## 1 Introduction
Additionally, factors such as sampling frequency and data collection duration are crucial parameters that significantly influence damage localization analysis [22]. In some cases, preprocessing techniques like data cleaning, normalization, filtering, and resampling are required to prepare signals for analysis. While statistical metrics such as kurtosis, peak selection, Root Mean Square (RMS), and crest factor are commonly used as health indicators, their utility for precise damage identification is limited [21]. Simultaneously, various analyses have been performed in the time and frequency domains. For instance, in [23], the authors focused on defect detection in robotic gearboxes, utilizing vibration signals acquired from a dedicated test rig, where bearing and gear element faults were artificially machined to provide ground truth cases. Their method involves the use of a binning technique as a resampling scheme, which synchronizes each vibration record with the robot's commanded joint angle. The resampled signals were then filtered and transformed with the Fast Fourier Transform (FFT) so that defect-related harmonics appeared in the frequency or order spectrum. Finally, Principal ComponentAnalysis (PCA) was employed to infer the state of the gearbox as healthy or damaged. In [24], a hybrid algorithm was proposed for damage localization and quantification. This approach combines the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) method with an autoregressive moving average (ARMA) model. Specifically, the method involves fitting an ARMA model to selected intrinsic mode functions (IMFs), with the most relevant IMFs identified as damage-sensitive features using correlation metrics such as Sample Distance Correlation (SDC) and Modified Distance Correlation (MDC). The accuracy and robustness of the proposed methods were validated using both a numerical shear-building model and an experimental benchmark structure. Their findings demonstrated the effectiveness of the extracted damage features in identifying, localizing, and quantifying damage under ambient excitations and non-stationary signals. However, these features are of high dimensionality, which for real-time applications are not suitable. Similarly, ref. [25] developed a scheme for portal-crane slewing bearing monitoring, where finite element stress analysis guided sensor placement for radial and axial vibration signal collection. These signals were decomposed via Ensemble Empirical Mode Decomposition (EEMD), with maximum-correlation kurtosis deconvolution used to isolate the Intrinsic Mode Function (IMF) carrying the strongest fault signature. This was then compared with the fault reference templates using Constrained Independent Component Analysis (CICA) to identify the crane's state. At limitation of this method is its dependence on prior knowledge of fault mechanisms, which can hinder the detection of atypical or novel failures. Ref. [26] examined the dynamic behavior of variable-section pile foundations embedded in liquefiable soil-rock strata through large-scale shaking-table tests. Seven computer-synthesized seismic records were applied, and acceleration, displacement, and pore water pressure responses were measured. Accelerometers installed along the pile captured peak accelerations, while the spectral analysis using FFT revealed variations in frequency and amplitude, where elevated seismic excitations significantly accelerated liquefaction and amplified pile top acceleration. Although the time evolution of individual damage was not analyzed, the multimodal system data for each excitation case provided clear insights into pile curvature, stiffness degradation, and lateral displacement. The time-frequency domain offers insights into non-stationary signals. Ref. [27] evaluated three time-frequency techniques for structural health monitoring of offshore wind turbines: the Continuous Wavelet Transform (CWT), the Hilbert-Huang Transform (HHT), and a novel Single-Mode Function (SMF) approach.