Comparison of the Function Regression Method and Data Classification Method for Limit State Function Approximation

Abstract:

To reduce the computational burden of the reliability analysis of complex engineering application, approximate method is always used to construct the surrogate model of the implicit limit state function. Since the limit state function is a classifier of the failure domain and safe domain, its approximation can be established by the function regression method and data classification method. In this paper, these two methods are tested to several limit state functions including linear function, highly nonlinear function, high dimensional function, series system and parallel system. Least squares support vector machines are used to construct the surrogate models. A detail comparison of function regression method and data classification method for limit state function approximation is given. The conclusions of this paper can give guidance for the engineers to choose an appropriate approximate method in the engineering applications.

• Periodical: Advanced Materials Research (Volumes 774-776)
• Pages: 1738-1744
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.774-776.1738
• Online since: September 2013
• Authors: Qi Ouyang, Xiao Qian Chen, Wen Yao
• Keywords: Limit State Function, LSSVM, Surrogate Model

References

[1] C. G. Bucher, U. Bourgund, A Fast and Efficient Response Surface Approach for Structural Reliability Problems, Structural Safety. 7(1990), 57-66.

DOI: 10.1016/0167-4730(90)90012-e

[2] I. Kaymaz, C. A. Mcmahon, A Response Surface Method Based on Weighted Regression for Structural Reliability Analysis, Probabilistic Engineering Mechanics. 20(2005), 11-17.

DOI: 10.1016/j.probengmech.2004.05.005

[3] D. L. Allaix, V. I. Carbone, An Improvement of the Response Surface Method, Structural Safety. 33(2011), 165-172.

DOI: 10.1016/j.strusafe.2011.02.001

[4] M. Paffrath, U. Wever, Adapted Polynomial Chaos Expansion for Failure Detection, Journal Of Computational Physics. 226(2007), 263-281.

DOI: 10.1016/j.jcp.2007.04.011

[5] G. Blatman, B. Sudret, Adaptive Sparse Polynomial Chaos Expansion Based on Least Angle Regression, Journal of Computational Physics. 230(2011), 2345-2367.

DOI: 10.1016/j.jcp.2010.12.021

[6] I. Kaymaz, Application of Kriging Method to Structural Reliability Problems, Structural Safety. 27(2005), 133-151.

DOI: 10.1016/j.strusafe.2004.09.001

[7] B. Hyeon Ju, B. Chai Lee, Reliability-Based Design Optimization Using a Moment Method and a Kriging Metamodel, Engineering Optimization. 40(2008), 421-438.

DOI: 10.1080/03052150701743795

[8] B. Echard, N. Gayton, M. Lemaire, Ak-Mcs: An Active Learning Reliability Method Combining Kriging and Monte Carlo Simulation, Structural Safety. 33(2011), 145-154.

DOI: 10.1016/j.strusafe.2011.01.002

[9] J. E. Hurtado, D. A. Alvarez, Neural-Network-Based Reliability Analysis: A Comparative Study, Computer Methods in Applied Mechanics and Engineering. 191(2001), 113-132.

DOI: 10.1016/s0045-7825(01)00248-1

[10] J. Deng, D. Gu, X. Li, Q. Zhong, Structural Reliability Analysis for Implicit Performance Functions Using Artificial Neural Network, Structural Safety. 27(2005), 25-48.

DOI: 10.1016/j.strusafe.2004.03.004

[11] H. M. Gomes, A. M. Awruch, Comparison of Response Surface and Neural Network with Other Methods for Structural Reliability Analysis, Structural Safety. 26(2004), 49-67.

DOI: 10.1016/s0167-4730(03)00022-5

[12] C. M. Rocco, J. A. Moreno, Fast Monte Carlo Reliability Evaluation Using Support Vector Machine, Reliability Engineering and System Safety. 76(2002), 237-243.

DOI: 10.1016/s0951-8320(02)00015-7

[13] J. E. Hurtado, Filtered Importance Sampling with Support Vector Margin: A Powerful Method for Structural Reliability Analysis, Structural Safety. 29(2007), 2-15.

DOI: 10.1016/j.strusafe.2005.12.002

[14] A. Basudhar, S. Missoum, A. Harrison Sanchez, Limit State Function Identification Using Support Vector Machines for Discontinuous Responses and Disjoint Failure Domains, Probabilistic Engineering Mechanics. 23(2008), 1-11.

DOI: 10.1016/j.probengmech.2007.08.004

[15] A. Basudhar, S. Missoum, Adaptive Explicit Decision Functions for Probabilistic Design and Optimization Using Support Vector Machines, Computers and Structures. 86(2008), 1904-(1917).

DOI: 10.1016/j.compstruc.2008.02.008

[16] J. E. Hurtado, D. A. Alvarez, An Optimization Method for Learning Statistical Classifiers in Structural Reliability, Probabilistic Engineering Mechanics. 25(2010), 26-34.

DOI: 10.1016/j.probengmech.2009.05.006

[17] X. Tan, W. Bi, X. Hou, W. Wang, Reliability Analysis Using Radial Basis Function Networks and Support Vector Machines, Computers and Geotechnics. 38(2011), 178-186.

DOI: 10.1016/j.compgeo.2010.11.002

[18] H. Dai, H. Zhang, W. Wang, A Support Vector Density-Based Importance Sampling for Reliability Assessment, Reliability Engineering and System Safety. 106(2012), 86-93.

DOI: 10.1016/j.ress.2012.04.011

[19] J. M. Bourinet, F. Deheeger, M. Lemaire, Assessing Small Failure Probabilities by Combined Subset Simulation and Support Vector Machines, Structural Safety. 33(2011), 343-353.

DOI: 10.1016/j.strusafe.2011.06.001

[20] J. A. K. Suykens, T. Van Gestel, J. De Brabanter, B. De Moor, J. Vandewalle, Least Squares Support Vector Machines, World Scientific Publishing Co. Pre. Ltd, London, (2002).

DOI: 10.1142/5089

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

[22] C. Cortes, V. N. Vapnik, Support Vector Network, Machine Learning. 20(1995), 273-297.

[23] K. De Brabanter, P. Karsmakers, F. Ojeda, C. Alzate, J. De Brabanter, et al. LS-SVMlab Toolbox User's Guide, (2011).