PSI - Issue 84

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

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1. Introduction Ensuring the safety and serviceability of bridge networks is a major challenge worldwide, as illustrated by numerous recent failures and the large proportion of aging structures in need of maintenance. Because real damage cases are rare and difficult to observe experimentally, the development of reliable SHM methods increasingly relies on techniques (e.g. vibration-based ones) that can operate under normal traffic and environmental conditions. Operational Modal Analysis (OMA) has become a cornerstone of this field (Magalhães & Cunha, 2011, Rainieri & Fabbrocino, 2014, Brincker & Ventura, 2015), enabling the continuous extraction of modal features sensitive to stiffness changes (Cabboi et al ., 2017, Quqa et al., 2021, He et al ., 2022, Tomassini et al., 2025). However, while unsupervised data-driven approaches are now routinely applied for damage detection at network scale, progressing from detection to robust damage localization and quantification remains difficult. The main limitation is the scarcity of labelled damage data and the impracticality of generating them on full-scale structures. To overcome this limitation, model-based strategies play a central role. Classical model updating, whether deterministic or Bayesian (Alkayem et al., 2018, Lam et al., 2018, García-Macías et al., 2020, Ierimonti et al., 2021, Li et al ., 2025), can provide detailed insight into the structural state, but its practical application is hindered by high computational costs when the space of the parameters is very large, causing possible ill-conditioning. Recent research has explored the use of surrogate models to approximate high-fidelity simulations with negligible evaluation time, enabling efficient probabilistic inference for SHM (Zhang et al., 2021). Yet, many existing approaches still rely on a single surrogate trained and tested on a single FE model, which may limit robustness and interpretability. In the above context, the present work introduces a multi-surrogate modelling framework designed to improve the reliability and scalability of model-based SHM in conditions where actual damage data are scarce. First, a global surrogate model is trained to reproduce the dynamic response of a bridge across a wide range of admissible damage parameters. Then, a collection of “local” surrogate models is generated, each restricted to a small subset of parameters associated with a specific damage hypothesis (e.g., a given portion, span, or support). This decomposition drastically reduces the dimensionality of the inverse problem, improving numerical conditioning and enabling efficient Bayesian inference for multiple competing scenarios. To further enhance robustness, the approach deliberately employs two independent FE models: one to generate the surrogate training data and another to produce validation damage scenarios. This avoids dependence on a single numerical formulation and provides a more realistic test of the methodology. Measured modal features from the monitored bridge are assimilated through Bayesian inference, and competing damage hypotheses are ranked using BIC (Gosh et al., 2006). 2. The proposed methodology The proposed framework consists of two major components (Fig.1): (i) a model-based component, where physics based numerical models and surrogate models are developed, and (ii) a data-driven component, where SHM data are acquired, processed, and used to update and compare damage hypotheses. Model-based component . The model-based stage begins with the development of two numerical representations of the bridge, each serving a distinct purpose in the workflow. The first, denominated as FEM A , is a computationally efficient beam-type finite element model, which is calibrated to match the global dynamic behaviour of the real structure. This simplified model is not intended to capture fine local effects; rather, it serves as a fast and flexible tool for generating a large synthetic dataset that spans a wide range of potential damage parameters across the bridge. Because surrogate models require thousands of training samples to learn the mapping between structural parameters and dynamic response, the beam model is ideal for this purpose due to its low computational cost. In parallel, a more detailed shell-element finite element model is developed and independently calibrated, denominated as FEM B . This model includes the bridge deck, girders, diaphragms, and other structural components with much higher geometric fidelity. In contrast to FEM A , FEM B is not used for surrogate training but for validating and testing the surrogate under realistic damage scenarios. By separating the model used for training from the one used to generate test scenarios, the framework avoids overfitting the surrogate to the assumptions of a single model. Once the global beam model has generated the required training data, a global surrogate model is constructed. This surrogate learns to emulate the