2024 Volume 80 Issue 15 Article ID: 23-15008
In hierarchical Bayesian model updating, the inherent variability of the model parameters is represented by a probability distribution. Its hyperparameters are then updated by minimizing the stochastic discrepancy between the model outputs and observations. To avoid subjective hypotheses in hierarchical Bayesian updating, the authors have considered applying the staircase probability distribution. The staircase distribution can discretizely and arbitrarily approximate a broad range of distributions. In this study, we aim to calibrate dependent parameters with modeling the joint distribution by a copula and its marginal staircase distributions. Bayesian model selection is also used to determine the optimal copula from several candidates that represent different correlation structures. The proposed approach is demonstrated using a three degrees of freedom spring-mass system. The results show that the proposed approach is capable of quantifying uncertainties in correlated parameters from limited prior information and available observations.
