## 1 Introduction  
When delving into modern and developed societies, one finds that strategically significant and intricately complete civil infrastructures and buildings constitute their core commonality. This commonality manifests broadly in widespread applications across transportation, industrial production, economic activities, and the protection of personnel and materials. Given the importance of these facilities, we cannot overlook their aging and degradation, nor can we afford the inestimable losses and harm that may result from failing to detect issues and take timely action. Furthermore, due to the large number and ubiquity of these structures, the majority of them are inevitably and frequently exposed to continuous environmental vibrations and severe disaster events, such as earthquakes, floods, tornadoes, and corrosion, as well as other uncertain factors like traffic loads, material aging, impacts, and environmental corrosion. Consequently, monitoring and assessing structural performance has become a fundamental requirement for enhancing structural integrity and safety. Structural health monitoring (SHM) and structural damage detection methods are continuously evolving, with research gaining new life across various scientific fields such as aerospace, civil, and mechanical engineering [1]. To achieve SHM, researchers employ a variety of different sensor devices to collect signal data, including acoustic, pressure, temperature, force, and accelerometer sensors. This has given rise to the processing of multivariate signals. The core objective of signal processing is to collect, analyze, and process multivariate signals such as vibrations, noise, temperature, and pressure generated during the operation of mechanical systems, extracting key features that reflect the system's state, thereby enabling early fault detection, precise diagnosis, and effective prevention. In recent years, SHM researchers have dedicated themselves to integrating and fusing various cutting-edge technologies--particularly those from different information technologies and engineering methodologies--to develop economical, accurate, and reliable monitoring methods. Additionally, various data mining techniques, visualization tools, and statistical computations frequently appear in monitoring and processing solutions. Beyond traditional vibration-based monitoring, detections methods related to sound, temperature, and motor current are now emerging, as mentioned by [PERSON] [2]. Moreover, changes in structural properties, such as stiffness, are significantly observable in variations of multivariate signals, and internal structural components can also be accurately represented through these signals. Therefore, it is crucial that signal processing techniques for monitoring changes in structural vibration responses are robust during the process of damage localization, quantification, and detection. The diversity of signals requires the adoption of correspondingly diverse processing techniques based on their specific characteristics, and for a particular signal, a so-called powerful signal technique is one that is appropriately adapted. For example, linear signals satisfy the superposition principle and can thus be analyzed using linear processing techniques such as linear filters and Fourier transforms. Nonlinear signals, however, do not satisfy the superposition principle, and they require nonlinear processing techniques such as nonlinear filters and Hilbert-Huang transforms to reveal their complex characteristics. Directly applying a highly powerful linear signal processing model cannot guarantee perfect representation of nonlinear signals. Therefore, in the process of studying nonlinear signal processing models, new and specific technologies are often required. In mechanical systems and structures, due to the complexity of operating conditions, external environmental interference, and the gradual aging and damage of materials and components, the collected signals are often non-stationary and nonlinear.