Probabilistic Model Updating for Structural Health Monitoring Using a Likelihood-Free Bayesian Inference Method

Bayesian inference has received considerable attention and is an accredited framework in structural health monitoring (SHM) to evaluate structural integrity. In Bayesian inference, structural parameters are estimated as probability density distributions (PDF) using measurements, and associated uncertainty is then naturally quantified. However, the likelihood function as a crucial component in Bayesian inference is usually analytically intractable due to model complexity. Furthermore, solving the likelihood function is computationally demanding. This study investigates a novel likelihood-free and computationally efficient Bayesian inference method, for probabilistic damage detection through model updating in SHM. The method is based on normalizing flow and conditional invertible neutral network (cINN) and is called BayesFlow. It consists of a training phase and an inference phase. In the training phase, a summary and a cINN are trained simultaneously given synthetic data. The summary network targets on automatically learning the most useful features from raw data for damage detection rather than handcrafted ones. The cINN aims to learn the posterior distribution of model parameters by sampling a Gaussian latent distribution and using the trained inverse function. Based on the summary network and cINN, Bayesian inference can be performed efficiently without evaluating any likelihood function in the inference phase. The performance of the BayesFlow is verified with a benchmark example, an 18-story steel frame. Results show that BayesFlow provides more accurate damage identification with less measurement data and lower uncertainties compared to traditional sampling-based Bayesian inference method.