A two-step variational Bayesian Monte Carlo approach for model updating under observation uncertainty

Engineering tests can yield inaccurate data due to instrument errors, human factors, and environmental interference, introducing uncertainty in numerical model updating. This study employs the probability-box (p-box) method for representing observational uncertainty and develops a two-step approximate Bayesian computation (ABC) framework using time-series data. Within the ABC framework, Euclidean and Bhattacharyya distances are employed as uncertainty quantification metrics to delineate approximate likelihood functions in the initial and subsequent steps, respectively. A novel variational Bayesian Monte Carlo method is introduced to efficiently apply the ABC framework amidst observational uncertainty, resulting in rapid convergence and accurate parameter estimation with minimal iterations. The efficacy of the proposed updating strategy is validated by its application to a shear frame model excited by seismic wave and an aviation pump force sensor for thermal output analysis. The results affirm the efficiency, robustness, and practical applicability of the proposed method.