A Practical Bayesian Framework for Structural Model Updating and Prediction

Abstract

Due to the influence of various uncertain factors, there will inevitably be certain errors between the prediction of finite-element (FE) model and observed data for a target structure. It is thus necessary to calibrate the initial FE model using the measured data to ensure the accuracy of the numerical model for the purpose of structural system identification and health monitoring. Although structural FE model updating methods have been extensively studied in the past few decades, the research based on deterministic methods in the current literature still occupies a large proportion, which cannot account for the uncertain effects during the model updating. The noise robustness of both the updating procedure and the generalization capability of the updated model are expected to be poor. The model updating based on the Bayesian theorem can quantify the uncertainty of model identification results, but it is computationally expensive for the Bayesian inference of regularization hyperparameters since the Hessian matrix is generally required to be evaluated repeatedly especially for a huge amount of uncertain model parameters. Also, effective prediction based on the refined FE model is still lacking in the literature, which is essential for judging and evaluating the quality of the updated model. This paper proposes a practical framework for structural FE model updating and prediction based on the Bayesian regularization with incomplete modal data. The structural model parameters and regularization hyperparameters are identified alternatively in an adaptive manner, and the Gauss-Newton method is used to approximate the true Hessian within the framework of the nonlinear least-squares algorithm. This is expected to improve the efficiency and robustness of model updating and prediction for handling large-scale FE models possessing a large number of uncertain model parameters. The proposed methodology is validated through the model updating and prediction conducted on a real-life pedestrian bridge based on field-testing data.