PSI - Issue 84

Laura Ierimonti et al. / Procedia Structural Integrity 84 (2026) 959–966

961

dynamic response of the structure (e.g., modal frequencies, mode shapes, rotations) as a function of a wide variety of potential damage parameters. In practice, the surrogate may be implemented using neural networks or other nonlinear regression techniques. Its role is to replace the FE model in the calculation of predicted dynamics, thereby enabling fast evaluations during Bayesian updating. To further enhance efficiency and reduce ill-conditioning in the inverse problem, the global surrogate is then decomposed into a suite of local surrogate models, each associated with a particular damage hypothesis. For example, one surrogate may consider stiffness reductions only in a given span, another in a specific girder, and so on. By restricting each local surrogate to only a few parameters, the dimensionality of the inference problem becomes much smaller, leading to more stable and interpretable parameter estimation. Instead of solving one large and poorly conditioned inverse problem, the framework evaluates several smaller, targeted scenarios, each represented by its own simplified surrogate.

Fig. 1. The proposed methodology.

Data-driven component. In parallel with the model development, real SHM data are acquired from the bridge. The monitoring system typically consists of accelerometers, displacement sensors, or strain gauges installed at key structural locations. These sensors capture the dynamic response of the bridge under traffic and environmental excitation. The raw measurements undergo a rigorous data postprocessing phase, where modal properties such as natural frequencies, vibration mode shapes, or strain/displacement patterns are extracted. These processed quantities form the observational data vector are used to inform the surrogate models. Once the observational features are available, they are integrated into the surrogate-based framework through Bayesian inference. For each local surrogate model, the posterior distribution of the corresponding damage parameters is computed by comparing the surrogate predicted dynamics with the measured modal features. Because surrogate evaluations are extremely fast, this Bayesian updating can be performed for many competing damage scenarios without prohibitive computational cost. To objectively determine which damage scenario best explains the observed SHM data, the framework employs a BIC based model class selection. The BIC provides a principled balance between goodness of fit and model complexity: it penalizes models with unnecessary parameters while rewarding those that match the data accurately. Each local surrogate model receives a BIC score, and the scenario with the lowest score is identified as the most plausible representation of the current structural state. In this way, the framework does not simply estimate damage parameters but also statistically ranks the different potential damage locations. The final outcome of the process is a ranked set of damage hypotheses, together with their estimated severities and associated uncertainties. These results can be directly used by engineers to support maintenance and inspection