A Bayesian modeling framework for model updating considering load variations and its application to structural damage identification

The hierarchical Bayesian modeling framework (HBM) for model updating fails to consider the influence of the load variations on the prediction errors, which may lead to poor accuracy in the prediction of structural responses by using the updated model. To tackle this issue, a Bayesian modeling framework incorporating two probabilistic models is proposed. One of them retains the probabilistic model defined in HBM to quantify the uncertainty of physical parameters. The other probabilistic model is constructed to quantify the uncertainty of prediction errors varying with the intensity of the input load. This probabilistic model utilizes two parameterized functions to characterize the dependence of mean and standard deviation of prediction errors on the input loads, where the parameters of these functions are modeled as Gaussian variables to endow robustness with the model. To select the optimal function type in terms of balancing the simulation accuracy and complexity, the model class selection approach is employed. Embedded with the two probabilistic models, the stochastic physical model updated by proposed Bayesian modeling framework can predict more accurate and robust structural responses than HBM, as demonstrated by linear and nonlinear dynamic examples. Subsequently, the proposed framework is combined with the convolutional neural networks to develop a damage identification method. In this method, the updated physical model is utilized to simulate intact and various damaged states of the monitored structure. The simulated responses are then used to train the networks as a classifier to predict the state of the monitored structure based on its real measurements. Results from the illustrative examples show acceptable classification accuracy, verifying the efficacy of the damage identification method.