PSI - Issue 84

Vanni Nicoletti et al. / Procedia Structural Integrity 84 (2026) 638–644

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1. Introduction This study introduces an innovative and cost-effective strategy for the structural health monitoring (SHM) of cable stayed bridges, based on the use of load-cell measurements on stay cables to perform both static and dynamic assessments of the structure. Load cells are exploited not only to monitor variations in axial cable forces under operational conditions (Mohammad Zarbaf et al, 2017), but also to capture high-frequency force fluctuations that allow the identification of the global dynamic properties of the bridge through Operational Modal Analysis (OMA). By enabling the extraction of both static and vibration-based information from the same sensing device, this approach significantly reduces the need for additional sensors, such as accelerometers installed on the deck, thereby simplifying the monitoring system layout and reducing costs, data volume, and maintenance requirements. A central contribution of the work is the development of an optimal sensor placement (OSP) methodology aimed at selecting the most informative stay cables to be instrumented. The proposed OSP algorithm maximizes the effectiveness of the monitoring system by ensuring high sensitivity to damage and accurate modal identification while minimizing sensor redundancy. The methodology is demonstrated through its application to a real cable-stayed bridge recently built in central Italy and equipped with an extensive SHM system. Nearly three years of monitoring data are analyzed to compare modal parameters identified from load-cell measurements with those obtained from traditional deck-mounted accelerometers. The close agreement between the two sets of results confirms the reliability and robustness of the proposed load-cell-based approach, highlighting its strong potential for advancing efficient and scalable SHM systems for cable-stayed bridges. 2. The proposed OSP strategy for monitoring cable-stayed bridges A major challenge in implementing combined static–dynamic SHM systems for cable-stayed bridges is optimizing the number and placement of monitored stays, since monitoring all stays is costly and generates excessive data (Sun et al., 2017, Masciotta et al., 2025). To address this, an Optimal Sensor Placement (OSP) strategy can be used to maximize SHM effectiveness. The proposed OSP procedure is based on both static parameters (stay axial forces measured by load cells) and dynamic parameters (modal force profiles derived from Operational Modal Analysis of high-frequency load cell measurements). Using modal force profiles ensures applicability to real bridges, including cases where significant differences exist between modal force and displacement mode shapes. The methodology employs the Particle Swarm Optimization (PSO – Gad A.G., 2022) algorithm to minimize an Objective Function (OF) that measures how effectively the selected stays provide informative SHM data. After defining the number of monitored stays and the vibration modes considered, the objective function is evaluated over possible sensor configurations, and the optimal stay selection is numerically obtained. The OF consists of three separate coefficients ( , with i = 1,2,3), each varying between 0 and 1 and reflecting a different aspect of the quality of stay selection. These aspects include sensitivity to damage in other stays and the relevance of each stay for identifying the selected mode shapes. The OF is defined as follows: OF= 1 1 + 2 2 + 3 3 (1) • 1 is the force damage sensitivity coefficient . It evaluates the sensitivity to variations in axial force in the stays caused by localized damage in other stays; • 2 is the force modal shape damage sensitivity coefficient . It evaluates the ability of a given sensor layout to distinguish between damaged and undamaged conditions using the MAC computed based on the modal force profile; • 3 is the orthogonality coefficient of the force modal profiles . It evaluates the correlation among modal force profiles for a given sensor layout, independently of damage. The objective is to minimize redundancy in the selected sensor configuration, ensuring that the considered modes are uniquely identified (AutoMAC based on modal force profiles); • w i are weight coefficients whose sum equals 1 and can be adjusted by the user to give more importance to certain contributions over the others. In this work, all coefficients are assumed equally distributed ( w 1 = 0.33; w 2 = 0.33; w 3 = 0.34).