## 1 Introduction  
In the areas of mechanical, civil, and transportation engineering, structural components are inevitably damaged in their long-term service process due to the coupled influence of multiple factors, typically material deterioration, environmental corrosion, temperature stress, and external load. The occurrence of damage may decrease the service performance of the structure and even lead to catastrophic accidents. Hence, the identification of early damage is critical to maintaining the integrity and safety of the structure. Compared with static damage identification, dynamic damage identification [1; 2; 3] has developed rapidly and attracted more and more researchers' attention. The main reasons are as follows: (i) This is a global damage detection pattern that does not require advanced knowledge of the local damage area. (ii) The dynamic response collected under environmental excitation can be used for damage identification analysis; furthermore, the normal use of the structure will not be affected during the experiment. (iii) With the rapid development of sensing technology, remote, and intelligent structural health monitoring can be realized. Among the initial research on dynamic-based damage identification, the modal-based dynamic damage identification research is the most in-depth and representative, while a series of related joint methods have been developed [4]. Modal-based damage identification methods mainly identify damage by comparing changes in structural modal parameters (e.g., natural frequency [5], mode shapes [6], damping ratios [7]) or modal derivative quantities (e.g., curvature mode shapes [8], strain mode shapes [9], flexibility matrix [10], etc.) before and after the damage, which can mostly reveal the spatial information of structural damage. However, the following problems still exist in practical applications: (i) the selection of the order of the modal parameters significantly affects the accuracy and sensitivity of damage identification because the low-order modal parameters are insensitive to slight damage, and the high-order modal parameters are equally sensitive to noise, although they are excellent in discriminating slight damage; (ii) Not only can structural damage lead to changes in modal parameters, but also environmental factors (noise, temperature, humidity) may cause significant changes in modal parameters. (iii) Modal-based identification methods usually require complex modal processing of the measured dynamic response, and part of the effective information is inevitably lost in the process; in addition, for some large civil engineering structures, the higher-order modal parameters are difficult to measure accurately (especially the higher-order mode shapes). Dynamic damage identification methods also include damage identifications that are based on signal processing [11; 12; 13] and damage identification based on statistical characteristics of the dynamic response. The latter utilizes statistical theory for damage detection directly in the time domain, and compared with other dynamic-based damage identification methods, this method is operationally simple and does not involve a complex modal processing procedure, which does not result in the loss of valid information. Moreover, this method combines a statistical theory in the field of mathematics, so it is highly resistant to the interference of measurement noise. A typical study using statistical characteristics of the dynamic response to identify the structural damage is as follows. [PERSON] et al. [14] first proposed a damage detection method based on statistical moments of dynamic response under Gaussian excitation. They combined the fourth-order statistical moment theory in the field of mathematical statistics to define a damage identification index that is sensitive to damage and insensitive to measurement noise. In subsequent studies, [PERSON] et al. [15; 16] extended the method based on response statistical moments.