An efficient method for generation of uniform support vector and its application in structural failure function fitting

• An efficient method is proposed for generation of uniform support vector.
• The method can increase the ratio of support vectors to the whole samples dramatically.
• Example analysis shows that the proposed method is accurate and efficient.
• The method can be applied to function fittings of multiple enveloped failure modes well.

The current response surface methods based on support vector usually need a large number of samples to fit an implicit structural failure function. To overcome this shortcoming, an efficient method for generation of uniform support vector is proposed. It is based on the features that support vectors are composed of failure samples and safe samples close to the limit state surface. The main steps are: (1) use the uniform design method to generate initial samples; (2) transform each obtained initial sample into a uniform sample pair based on the safe load and failure load close to the limit load. A main advantage of this method is that it can increase the proportion of support vectors to the whole samples and uniformity of support vectors in space dramatically and it requires less samples in function fitting. Besides, it can be applied to function fittings of large structures under ultimate limit state, where multiple failure modes may be enveloped. The proposed method as well as the relevant techniques of data normalization and parameters optimization of kernel function model of support vector machine, is used in the structural failure function fitting. Numerical examples show that this method can achieve a good fitting of implicit failure function, and the reliability results are accurate, too.