Neural Markov chain Monte Carlo for structural health monitoring: Bayesian inversion via normalizing flows and variational autoencoders

Structural health monitoring systems generate high-dimensional observational data, requiring efficient computational strategies to infer hidden structural health parameters. This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle such inverse problems that (i) must be solved multiple times, and (ii) are characterized by intractable or unavailable likelihood functions. The posterior probability distribution over parameters of interest is estimated via differential evolution Metropolis sampling, empowered by learnable mappings. First, a variational autoencoder performs probabilistic feature extraction from observational data. The resulting latent structure inherently quantifies uncertainty, capturing deviations between the actual data-generating process and the training data distribution. At each step of the MCMC random walk, the algorithm jointly samples from the data-informed latent distribution and the space of parameters to be inferred. These samples are fed into a neural likelihood estimator based on normalizing flows, specifically real-valued non-volume preserving transformations. The scaling and translation functions of the affine coupling layers are modeled by neural networks conditioned on the unknown parameters, allowing the representation of arbitrary observation likelihoods. The proposed methodology is validated on two structural health monitoring case studies involving damage detection, localization, and quantification.