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

TL;DR

The paper addresses data-sparse population-based SHM for ship hull plates by formulating a partially pooled hierarchical Bayesian model to learn local deflection amplitudes $\tilde{w}$ and shared hyperparameters from FE-generated strain data $\varepsilon$. A Gaussian Process surrogate replaces the expensive FE model in the likelihood, enabling efficient MCMC (NUTS) inference. Results show that partial pooling yields tighter posterior uncertainty and more reliable damage detection for a data-scarce plate, compared with an independent no-pooling model, highlighting the value of information sharing in PBSHM. The approach demonstrates robust uncertainty quantification and practical decision-support improvements for structural integrity monitoring in large-scale marine 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.

Figures (6)

• Figure 1: (a) FE model of the subject geometry including the monitored plates (within red boundaries), and (b) representative out-of-plane deflection with strain sensor at the center. Adapted from the original work of the authors aravanis_2023.
• Figure 2: Clusters of generated observations of transverse strain for the six plate components. The brown markers show Plate 6 with scarce data.
• Figure 3: GPR surrogate model for Plate 6. Red markers represent the training-set (FE test data), the blue line shows the posterior predictive mean, and the shaded region indicates a $2 \sigma$ credible area. Note that for the construction of the likelihood function we use only the mean of the GPR.
• Figure 4: DAGs representing (a) the hierarchical (partial-pooling) model and (b) the independent model.
• Figure 5: KDE-based posteriors of hierarchical model parameters/hyperparameters (left panel) and trace plots (right panel). Dashed magenta lines show the prior distributions applied to the shared parameters. The color scheme for $k=\{1,\ldots,6\}$ follows: blue, orange, green, red, purple, and brown.