On the use of reliability methods and Hamiltonian Monte Carlo for complex identification problems in structural dynamics

Abstract

This contribution focuses on the solution of complex Bayesian model updating problems related to structural dynamical systems. By adopting the paradigm of Bayesian model updating with structural reliability methods (BUS), the problem of sampling the posterior distribution is restated as that of generating samples conditional on an especially devised failure event. To address the latter, the well-established subset simulation method is appropriately integrated with a Hamiltonian Monte Carlo technique to obtain samples at each simulation level. In this setting, a candidate state is first determined by simulating the trajectory of an auxiliary dynamical system, and then accepted or rejected based on the traditional Metropolis-Hastings rule. Such an approach has proven efficient in drawing samples from complex target distributions, and thus, it is adopted as an effective tool to explore involved domains related to challenging model updating problems. To assess the performance of the method, two test problems as well as one application example associated with a nonlinear structural dynamical model are investigated. Numerical results indicate that the proposed approach can be regarded as a viable alternative to address a class of complex identification problems in structural dynamics, including locally identifiable cases, models that are strictly unidentifiable based on available data, and cases with a large number of model parameters.