Probabilistic Bayesian Model Updating of Two Laboratory-Scale Structures Using Ambient Vibration Measurements

Abstract

Abstract

High-fidelity numerical modeling plays a central role in structural health monitoring (SHM), particularly for materials such as glued laminated timber and masonry, which exhibit heterogeneity, anisotropy, complex boundary conditions, and environmental sensitivity. These characteristics often introduce considerable uncertainty in parameter estimation and model prediction and affect the results. Controlled laboratory testing offers an ideal environment for rigorous validation of probabilistic model updating techniques. This study implements a surrogate-assisted Bayesian model updating framework, with primary focus on a full-scale glued laminated timber beam tested under ambient vibration. A laboratory-scale two-span masonry arch bridge (MAB), constructed at the Universitat Politècnica de Catalunya within the PONT3 Project, is additionally considered to demonstrate transferability of the framework. Ambient vibration data were collected using accelerometers. Modal parameters were identified through output-only operational modal analysis (OMA) methods, and corresponding finite element (FE) models were built. Bayesian inference was performed using the Metropolis-Hastings Markov Chain Monte Carlo (MH MCMC) algorithm to estimate the posterior distributions of uncertain model parameters. The study also examines the influence of uncertain parameter selection on surrogate model accuracy for the timber beam. Gaussian Process surrogate models were trained using 1,000 FE simulations for each parameter set, and their accuracy was evaluated through 10-fold cross-validation. The comparison of two different datasets demonstrates that statistical definition of uncertain parameters significantly affects surrogate predictive capability, which in turn affects the stability of Bayesian updating and the credibility of the results. Posterior distributions of stiffness, density, and boundary parameters were obtained and compared for the timber beam. Fig. 1 presents the posterior distributions of model mechanical parameters and quantifies the associated uncertainty estimated based on the more accurate surrogate model. Improved surrogate performance resulted in more consistent posterior estimates and reduced uncertainty distribution. The same probabilistic framework was applied to the laboratory MAB using an accurate surrogate model, and the updating results are reported to demonstrate methodological transferability. The findings highlight the importance of appropriate uncertainty characterization in surrogate-assisted Bayesian model updating using ambient vibration data. Careful selection of prior parameter bounds enhances surrogate performance and improves the reliability of posterior parameter estimation using only ambient vibration data. The proposed framework provides a systematic basis for probabilistic model updating and uncertainty quantification in complex structural systems. This approach supports future applications in damage detection and structural health monitoring.