High-Order Reliability Analysis of Nonlinear Steel Frames Using SVM-Reconstructed Limit State Function

In complex nonlinear steel frames, the limit-state function is typically nonlinear and implicit, which hinders the direct application of traditional first- and second-order reliability methods (FORM/SORM). A reliability analysis approach for steel frames was developed by reconstructing the limit state function using a support vector machine (SVM). Finite-element response samples were employed to construct an explicit SVM surrogate model of the limit state function. The particle swarm optimization (PSO) is adopted to globally optimize the model hyperparameters, thereby enhancing the predictive accuracy and stability of the reconstructed limit-state function. The reconstructed limit-state function was subsequently incorporated into the FORM and SORM frameworks to enable the efficient evaluation of failure probabilities and reliability indices for steel frames. The proposed approach is validated through multiple benchmark examples, including explicit nonlinear limit-state functions and multistory multispan rigid frame structures. The results indicate that the SVM-reconstructed limit-state function accurately captures the non-linear characteristics of the structural responses. The corresponding reliability estimates were in good agreement with the Monte Carlo simulation (MCS) results and previously reported findings. Compared with FORM, SORM significantly improves the accuracy of reliability and failure probability estimation, with the Tvedt formulation demonstrating the highest level of consistency.