###### Abstract
This allows for calculating gradients efficiently during the optimization process. In turn, exploiting these gradients in a gradient-based optimization scheme, leads to a fast convergence of the inverse problem. This approach was extended to solve elastodynamic problems in geophysics applications [38], where scaling is applied on the shear modulus, rather than the density. The robustness of the approach is further demonstrated for a numerical example with artificial noise. Based on the use of density scaling, [PERSON] et al. [39] introduced a model-based approach, where the inverse problem is solved in two steps. In the first step, a coarser resolution is used to identify the area of the defects (in the form of voids) and, in a second step, in the area around the defect, the material properties are modeled in a refined manner, to obtain a sharp resolution for the representation of the void. Similarly, the Finite Cell Method (FCM) allows for modeling features in the plate without the use of extensive mesh refinement. This concept was combined with Particle Swarm Optimization (PSO) by [PERSON] et al. [40] for damage detection and localization. An approach where Reduced Order Models (ROMs) are exploited in the inverse setting was given by [PERSON] and [PERSON] [41], who used a ROM for the Spectral Finite Element Method (SFEM) in the frequency domain in combination with CNNs for damage detection and RNNs for damage localization. This approach allows for damage detection, localization, and severity estimation. Despite the efficiency of the demonstrated model-based approaches, the computational toll remains high as long as a high-fidelity model needs to be solved, which prohibits their application in real-time or near-real-time monitoring. ROMs, in contrast, allow for expedited evaluations of the forward model. One class of ROMs is projection-based Model Order Reduction (MOR), where the matrices of the Full Order Model (FOM) are projected into a lower-dimensional space [42]. In this space, the governing equations are solved efficiently, while the solution of the system is subsequently transformed into the original space to recover the full solution. For wave propagation problems, however, the Kolmogorov \(n\)-width, which is a measure of the accuracy with which low-dimensional spaces can represent the solution of a high-dimensional problem, decays slowly. Thus, the size of the reduced bases needed to achieve the acceptable levels of accuracy might not lead to substantial computational gains [43]. An efficient use of projection-based ROMs for wave propagation can be realized through local projection bases [44]. Thereby, the initially collected snapshots, based on which projection bases are constructed, are clustered, with a separate basis being constructed for each cluster. This leads to bases of smaller size; however, it also requires the selection of an optimal basis at each time step of the online solution. While projection-based ROMs aim to reduce the number of Degrees of Freedom (DOFs), an alternative approach, proposed by [PERSON] [45] aims at reducing the number of linear system solutions required, which are also the most computationally demanding part of such a simulation. To this end, the ROM is evaluated in the frequency domain for the principal frequencies, which are significantly less than the number of time steps that would be required to solve the problem in the time domain. Such a frequency domain-based ROM was used by [PERSON] et al. [46] for damage localization. Building on a similar concept, the surrogate demonstrated in the present paper is evaluated in the frequency domain, only for a discrete subset of frequencies of interest. This concept was further applied to develop an ROM based on FRFs for detection of single defects in the authoring team's previous work [47]. Through geometrical transformations, defects of equivalent FRF values were found, and then, the FRFs are interpolated exploiting the Matching Pursuit algorithm.