A hierarchical Bayesian approach for population-based structural health monitoring in ship hull structures

Abstract: Structural health monitoring (SHM) strategies involve the processing of structural response data to indirectly assess an asset's condition. These strategies can be enhanced for a group of structures, especially when they are similar, since mutual underlying physics are expected to exist. The concept behind population-based SHM exploits the sharing of data among individuals, so that data-rich members can support data-scarce ones. One approach to population-level modeling is the hierarchical Bayesian method, where the model is structured hierarchically in terms of its parameters, and correlation among learning tasks is enabled by conditioning on shared latent variables. This work investigates the application of a hierarchical Bayesian model to infer expected distributions of deflection amplitudes at both the population and domain levels, with the aim of detecting excessive initial deflections in a population of plate elements. Although these damages are typically localized, they can trigger unexpected events, if not properly monitored. The work is conducted in a numerical setting using a Finite Element model to generate strain response data, which serve as the monitoring data. Bayesian inference was conducted using Markov Chain Monte Carlo (MCMC), with a surrogate model employed to calculate the likelihood function. The hierarchical approach was compared to an independent model for a plate component with few data. The results revealed that, under data sparsity conditions, the hierarchical model can offer more robust results in terms of uncertainty, which is essential for decision-making tasks.