Normalizing Flow Enhanced Global and Local Sampler for Bayesian Parameter Updating and State Estimation in Finite Element Models

Abstract Finite element (FE) model updating is essential for design, analysis, or response prediction of engineering systems. However, uncertainties from various sources often lead to discrepancies between model predictions and actual observations. Bayesian parameter updating and state estimation provide a probabilistic framework by estimating posterior distributions of parameters or states that define the FE model. Yet, traditional simulation methods like Markov Chain Monte Carlo (MCMC) face significant challenges in high-dimensional, multimodal spaces or when priors differ greatly from posteriors. This study introduces the Normalizing flow Enhanced GlObal and Local sAmpler (NEGOLA) that integrates normalizing flow, a machine learning technique for transforming simple distributions into complex ones, with a Gaussian kernel to generate new samples in Bayesian model updating. By concurrently running multiple chains and alternating between normalizing flow (global sampler) and Gaussian kernels (local sampler), NEGOLA achieves faster convergence and requires fewer FE model evaluations compared to conventional methods. The effects of the number of Markov chains and the switching steps in the NEGOLA algorithm are studied to provide insight into an optimal configuration of the algorithm. The algorithm was validated using single- and multiple-degree-of-freedom (SDOF and MDOF) dynamic systems and outperformed traditional approaches such as the unscented Kalman filter (UKF) and transitional MCMC (TMCMC) in scenarios involving time-varying parameters and abrupt changes. It was found that NEGOLA converges 20.3 times faster than the UKF in the SDOF system and requires 59.37% fewer FE model evaluations than TMCMC in the MDOF system. Results show that NEGOLA enhances convergence rates and accuracy, making it a promising tool for Bayesian model updating under uncertainty.