## 4 Discussion  
This study examines three types of excitation scenarios in a 3-DoF structure: ambient vibration (AV vs. AVD), transient impulse response (ID vs. IH), and forced response with a shaker at three harmonic excitations (\(f_{d1}\), \(f_{d2}\), and \(f_{d3}\)). The vibration signals were analyzed using Power Spectral Density (PSD) and Continuous Wavelet Transform (CWT):  
* **Ambient vibration (AV/AVD):** Under ambient excitation, the damaged case (AVD) exhibited higher amplitudes of the spectral peaks and greater energy density across most frequencies compared to the healthy case (AV). * **Transient impulse (ID/IH):** The scalogram images revealed localized energetic differences in the timing of frequency components between the ID and IH cases, where PSD alone did not allow for observation of these behaviors. PSD showed a high attenuation in most of the spectral peaks in the ID case. In contrast, CWT revealed consistently higher energy density across most of the frequency components in this case. * **Shaker excitation (\(f_{d1}\), \(f_{d2}\), and \(f_{d3}\)):** Since the excitation frequencies lie close to the structure's natural frequencies, these modal frequencies appear with low amplitude in both PSD and CWT. Nevertheless, PSD retains adequate frequency resolution to identify spectral components, while CWT provides important details of temporal energy density variations across frequency bands close to the excitation frequencies. Across all excitation scenarios, the S3 sensor typically registered the highest power spectral density and the greatest accumulated total energy over time \((ES_{3}(s))\) near the first and third natural frequency (\(f_{n1}\) and \(f_{n3}\)). On the other hand, the S2 sensor showed higher spectral power and higher total accumulated energy \(ES_{2}(s)\) around the second natural frequency \((f_{n2})\), except in the \(f_{d3}\) case. Moreover, the total energy analysis \((TES_{i})\) revealed a significant difference in sensor energy contributions between the healthy and damaged conditions of the test rig structure in the AV and AVD cases. Natural frequencies estimated via CWT aligned closely with the PSD measurements. However, slight discrepancies were presented in both methods, which depended on the windowing and time-frequency resolution characteristics. Consequently, the relative errors (REs) between experimental frequencies of the AVD, ID, IH, \(f_{d1}\), \(f_{d2}\), and \(f_{d3}\) cases and the AV case (test rig structure in healthy conditions) remained lower than the theoretical values. In addition, the contribution of each method for the analysis of the natural frequencies, as well as the contribution of each sensor in each excitation case, was highlighted. Structural Health Monitoring (SHM) techniques are crucial for evaluating the condition of structures, enabling early maintenance interventions and monitoring factors that could compromise structural integrity. A structure's physical properties, including mass, stiffness, and damping, dynamically change over time due to environmental conditions, material degradation, and mechanical wear. Such alterations directly manifest in the structure's dynamic characteristics, such as natural frequencies, mode shapes, and damping ratios, which are governed by its stiffness and inertia matrices. Depending on the structure, various types of damage--including corrosion, fatigue cracks, loose connections, or localized deformations--can induce characteristic alterations in these modal parameters. Through continuous monitoring of vibration signals under different excitation scenarios, such as ambient vibration or transient excitations, and by applying advanced signal processing techniques, subtle deviations from baseline (healthy state) behavior can be detected. This allows for signaling the onset of damage before catastrophic failure occurs.