PSI - Issue 84

Antonio S. López-Cuervo et al. / Procedia Structural Integrity 84 (2026) 223–230 229 high correlation ( MAC=0.93 ). This loss of independence is consistent with the propagation of FEM modeling discrepancies into the OSP problem, since EfI maximizes the linear independence of the numerical target modes. Indeed, Fig. 7(b) reports the MAC matrix between the identified modes and the FEM predictions. Modes 1 and 3 show an excellent agreement with their numerical counterparts ( MAC ≥ 0.99 ), while Mode 2 does not match the corresponding FEM target mode ( MAC=0.02 ) and is instead highly similar to FEM Mode 1 ( MAC=0.94 ). Consequently, the EfI-optimal sensor layout derived from the FEM does not necessarily guarantee orthogonality when the experimentally identified modes differ from the target modes used in the optimization, which explains the observed AutoMAC structure. A similar behavior is observed for AVT-SG-2. The AutoMAC matrix in Fig. 7(c) exhibits the same pattern, with near-zero MAC values between Modes 1 and 3 and elevated MAC values between Modes 1 and 2. Consistently, the FEM–OMA MAC matrix in Fig. 7(d) shows a high correspondence for Modes 1 and 3, whereas Mode 2 presents an almost null agreement with its FEM counterpart ( MAC=0.17 ). However, the identified Mode 2 shows a notable similarity with FEM Mode 1 ( MAC=0.77 ), again indicating a misalignment between the numerical target modes and the experimental modal basis. Overall, these results highlight that the performance of EfI is critically dependent on the fidelity of the underlying FEM, as FEM–experiment discrepancies can translate into reduced modal independence in the identified basis.

Fig. 7. AutoMAC and MAC matrices for the displacement and strain mode shapes: (a) AutoMAC matrix of the identified modes in AVT-Acc-1, (b) MAC matrix between FEM and identified modes in AVT-Acc-1, (c) AutoMAC matrix of the identified modes in AVT-SG-2, and (d) MAC matrix between FEM and identified modes in AVT-SG-2. 4. Conclusions This work has presented a full-scale demonstration of strain-based OMA using resistive SGs, supported by an EfI based OSP strategy. A low-cost SG data acquisition system has been implemented and two AVTs have been conducted using two different sensor layouts. The results have been benchmarked against those obtained from two additional accelerometer-based tests. In terms of natural frequencies, the SG-based estimates have been consistent with the accelerometer-based ones, with residual differences attributable to thermal variations across campaigns. In terms of mode shapes, the agreement with the FEM has exhibited similar trends for strain and displacement modes, indicating consistent identification of strain mode shapes. Overall, the results have indicated that SG-based OMA can provide a viable and low-cost alternative to FBG-based deployments for the dynamic characterization of civil structures. Future work will include the application of strain gauges to reinforced-concrete bridges, where lower strain amplitudes are expected. Acknowledgements This work is partially funded by BUILDCHAIN and SMART-BRIDGES projects. BUILDCHAIN has received funding from the European Union’s Horizon Europe research and innovation program under grant agreement 101092052. SMART-BRIDGES is funded by MCIN/AEI/10.13039/501100011033. Antonio S. López-Cuervo is supported by an FPU contract-fellowship from the Spanish Ministry of Universities