Hybrid nested sampling method for identifying the uncertainty of the high-dimensional updating parameters in Bayesian structural model updating

Abstract

Bayesian inference is a practical and straightforward approach to quantifying the uncertainty of the model parameters in structural finite element model updating. Sampling methods are frequently used to estimate the uncertainty of the selected updating parameters in a statistically principled way. Generally, uncertainty can be described by global optimum, local optimum, expectation, variance, and marginal probability density function (PDF). However, it is rare to see model updating methods focusing on studying the high-dimensional distribution of the updating parameters due to the computational cost. This paper develops a hybrid nested sampling method to identify the global optimum and high-dimensional confidence interval simultaneously. The proposed method samples the posterior PDF by shrinking the range of the live sample set layer by layer and achieves the global optimum guided by a hybrid search strategy. Finally, the performance of the proposed method was investigated by numerical simulations and an actual shear-type structure’s model test. After analysis and comparison, the results show that the proposed method performs very well in accuracy and robustness.