PSI - Issue 84

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

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4. Issues in dynamic identification based-on dynamic-recorded force data The OSP strategy previously described allows the static and dynamic properties of the bridge to be taken into account. However, for the dynamic behaviour, it has been stated that the proposed strategy considers mode shapes obtained from force measurements dynamically recorded. It is well known that OMA applied to bridges yields displacement-proportional mode shapes when measuring accelerations or velocities, but produces modal force profiles when measuring forces, which generally differ from displacement modes (Garcia-Macias et al, 2023).

Fig. 4. (a) comparison between reconstructed modal displacements from load cells and identified ones from accelerometric recordings; (b) comparison between modal force profiles identified from load cell recordings and OMA and modal displacements from accelerometer recordings and OMA Differences depend on stiffness distribution, particularly the axial stiffness of stays and the flexural stiffness of the deck, and are minimized if stiffnesses are uniform (Fan et al., 2024). Measuring forces near stay-to-deck connections further reduces errors. Converting modal force profiles into modal displacements allows physical interpretation, comparison with numerical modal analysis, model calibration, and development of displacement-based damage localization procedures. This conversion is done using the structure’s dynamic compliance matrix ( ) , evaluated at the identified resonant frequencies either experimentally (via shaker tests on monitored stays) or numerically (using a calibrated FE model). A procedure for the numerical computation is described by the authors in Quarchioni et al. (2025). The procedure for reconstructing displacement mode shapes from force-based modal profiles is applied to the case study bridge. Load-cell recordings from a full on-site test (October 7, 2022), which also included deck acceleration measurements, allow a direct comparison between reconstructed displacements from load cells and experimentally identified modal shapes from accelerometers. Using =4 monitored stays along the deck and =7 target modes, displacement modal shapes are obtained from experimentally measured modal forces , which are oriented along the stays’ principal directions. To ensure consistency with the global reference system of the accelerometers, the modal forces are transformed using a rotation matrix. The quality of the reconstructed mode shapes is assessed using the MAC matrix, showing very high correlation (MAC > 0.98) with accelerometer-based modes (Fig. 4 a ), confirming the effectiveness of the load-cell-based reconstruction. A comparison between mode shapes derived directly from force-based profiles and those from accelerometers also shows general agreement ( Fig. 4b ); although less precise than that obtained with the proposed reconstruction procedure, the bridge’s near-uniform stiffness yielding an average MAC of 0.87 for the first seven modes, a very satisfying result. These results demonstrate the high reliability of the proposed procedure for reconstructing displacement modal shapes from modal force profiles, while also showing that satisfactory results can