Reproducing kernel-based support vector machine for structural reliability analysis Lu, Da-Gang; Li, Gong-Bo
How to choose a kernel function for a support vector machine (SVM) is an important ingredient for high-dimensional and nonlinear classification and regression problems to overcome the curse of dimension. In this paper, a reproducing kernel of Sobolev Hilbert space is introduced to be an admissible kernel for SVMs. Then a support vector regression (SVR) machine based on the reproducing kernel (RKSVR) is constructed, and a hybrid approach to structural reliability analysis is proposed. To minimize the number of simulation and fill in the basic random variable space uniformly, the uniform design (UD) is applied to choose experiment points in the space of basic random variables. The Genetic algorithm (GA) incorporating the gradient information in FORM is employed to search for the global design point to avoid fall into the local optimal solutions. A numerical example is provided to demonstrate the accuracy, efficiency and applicability of the new reproducing kernel-based support vector regression meta-model for structural reliability analysis, compared with the support vector regression machine based on the Gaussian kernel.
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