An effective implementation of reliability methods for Bayesian model updating of structural dynamic models with multiple uncertain parameters

The implementation of reliability methods in the framework of Bayesian model updating of structural dynamic models using measured responses is explored for high-dimensional model parameter spaces. The formulation relies on a recently established analogy between Bayesian updating problems and reliability problems. Under this framework, samples following the posterior distribution of the Bayesian model updating problem can be obtained as failure samples in an especially devised reliability problem. An approach that requires only minimal modifications to the standard subset simulation algorithm is proposed and implemented. The scheme uses an adaptive strategy to select the threshold value that determines the last subset level. Due to the basis of the formulation, the approach does not make use of any problem-specific information and, therefore, any type of structural model can be considered. The approach is combined with an efficient parametric model reduction technique for an effective numerical implementation. The performance of the proposed implementation is assessed numerically for a linear building model and a nonlinear three-dimensional bridge structural model. The results indicate that the proposed implementation represents an effective numerical technique to address high-dimensional Bayesian model updating problems involving complex structural dynamic models.