams, C.K.I. (1998), Prediction with Gaussian processes: from the linear regression to linear prediction and beyond, Technical report, Aston University, Birmingham, UK.
- Zhao, G.F. (1996), Reliability theory and its applications for engineering structures, Dalian University of Technology Press, Dalian, PRC.
- Zhao, H.B. (2008), "Slope reliability analysis using a support vector machine", Comput. Geotech., 35(4), 59-67.
- Zhao, W.T., Qiu Z.P and Yang, Y. (2013), "An efficient response surface method considering the nonlinear trend of the actual limit state", Struct. Eng. Mech., 47(1), 45-58. https://doi.org/10.12989/sem.2013.47.1.045
연구 과제 주관 기관 : National Natural Science Foundation of China