Support vector machine response surface method based on CVT sampling

Conventional support vector machine (SVM) response surface method for structural reliability analysis uses random numbers drawn from uniform distribution to select training samples. However, random numbers nominally obeying uniform distribution cannot guarantee that the obtained training samples will uniformly cover the entire design space. The nonuniformly distributed training samples often make SVM response surfaces unable to accurately approximate the limit state function (LSF), and hence lead to erroneous reliability results. To solve this problem, a new SVM response surface method is proposed, and it is the CVT sampling based SVM response surface method where CVT (Centroidal Voronoi Tessellation) algorithm is adopted to select training samples. Experiments show that CVT algorithm greatly improves training samples' spatial uniformity, ensures SVM good generalization ability and learning ability for small samples, and makes it more accurately approximate the LSF and produce more precise failure probabilities. Meanwhile, as the sample quality becomes much better, the required sample number for stable failure probability results is significantly decreased.