PSI - Issue 84

Alberto Barontini et al. / Procedia Structural Integrity 84 (2026) 352–359

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Nomenclature effective independence distribution of the sensor set fractional eigenvalue distribution matrix correlation length number of modes Fisher Information Matrix (FIM) Var(Φ ) elementary variance of the residual of the distribution of mode shapes weight value ∈ [0,1] spatial distance between the i and j degrees of freedom ̅ ratio between the greatest distance among degrees of freedom and number of sensors eigenvalues of FIM mean of the determinant of the FIM ∗ maximum value of the mean of the determinant of the FIM for the same number of sensors Σ covariance matrix standard deviation of the determinant of the FIM ∗ maximum value of the standard deviation of the determinant of the FIM for the same number of sensors Φ mode shape matrix partitioned to candidate sensor locations and target modes Φ mean mode shape matrix Φ residual of the distribution of mode shapes Ψ eigenvectors of FIM 1. Introduction As infrastructure networks worldwide continue to age, vibration-based Structural Health Monitoring (SHM) has become essential for cost-effective management of critical assets, as bridges. SHM enables automated condition assessment by continuously collecting data through networks of strategically deployed sensors, providing near real time information on the system’s dynamic behaviour to support informed maintenance and safety decisions (Barontini et al., 2019; García-Macías et al., 2023; Hormazábal et al., 2023; Magalhães et al., 2012). Rather than relying solely on periodic inspections, SHM systems allow asset managers to detect damage, track structural performance over time, and prioritise interventions, thereby reducing life-cycle costs and minimising service disruptions (Y. An et al., 2019; Barontini et al., 2021; Orcesi & Frangopol, 2011). A key aspect of effective SHM is the optimisation of sensor locations to balance installation and maintenance costs with the quality and usefulness of the data collected. This challenge is addressed by Optimal Sensor Placement (OSP) field (Ostachowicz et al., 2019). The classical formulation of OSP resorts to a reliable preliminary numerical model of the structure, which is used to predict its modal properties and to identify the optimal locations for a minimal number of sensors. However, for existing structures, which are often modified over time and may have experienced deterioration, significant uncertainties in their geometry, structural details, material properties and current condition are common. These uncertainties can compromise the reliability of the numerical model. While this issue is particularly evident in complex historic structures (Chaves et al., 2023), it also affects bridges and other infrastructure systems. A recently explored alternative relies on data-driven optimisation of the sensor network to overcome the limitations of inadequate preliminary models by leveraging real data (Chaves et al., 2025; Masciotta et al., 2025). Nonetheless, this approach requires the availability of extensive experimental data, which in many practical situations may be unavailable or impractical to obtain. To address these challenges, OSP for the dynamic identification of bridges should be formulated within a stochastic framework that explicitly accounts for the inherent uncertainties associated with real structures. With the aim of developing a statistically robust approach to this problem, the present work focuses on an essential first stage: the analysis and comparison of existing solutions reported in the literature. While several studies have addressed sensor location optimisation based on models with deterministic properties, considerably less attention has been devoted to approaches that explicitly account for modelling errors due to uncertainties. These uncertainties may be epistemic, arising from limitations in the preliminary model, or aleatory, inherent to the physical system itself