Monte Carlo simulation using support vector machine and kernel density for failure probability estimation

•Failure probability calculation using Monte Carlo simulation and support vector machine•Adaptive learning framework for the support vector machine as the metamodel of the performance function•Selection methodology of the experimental point considering the density of the existing experimental point•A methodology to gauge the maturity of the support vector machine and the end of the active learning Monte Carlo simulation requires a large number of sampling points. In a Monte Carlo simulation, the performance function is calculated for all sampling points to determine the failure of the design. If the calculation of the performance function involves large numerical models, a tremendous numerical cost is inevitable. In this study, a support vector machine was applied as a metamodel of the performance function to overcome this drawback. Kernel density and a modified margin of the support vector machine were used for the active learning of the support vector machine. The proportion of the support vector machine's modified margin in the design space was applied as the criterion to end active learning. The proposed method is applied to some numerical examples and examined.