Bayesian Inference for Damage Localization Under Uncertainty

Summary (5 sentences)

Bayesian model updating frames structural damage identification as a probabilistic inverse problem: given measured structural responses, update the prior belief about structural parameters (stiffness, damping) to a posterior distribution. The posterior encodes both the most likely damage state and the uncertainty in that estimate. Markov Chain Monte Carlo (MCMC) sampling is typically used to draw samples from the posterior when it is not analytically tractable. This approach is particularly powerful for SHM because it can distinguish between genuine damage and measurement noise in a statistically rigorous way. The posterior predictive distribution can also be used to forecast future structural responses under uncertain loading.

SHM Problem It Solves

Damage localization in structures where measurement noise, model uncertainty, and limited sensor coverage make deterministic identification unreliable. Bayesian methods provide confidence intervals on damage location and severity, enabling risk-informed maintenance decisions.

Method Snapshot

The posterior over structural parameters $\theta$ (e.g., element stiffnesses) given measurements $\mathbf{y}$:

$p(\theta | \mathbf{y}) \propto p(\mathbf{y} | \theta) \cdot p(\theta)$

• $p(\mathbf{y} | \theta)$: likelihood from the structural model (FEM or surrogate)
• $p(\theta)$: prior encoding healthy-state knowledge

Damage is detected when the posterior mean of $\theta_i$ deviates significantly from the healthy-state prior.

What I Would Reproduce

Apply Bayesian model updating to a 5-DOF shear frame with a 30% stiffness reduction at DOF 3. Use Metropolis-Hastings MCMC to sample the posterior. Visualize the marginal posteriors for each stiffness parameter and confirm that the damaged element is correctly identified with high posterior probability.

Failure Modes

• MCMC is computationally expensive for high-dimensional parameter spaces (many structural elements).
• Posterior is sensitive to the choice of prior — a poor prior can dominate when data is limited.
• Requires an accurate forward model; FEM model error is often not accounted for.

Transfer to/from Host Group (MSCA-aligned)

From host group: Validated FEM models provide the forward model for the likelihood computation. Experimental modal data can inform the prior. To host group: Posterior uncertainty estimates feed directly into structural reliability analysis and probabilistic maintenance scheduling.

3 Follow-Up Questions

1. How can surrogate models (e.g., Gaussian processes, neural networks) replace expensive FEM evaluations in the likelihood to make MCMC tractable?
2. Can the Bayesian framework be extended to online (sequential) damage tracking using particle filters?
3. How does the method handle non-stationary loading conditions where the structural response statistics change over time?