Updated reliability assessment of structural dynamical systems using a two-phase subset simulation method

The identification of structural dynamical systems based on measured responses plays a crucial role in various engineering applications. Bayesian model updating [1] constitutes one of the prevalent formulations to address this task, where available data and prior engineering knowledge are leveraged to obtain a posterior (updated) joint distribution of the model parameters, which in turn allows updating the system reliability. This work focuses on estimating the updated first-passage probability of structural dynamical systems under stochastic excitation. The problem is cast in the framework of Bayesian model updating with structural reliability methods (BUS), in which an auxiliary failure event allows characterizing both the posterior distribution and updated failure probability [2]. Then, a two-phase subset simulation approach is implemented to explore the posterior distribution (Phase I) and the target failure domain (Phase II) in a sequential manner. In both phases, a sampling strategy based on Hamiltonian Monte Carlo is used [3]. The method offers several advantages pertaining to its practical implementation. A numerical example involving a four-story building model equipped with nonlinear dissipation devices and subject to non-stationary stochastic excitation is studied. Numerical results suggest that the approach represents a promising alternative for data-informed reliability analysis in a class of structural engineering applications. [1] J. L. Beck and L. S. Katafygiotis, “Updating models and their uncertainties. I: Bayesian statistical framework,” J. Eng. Mech., vol. 124, no. 4, pp. 455–461, 1998. [2] D. Straub, I. Papaioannou, and W. Betz, “Bayesian analysis of rare events,” J. Comput. Phys., vol. 314, pp. 538–556, 2016. [3] H. A. Jensen, D. J. Jerez, and C. Figueroa, “On the use of reliability methods and Hamiltonian Monte Carlo for complex identification problems in structural dynamics,” Mech. Syst. Signal Process., vol. 229, p. 112547, 2025.