Real-time probabilistic model updating and damage detection using Machine Learning-based likelihood-free inference

Abstract

Bayesian inference plays a significant role in model updating and damage detection in civil infrastructures, due to its ability to effectively quantify uncertainties by estimating the posterior distributions of model parameters. Nevertheless, its practical application faces two main challenges. First, the traditional Bayesian inference relies on sampling methods to approximate the posteriors of model parameters, which demands considerable computational resources. Second, the complexity of models, such as those with multi-level model where sub-models are hierarchically integrated, often results in an intractable likelihood function. To tackle these challenges, this study proposes a probabilistic parametric estimator (PPE), a machine learning-driven approach for likelihood-free inference, aimed at expediting probabilistic model updating and accurate damage detection. In our framework, synthetic data are generated using the physical model and the prior knowledge of model parameters. This data is then employed to train fully convolutional neural networks (CNN). To accurately quantify uncertainties, we employ the heteroscedastic loss function for training the CNN model. This approach allows for the direct estimation of critical posterior distribution characteristics, such as the posterior mean and variance, simultaneously. Once trained on synthetic data, the PPE model is capable of estimating model parameters and their associated uncertainties almost instantaneously. Moreover, the trained PPE model is able to process data of varying measurement lengths without the need for re-training. To showcase the effectiveness of the proposed PPE method, two case studies are presented: a steel pedestrian bridge and a real-world 490-meter cable-stayed bridge. A comparative study is also conducted between the proposed PPE approach, a normalizing flow (NF)-based likelihood-free inference. The results indicate that the PPE outperforms the NF approach in both computational efficiency during training and inference phases, as well as in the accuracy of model updating and damage detection.