PSI - Issue 84

640 Vanni Nicoletti et al. / Procedia Structural Integrity 84 (2026) 638–644 All coefficients are obtained through numerical analyses carried out on a finite element model of the bridge that accurately reproduces the measured static and dynamic behavior of the structure. The analytical formulation of the three c i coefficients, together with a detailed procedure for their determination based on the numerical model of the investigated structure, are discussed in detail in Nicoletti et al. (2025). The number of monitored stays ( ) and considered modes ( ) are predefined by the user. The optimal sensor layout is then identified by iterating over possible combinations of stays and minimizing the OF using the PSO algorithm and with the support of a custom-made MATLAB routine ( Fig. 1 ). During the optimization, the OF coefficients are updated by recalculating sensitivity, MAC, and AutoMAC metrics using only the selected stays. The process iterates until convergence, defined by a negligible variation of the best OF value over successive steps (Kumar et al., 2025). The optimal configuration from each PSO step initializes the next one. Finally, the optimal number of sensors can be determined by repeating the procedure for different values of and selecting the minimum number of stays that ensures an adequate OF minimization.

Fig. 1. Schematization of the optimal sensor placement procedure for cable-stayed bridges.

3. Application to a real cable-stayed bridge The proposed OSP strategy is applied to identify the optimal number and configuration of monitored stays for a real bridge considered as case-study and equipped with a combined static–dynamic SHM system ( Fig. 2 ). The case study is the recently built “Filomena Delli Castelli” bridge over the Saline River in central Italy. It is a 189 m -long, three-span steel–concrete cable-stayed bridge with varying deck width (19.2– 22.8 m) and includes a carriageway, pedestrian/cycle path, and technical spaces for stay connections to the deck. The deck consists of I-shaped girders, cross-beams, and a concrete slab partially lightened under the pedestrian path. The four inclined steel-tube pylons (up to 36.4 m high) are partially concrete -filled, connected under the deck, and anchored into plinths on piles. The deck features multidirectional pot bearings and Lead Rubber Bearings for seismic isolation, allowing horizontal displacements and improved energy dissipation. The bridge’s stay cable system comprises 40 stays—36 anchored to the deck and 4 to the abutments—arranged in two longitudinal lines, with 20 on the upstream side and 20 on the downstream side. Due to the outward transverse inclination of the pylons, the stays are inclined both longitudinally and transversely. Each stay consists of bundles of waxed, bi-plated parallel strands, with each strand made of seven galvanized low-relaxation steel wires sheathed in high-density polyethylene. This case study was extensively investigated by the authors both experimentally and numerically. Readers interested in the experimental activities performed on the bridge may refer to Innocenzi et al. (2022) and Gara et al. (2026), while, for the finite element modelling and numerical investigations (including the model updating) to Gara et al. (2026).