This work explores the vibratory characterization of a mechanical structure using neural networks, a novel approach that links simulation-based studies and experiments on a 2D frame. While traditional structural reliability analyses rely heavily on simulations, this research integrates data from an instrumented test bench and compares it with numerical models. A preliminary investigation focused on the statistical distribution of the first-passage time (FPT) in a numerical model. Then, this analysis was validated against experimental data collected from a two-stage mechanical structure. A key component of the study is the exploration of the influence of a tuned mass damper (TMD) on the FPT to demonstrate its role in safeguarding the structure against vibratory solicitation. The study goes further by proposing an innovative method for predicting the safety domains of the structure using artificial neural networks. This method identifies critical safety parameters by analyzing the features of the excitation signal and the characteristics of the TMD. The results demonstrate that the safety domain can be accurately determined through this approach and offer an effective and practical solution for the assessment of structural reliability. In general, this work contributes to the field by integrating experimental laboratory measurements with advanced machine learning techniques to highlight a more robust method to assess and enhance the safety of mechanical structures.