Vibration-based Bayesian FE-Model Updating for High-rise Buildings

Abstract

This research addresses a persistent challenge in structural engineering: the frequent mismatch between the measured dynamic properties of high-rise buildings and those predicted by their design models. Previous deterministic model updating studies on structures such as the New Orleans Tower, including those by Moretti et al. (2023) and Ritfeld et al. (2025), were constrained by two major limitations. First, they did not utilize all available modal information, particularly torsional modes, which can provide valuable insight into the structural behaviour. Second, they lacked a means to quantify uncertainty in the estimated parameters, leading to results with unknown reliability.

The primary objective of this thesis was to overcome these limitations and enhance both the accuracy and reliability of structural parameter estimation. To this end, a vibration-based Bayesian finite element (FE) model updating approach was implemented. A simplified three-dimensional FE model, formulated as a lumped-mass stick model, was developed for the New Orleans Tower. The model was specifically designed to capture both torsional and shear deformations while maintaining the computational efficiency required for Bayesian inference.

Within this framework, the Bayesian methodology employs Bayes’ theorem together with Markov Chain Monte Carlo (MCMC) sampling to treat uncertain structural parameters, such as foundation stiffnesses and the concrete modulus of elasticity, as random variables. This produces a posterior probability distribution that formally quantifies the uncertainties associated with the updated parameters. The prior distributions were defined based on literature and engineering judgement, while the likelihood function was defined through a data-generating process. Furthermore, a novel mode-matching method based on the modal participation mass ratio was developed to robustly pair measured and modelled modes.

Model updating was performed for the New Orleans Tower through four different cases, each incorporating additional modal information. Overall, the Bayesian updating successfully produced models that closely matched the measured data. Across these cases, several advantages of the Bayesian approach were demonstrated, including the ability to detect parameter redundancy and overfitting, identify uninformative parameters, improve the solution through uncertainty reduction, and reveal the existence of multiple possible solutions.

The proposed modelling approach also exhibited improved performance compared to simplified analytical beam models. It successfully captured the third bending mode without compromising the accuracy of the lower modes. The first torsional mode was also well represented; however, the inclusion of the second torsional mode proved unsuccessful. This limitation is likely due to missing parameters or model features within the updating scheme rather than to deficiencies in the modelling approach itself.

The case study further revealed significant model inadequacies for higher modes. These inadequacies were primarily attributed to the exclusion of the effect of the adjoining low-rise structure and the assumption of rigid connections between structural elements. For studies where models with accurate higher modes are required, these effects may not be neglected.