Non-probabilistic reliability analysis method for implicit limit state function

Since the non-probabilistic reliability index based on convex model scale factor is difficult to be solved for implicit limit state function, a support vector machine (SVM) regression is proposed. The proposed method employs SVM regression to fit the actual limit state function, and an optimization problem is constructed to obtain the index and design point. The design point is used to update the sampling center in the SVM training procedure. The full procedure is repeated until the given convergence criterion is satisfied. The special iteration guarantees the actual limit state function can be well approximated, hence the precision of the proposed method is high. Simultaneously, since the limit state function surrogate is adopted, the efficiency of the proposed method is high. Four numerical examples demonstrate the excellent behavior of the proposed method. An application of the proposed method in a wing reliability analysis also shows its value in engineering.