High-fidelity digital twins in structural dynamics rely on inverse identification techniques that exploit the multi-scale information content of dynamic signals and remain stable under modal misalignment. In frequency-domain formulations, classical pointwise misfit measures often struggle when simulated and measured responses exhibit spectral shifts. To address this limitation, this contribution investigates a signal-based multi-scale identification framework based on optimal transport distances defined on power spectra. The proposed approach extends recent work by M´etivier et al. [1] on graph-space optimal transport for time-domain waveform inversion to the frequency domain. Power spectra are compared using a graph-space Wasserstein distance defined on discrete frequency–amplitude graphs with uniform measures. This formulation accounts for spectral proximity and provides a geometrically informed misfit that remains meaningful under frequency shifts. The inverse problem is solved using an adjoint-based optimization framework. Forward simulations are performed in the time domain and transformed into the frequency domain for misfit evaluation. A signal-based multi-scale strategy progressively enriches the frequency content used in the misfit, enabling coarse-to-fine parameter updates. At early optimization stages, the restriction to low-frequency content allows the use of coarser time discretizations, leading to reduced computational cost. The method is demonstrated on synthetic dynamic response data from a beam with spatially varying material properties. Preliminary results suggest that the proposed misfit formulation offers promising robustness with respect to modal misalignment and noise, highlighting its potential for scalable parameter identification in digital twin applications.