r - The Hong Kong Polytechnic University

The 5th Cross-strait Conference on Structural and Geotechnical Engineering (SGE-5)
Hong Kong, China, 13-15 July 2011
A NEW RELIABILITY ANALYSIS METHOD BASED ON UNIFORM DESIGN
METHOD AND SUPPORT VECTOR MACHINES
X. L. Yu 1 , J. B. Yu 1 , H. B. Zheng 1 and Q. S. Yan 1
1
School of Civil Engineering and Transportation,
South China University of Technology, Guangzhou, China. Email: XLYU1@scut.edu.cn
ABSTRACT
To mostly engineering structures, the performance functions can not be expressed explicitly. Their structural
response can only be obtained by numerical methods. The reliability analysis needs times of finite element
calculations. It costs much time and it is difficult in calculating the failure probability. Response surface method
(RSM) is an effective way to solve such problems. Over the last decade, support vector machines (SVM) with
good ability of generalization obtained a widely application in data classification and regression analysis. In
order to improve the computational efficiency and make RSM suitable well to large and complex engineering
structures, the reliability analysis method based on uniform design method (UDM) and SVM was proposed.
UDM is adopted to select training data and SVM is used as response surface. Structural reliability index is
calculated in combination with the traditional reliability analysis methods (such as, the first-order reliability
method (FORM), the second-order reliability method (SORM) or Monte Carlo simulation method (MCSM)).
Numerical examples show that sampled with the UDM can greatly reduce the number of samples required for
training by SVM model, and a very good approximation of the limit state surface can be obtained to get the
failure probability.
KEYWORDS
Reliability, support vector machine, uniform design method, response surface method.
INTRODUCTION
The RSM developed in recent years is an effective way to solve the structural reliability problems with implicit
performance function. The basic idea of RSM is to replace the true performance function which is originally
implicit or takes long time to determine with an explicit function (usually polynomial) which is easy to deal with
so as to simplify the reliability analysis. Polynomial-based RSM usually use traditional quadratic polynomial to
explicitly approximate the response surface of limit state function, whose effectiveness is significantly affected
by the shape of limit state function. When the function used by RSM is not a good approximation of the true
structural response function, the results of RSM are sensitive to the values of parameter f (Guan et al. 2001).
Artificial Neural Network (ANN) has been widely adopted in structural reliability analysis for its ability to
approximate function well. However, due to the traditional Empirical Risk Minimization (ERM) principle, when
employed in the training process, ANN has suffered difficulties in generalization and overfitting the data. Since
some prior knowledge (such as, the determination of hidden nodes) is needed to fix the structure of the network
ANN has some defects, which limit the application of ANN to reliability analysis to some extent.
Based on statistical learning theory, Support Vector Machines (SVM) (Cortes et al. 1995; Vapnik 1995, 1999) have
strict mathematical basis. With the characteristics of structural risk minimization, the machine learning models
designed by SVM have been widely used in data classification and regression analysis over a decade. Compared
with ANN, SVM has some more advantages, for there is no locally optimization problem in SVM, which
improves the generalization ability of learning machine. SVM was used as response surface function (JIN et al.
2007; ZHAO et al. 2008). SVM was applied to reliability analysis. In their studies, the training data were
generated by interpolation iteration in the center points. In this case, SVM only fit well with limit state surface
in the design point similar to the traditional RSM, which doesn’t make full use of the generalization ability of
SVM. In order to improve the computational efficiency of SVM, least squares support vector machine (LS-SVM)
was used as response surface function (JIN et al. 2007). LS-SVM-based reliability analysis was performed in
conjunction with training data produced by orthogonal design, which needs more samples.
In order to improve the computational efficiency and to apply SVM-based reliability method to practical
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