This article evaluates the use of experimental frequency response functions for damage detection and quantification of a concrete beam with the help of model updating theory. The approach is formulated as an optimization problem that intends to adjust the analytical frequency response functions from a benchmark finite element model to match with the experimental frequency response functions from the damaged structure. Neither model expansion nor reduction is needed because the individual analytical frequency response function formulation is derived. Unlike the commonly used approaches that assume zero damping or viscous damping for simplicity, a more realistic hysteretic damping model is considered in the analytical frequency response function formulation. The accuracy and anti-noise ability of the proposed approach are first verified by the numerical simulations. Next, a laboratory reinforced concrete beam with different levels of damage is utilized to investigate the applicability in an actual test. The results show successful damage quantification and damping updating of the beam by matching the analytical frequency response functions with the experimental frequency response functions in each damage scenario.

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.