Nonparametric Bayesian stochastic model updating with hybrid uncertainties

This work proposes a novel methodology to fulfil the challenging expectation in stochastic model updating to calibrate the probabilistic distributions of parameters without any assumption about the distribution formats. To achieve this task, an approximate Bayesian computation model updating framework is developed by employing staircase random variables and the Bhattacharyya distance. In this framework, parameters with aleatory and epistemic uncertainties are described by staircase random variables. The discrepancy between model predictions and observations is then quantified by the Bhattacharyya distance-based approximate likelihood. In addition, a Bayesian updating using the Euclidian distance is performed as preconditioner to avoid non-unique solutions. The performance of the proposed procedure is demonstrated with two exemplary applications, a simulated shear building model example and a challenging benchmark problem for uncertainty treatment. These examples demonstrate feasibility of the combined application of staircase random variables and the Bhattacharyya distance in stochastic model updating and uncertainty characterization.