## 2 Materials and Methods
### Experimental Setup of Three-Degree-of-Freedom (3-DoF) Structure
In this study, the experimental tests were carried out in the Applied Mechanics Laboratory of the University of Salerno, a facility equipped with tribology machines, a 3D industrial printer, a robotic arm, and large-scale mechanical systems. The operation of these equipment generated broadband environmental noise that served as ambient excitation for the test rig. The structural response under such ambient conditions is essential for dynamic characterization and structural health monitoring (SHM). Several studies have employed ambient vibration data to detect anomalies and assess the influence of environmental variations on structural behavior [32,33]. Figure 7 presents one of the acceleration measurements obtained from each sensor according to their respective location in the structure. Sensors S2 and S4 present the smallest range of acceleration magnitude variations compared to the other sensor positions. 2. AVD Case (Ambient Vibration with Damage): Similar to the previous case, the structure was excited with ambient vibration; however, in this scenario, structural damage was simulated by introducing the Half  
Figure 2:2 Vibration pattern analysis of the 3-DoF structure using signal processing techniques. Figure 2:3 Acceleration measurements under Ambient Vibration (AV) without damage. Cut Bar (HCB), as previously described. The purpose of this test was to analyze and compare the dynamic response of the structure under conditions of damage. Figure 8 illustrates the behavior of one of the acceleration measurements recorded. This case specifically aims to compare the vibration data under healthy (AV) and damaged (AVD) conditions. Notably, the acceleration signals in both scenarios exhibit a similar temporal evolution. However, the values of the accelerations increase slightly between the range of variations of \(\pm\)0.01 m/s\({}^{2}\) in the S2 sensor. 3. ID Case (Initial Displacement of the Third Mass of the Structure): This experiment was conducted to evaluate the structural response to a transient excitation induced by an initial displacement of the third mass, \(M_{3}\). The excitation corresponds to a step-like input resulting from the sudden release of the mass after being manually displaced from its equilibrium position. The displacement amplitude \((x_{d})\) ranged approximately between 2 cm and 3 cm. However, the displacement was applied manually, without a precise positioning or measuring device, resulting in uncontrolled initial conditions across repetitions. Figure 9 illustrates how the displacement was performed on the test rig. Although the amplitude and exact duration of each displacement varied slightly, the excitation consistently produced a free-decay response characteristic of an initial condition test. Figure 10 shows the vibration response of the structure, where dynamic variations are less pronounced in the measurements from the S1 sensor, and the S2 sensor exhibits the smallest range of acceleration magnitude variations compared to the S3 and S4 sensors. Such behavior is due to how vibrational energy is distributed across the structure. Figure 2:4 Acceleration measurements under Ambient Vibration with Damage (AVD). Figure 2:5 Initial displacement of the mass \(M_{3}\). * IH Case (Impact Hammer in the Third Mass of the Structure): This experiment utilized transient excitation in the form of an impulse generated by an impact hammer, following methodologies commonly applied in structural health monitoring of concrete beams and pipeline systems to detect minor structural changes and assess damage severity levels [10; 34; 35]. The impact was applied to the third mass, \(M_{3}\), of the structure using a USAG 382 hammer with a mass of 500 g, a length of 320 mm, and a flat square head measuring 118 mm. Due to the manual application of the impact, the input force was not instrumented, and neither the exact amplitude nor the duration of the impact was recorded.