PSI - Issue 78

Francesco Mariani et al. / Procedia Structural Integrity 78 (2026) 875–882

876

sensor networks to facilitate the continuous collection of heterogeneous data during and following seismic events. However, processing and integrating these diverse data streams to infer damage from structural response requires ad vanced computational strategies capable of capturing both nonlinear and uncertain behaviours under seismic loads. The SHM methodologies can be broadly categorised into two approaches: data-driven and model-based. Data-driven techniques are employed to analyse sensor data, utilising statistical analysis or machine learning to identify anomalies or persistent deviations that may indicate structural damage [Rafiei and Adeli (2018); Jiang et al. (2023)]. These meth ods circumvent the necessity for explicit modelling of structural behaviour, thus o ff ering expediency and adaptability. However, they frequently lack physical interpretability. Conversely, model-based approaches utilise physics-informed numerical models, which are calibrated using sensor data to reveal damage by correlating observed responses with underlying structural states [Ierimonti et al. (2023); Giri et al. (2024); Giglioni et al. (2025)]. In seismic zones, where dynamic e ff ects are dominant, this mechanistic insight is essential not only for the detection of damage but also for its localisation and quantification in terms of severity and extent. However, the inverse problem of identifying dam age from observed seismic responses is typically ill-conditioned: multiple plausible damage scenarios can produce similar responses, especially when a ff ected by ambient noise or environmental variability. Small perturbations in data or model parameters can lead to large variations in inferred damage states, undermining confidence in the assess ment. As demonstrated in the research by Farrar and Worden (2013) and Mao et al. (2023), artificial neural networks (ANNs) have been shown to be e ff ective in a variety of engineering applications, particularly in the domains of clas sification and regression. However, conventional artificial neural networks (ANNs), characterised by fixed, determin istic weights, struggle with ill-conditioned inverse problems that are common in seismic structural health monitoring (SHM). It is evident that they are capable of producing single-point estimates even in circumstances where multi ple damage scenarios exist with equal probability, thus disregarding the inherent uncertainty in the data and model. In order to address these limitations, the present paper proposes the use of a Bayesian Neural Network (BNN) as a surrogate model for seismic SHM. In contradistinction to conventional ANNs, BNNs characterise their weights as probability distributions, thereby facilitating the modelling of uncertainty in both the data and the structural response. This probabilistic formulation enables the BNN to generate distributions of potential damage scenarios rather than deterministic outputs, thereby enhancing interpretability and robustness in damage assessment [Chang et al. (2018); Ogunjinmi et al. (2022); Magris and Iosifidis (2023); Jospin et al. (2022); Cha et al. (2024)]. The validity of the proposed approach is demonstrated through a real-world case study involving a post-tensioned concrete box girder bridge located in a seismically active area. This case study emphasises the practical applicability of the BNN-based framework and its capacity to enhance the reliability of post-seismic damage evaluation and decision making under uncertainty. The proposed method, summarized in Figure 1, is structured into two main stages, o ffl ine and online, and is based on the following key steps: 1. O ffl ine phase: this steps are dedicated to the preparation and training of a Bayesian Neural Network (BNN) that serves as a surrogate model for structural damage detection. This phase includes the following key steps: (a) Finite Element (FE) Model calibration: starting from available design information, model parameters such as material properties and boundary conditions are iteratively adjusted until the FE model accurately replicates the results of non-destructive testing (NDT) campaigns. The calibrated FE model forms the basis for data generation. (b) Identification of damage-sensitive features and sensor mapping: parameters that exhibit significant sensi tivity to damage and are measurable either directly or indirectly are identified. Corresponding measure ment points are defined within the FE model to reflect the sensor layout on the actual structure, ensuring consistency between simulated and monitored data. (c) Input dataset generation: a set of mechanical parameters combinations, representing both healthy and damaged conditions, is created using Latin Hypercube Sampling (LHS). This sampling technique provides broad and e ffi cient coverage of the parameter space while keeping the number of required simulations manageable. 2. Methodology