## 1 Introduction
In addition to traditional failure modes such as concrete crushing, rebar yielding, and shear cracking, FRP-strengthened R/C structures are also vulnerable to premature failures like plate-end and intermediate crack-induced interfacial debonding. To address the risks mentioned above and to mitigate the lack of information on damage progression, Structural Health Monitoring (SHM) methods are widely employed. These methods involve placing sensors on structural components to record regular measurements and using mathematical models to assess changes in dynamic properties as damage progresses. By analyzing changes in natural vibration frequencies, mode shapes, and modal damping factors, SHM enables the non-destructive detection of damage, identification of its location, and assessment of the associated failure risk over the structure's lifespan [20; 21; 22; 23]. Thereby, alterations in dynamic properties, such as modal frequencies, mode shapes, and modal damping ratios, can be effectively used. Previous studies have utilized experimental dynamic testing and modal analysis to identify the progression of damage in strengthened R/C structures [24; 25; 26; 27]. [PERSON] et al. [28] focused on evaluating shear-damaged R/C beams that were strengthened using CFRP strengthening with the NSM method. Modal analysis was used to assess the effectiveness of the strengthening by examining changes in the beams' dynamic properties, such as the modal frequencies and mode shapes. The study highlights how these changes can provide insights into the extent of shear damage and the improvements in structural performance after CFRP strengthening with the NSM method. [PERSON] [7] investigated the effects of glass fiber-reinforced polymer (GFRP) strengthening on damaged R/C beams through vibration analysis. The findings show that GFRP application improves the dynamic behavior of the beams, particularly by increasing their modal frequencies and reducing the extent of damage-inducedfrequency drops. The vibration analysis effectively captures the improvements in structural performance, indicating that GFRP strengthening enhances both stiffness and overall damage resistance in the R/C beams. [PERSON] et al. [29] showed that after a significant reduction in the first modal frequency value of an R/C beam induced by cracking under loading, the application of a composite plate along the flexural face of the beam provides an increase in the modal frequencies and small variations in the damping ratios. [PERSON] et al. [30] presented notable findings from the dynamic-based analysis, highlighting both the effectiveness of the strengthening technique and the reliability of using a numerical finite element model to assess the increase in the load-bearing capacity of the strengthened bridge. [PERSON] et al. [31] investigated the use of vibration monitoring methods to assess damage and evaluate the effectiveness of FRP strengthening in R/C beams. They explored how vibration-based methods can detect structural damage and monitor improvements after FRP application. The study focuses on comparing modal parameters, such as frequency changes, to identify damage and assess the impact of FRP strengthening. The findings suggest that vibration monitoring is an effective technique for both detecting damage and evaluating the performance of FRP strengthening in enhancing the structural integrity of R/C beams. In the literature, wavelet transform techniques are also effectively applied to detect and localize damage in beam-type structures, using both static and dynamic tests. [PERSON] et al. [32] performed wavelet analysis to R/C beams subjected to gradually applied static bending tests, while [PERSON] and [PERSON] [33] integrated wavelet transform with mode shapes to detect damage. Together, these works underscore the effectiveness of wavelet-based approaches in identifying structural damage in various loading conditions.