r - The Hong Kong Polytechnic University

P
P
P
P
P
P
P
P
P
P
P
P
4 5 4 A
2 4 1 5 1 4 2
2 4 1 5 1 4 2
2 4
1
5
1
4 2
2
4
1
5
1
4
2
2
4
1
5
1
4
2
2
4
1
5
1
4
2
1 3 3
4 5
1
4
1 3 3 1
4 5 4
1
4
3
5
3
1
4
1 4 3 5 3 4 1
1
4
3
5
3
4
1
1 3 3 1
12x4=48
7.5 3.5 7.5
Figure 2 Diagram of the framework(unit:m)
Table5 Statistical parameters of variables
Standard Distribution
Variables Unit Mean μ
αi
deviationσ Type
A m 2 0.25 0.025 Log-normal 0.08333
1
A m 2 0.16 0.016 Log-normal 0.08333
2
A m 2 0.36 0.036 Log-normal 0.08333
3
A m 2 0.2 0.02 Log-normal 0.26670
4
A m 2 0.15 0.015 Log-normal 0.20000
5
P kN 30 7.5 Extreme-I
There are 6 random variables. In accordance with the distribution, samples were distributed uniformly within
μ − 3 σ , μ + 3σ
. In order to ensure the accuracy of response surface, uniform distribution experimental design
[ ]
U is used to decide 25 tests. Put these into deterministic finite element model established and then
6
table ( 5
25 )
the displacements of the structure are obtained.
The reliability index from Monte-Carlo simulation based on importance sampling using 2000 simulations is
1.4391 (Zhao 1996) and from traditional RSM is 1.4538(Zhao 1996). The reliability index based on Kringing
simulation using 60 simulations is 1.4308 (Zhang et al. 2005). The reliability index is 1.4408 calculated by
UDM-SVM RSM in this paper. It is evident that these results correspond quite well.
CONCLUSIONS
The reliability method based on support vector machine and uniform design method was discussed. The
calculation results of examples show that the SVM can well approximate the limit state surface on the case of
the limit state surface with a higher degree of nonlinearity. And it has high accuracy. Training data determined
by the uniform design method can significantly improve the computational efficiency of SVM. The analysis
results show that the method is feasible and has a good prospect, which provides a new way for structural
reliability analysis.
REFERENCES
Guan, X. L. and Melchers, R. E. (2001). “Effect of response surface parameter variation on structural reliability
estimates”, Structural Safety, 16(3), 229-230.
Cortes, C. and Vapnik, V. N. (1995). “Support vector networks”, Machine Learning, 20(3), 273-297.
Vapnik, V. N. (1995). The Nature of Statistical Learning Theory, New York: Springer, Verlag.
Vapnik, V. N. (1999). “An overview of statistical learning theory”, IEEE Transaction on Neural Networks, 10(5),
988-998.
Jin, W. L., Tang, C. X. and Chen, J. (2007). “SVM based on response surface method for structural reliability
analysis”, Chinese Journal of Computational Mechanic, 24(6), 713-718.
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