## 1 Introduction  
Vibration is an inherent property of structures and bad vibrations will cause damage to structures [1]. Operational modal analysis (OMA) identifies structural modal parameters (modal natural frequency, modal shape, damping ratio) from the output displacement response signal of the structure [2, 3], which can be used for damage identification [4], structural design [5], structural health monitoring of aircraft wings [6], and building performance assessment [7]. Manifold Learning [8] has become a research focus in information science since it was first proposed in 2000. Assuming that the data are uniformly sampled from a low-dimensional manifold in a high-dimensional Euclidean space, the purpose of manifold learning is to find the low-dimensional embedding in the high-dimensional space and find the corresponding embedded transformation matrix [9]. Based on this concept, the dimensionality reduction process of manifold learning needs to keep the data after dimensionality reduction satisfying the geometric constraint relation related to high-dimensional space manifold. At present, the more widely applied algorithms of manifold learning include principal component analysis (PCA) [10], isometric feature mapping (Isomap) [11], Laplacian eigenmaps (LE) [12], locally linear embedding (LLE) [13] and so on. Manyresearchers have applied manifold learning to operational modal analysis. [PERSON] et al. used principal component analysis for operational modal parameters identification to solve the problem of false modal in other identification methods [14]. [PERSON] et al. used locally linear embedding to identify operational modal parameters of complex three-dimensional continuous structures [15]. [PERSON] et al. used isometric feature mapping to identify the operational modal parameters of three-dimensional structures [16]. The method mentioned above is suitable for linear time-invariant structures. However, operational modal parameters of many structures are time-varying [17]. A linear structure whose system parameters (i.e., mass, stiffness, or damping) change over time is called a linear time-varying (LTV) structure. For example, during the flight launch of missile or rocket, the mass of the whole structure is gradually reduced due to the constant consumption of fuel [18]. With the activity of human flow, the structure characteristics of large human gathering places change, such as stadiums [19]. Therefore, time-varying systems are different from constant system. Time-varying structures need to identify time-varying parameters, which can monitor the state of the structures. At present, the time-domain and frequency domain methods are used to identify the operational modal parameters of time-varying structures [20; 21]. [PERSON] et al. analyzed and summarized the advantages and disadvantages of these methods in detail [22]. The time-varying structures can be divided into fast time-varying structures and slow-time-varying structures [23] and [PERSON] pointed out the system whose variation in coefficient is much less than variation in solution is called slow time-varying system [24]. For example, when a train passes a bridge quickly, the train works together with the bridge to form a unified dynamic system. The mass distribution and stiffness distribution of the system change rapidly with time, which forms a fast time-varying structural dynamics problem [25]. The mechanical arms in industrial manufacture can be regarded as slow time-varying structures [26]. The vibration response signals of linear slow-time-varying structures cannot be obtained completely at one time, but need to be obtained by continuous sampling over time. Therefore, the moving window method based on the theory of \"short time-invariant\" can be well applied to the identification of operational modal parameters of linear slow-time-varying structures. At present, the moving window method has been applied to some algorithms to identify the operational modal parameters of linear slow-time-varying structures. [PERSON] et al.