基于 RBF 和主动学习的非概率可靠度求解方法

When the failure domain and the hyper-ellipsoid uncertainty domain interfere with each other in non-probabilistic reliability analysis, non-probabilistic reliability is more applicable than the non-probabilistic reliability index. To improve the solution efficiency of structural non-probabilistic reliability of the hyper-ellipsoid model, this paper proposes an active learning method to solve non-probabilistic reliability problems. The jackknifing variance of the Radial Basis Function (RBF) model at the unknown point is derived by combining the cross-validation and the jackknifing methods, so as to estimate the uncertainty of the predicted values. To solve the non-probabilistic reliability, the is employed which is based on the variance. Based on the jackknifing variance, non-probabilistic reliability is solved using the active learning function of RBF. An effective convergence criterion is then proposed to terminate the process of active learning of non-probabilistic reliability analysis. Three numerical examples reveal that this method proposed can estimate the exact non-probabilistic reliability value under the condition of less calculation of the limit state function, and has strong applicability in structural non-probabilistic reliability analysis.