High-Dimensional Bayesian inference for model updating with neural likelihood approximator powered by dimensionality-reducing flow-based generative model

Abstract

Bayesian model updating provides a principled approach to approximating the posterior probability density function (PDF) of model parameters using incomplete and noisy data. However, the likelihood function is usually intractable, and evaluating it remains computationally prohibitive, especially for high-dimensional structural models. In this study, a novel Bayesian model updating framework is proposed that integrates a neural likelihood approximator (NLA) with a dimensionality-reduction flow-based generative model. The aim is to efficiently estimate the PDF of model parameters. The framework employs a masked autoregressive flow combined with a surjective neural network to map high-dimensional modal data into a simpler latent space. This transformation allows for the representation of the complex likelihood function with high accuracy and reduced computational cost. Specifically, the NLA learns the mapping between a multivariate standard Gaussian distribution and complex modal data through a sequence of invertible transformations conditioned on model parameters. This task is particularly challenging in structural dynamics because modal shapes can be highly sensitive to slight changes in model parameters and are often high-dimensional, making it difficult to capture their intricate relationships with the underlying physical system. Additionally, by enabling rapid computation of the log-likelihood, the framework significantly accelerates posterior estimation through the learned NLA combined with a prior distribution via Markov Chain Monte Carlo (MCMC). The proposed method is validated through case studies on an 18-story shear building and a steel pedestrian bridge, where modal data with dimensions of 342 and 220, respectively, are predicted, and the posterior distributions of 18 and 15 model parameters are estimated. The results demonstrate the capability of the proposed method to predict complex modal shapes and provide accurate posterior estimates.