A Least Square Support Vector Machine Approach Based on Uniform Design Method for Structural Reliability Analysis
Since the performance functions of large complex structures can not be expressed explicitly in the process of reliability analysis, support vector machines (SVM) with good ability of generalization are used as the response surface function based on the small training samples. The uniform design method was adopted in selecting the training data. The least support vector machines (LS-SVM) were used to find the support vectors. The limit state function was expressed by the LS-SVM regression. Reliability analysis was then performed by the usual reliability method (e.g., the first-order reliability method, the second-order reliability method or Monte Carlo) on the response surface. The results of calculations of numerical examples and a typical cable-stayed bridge show that LS-SVM using the uniform design method can well approximate the real response of complex structures which has a good efficiency and accuracy and can be applied in complex structures.
X. L. Yu et al., "A Least Square Support Vector Machine Approach Based on Uniform Design Method for Structural Reliability Analysis", Advanced Materials Research, Vols. 163-167, pp. 3348-3353, 2011