Latent space-based stochastic model updating

Model updating of engineering systems inevitably involves handling both aleatory and epistemic uncertainties. Addressing these uncertainties poses significant challenges, particularly when data and simulations are limited. This study proposes a novel latent space-based method for stochastic model updating that leverages limited data to effectively quantify uncertainties in engineering applications. By extending the latent space-based approach to multi-observation and multi-simulation frameworks, the proposed method circumvents the need for probability estimations at each iteration of Markov Chain Monte Carlo (MCMC) simulation, relying instead on an amortized probabilistic model trained using a variational autoencoder (VAE). This method is validated through numerical experiments on a two-degree-of-freedom shear spring model, demonstrating superior efficiency and accuracy compared to existing methods in terms of uncertainty quantification (UQ) metrics, such as Bhattacharyya and Euclidean distances. Moreover, the applicability of the method to time-series data is verified using the model calibration problem of the NASA UQ Challenge 2019. The results underscore the potential of the latent space-based method in practical engineering applications, providing a robust framework for uncertainty quantification within the scope of benchmark problem, and demonstrating its effectiveness in handling high-dimensional data.