## 1 Introduction
proposed moving window EASI algorithm identify the operational modal parameters of the linear slow-time-varying system [27]. [PERSON] et al. proposed a moving window second order blind identification method for identifying operational modal parameters of linear slow-time-varying structures, and the performance of this method is better than the moving window independent component analysis [28]. [PERSON] et al. combined moving window with principal component analysis to effectively identify the operational modal parameters of the slow-time-varying system [29; 30]. [PERSON] et al. propose an operational modal analysis (OMA) method that uses eigenvector recursive PCA with a forgetting factor to identify the transient natural frequencies and transient modal shapes [31]. In addition, there are many time-domain methods for operational modal analysis. Some methods involve choosing a mathematical model to idealize the structural dynamic responses, including autoregressive moving average (ARMA) [32] and autoregressive (AR) model updating [33]. Based on singular value decomposition and QR factorization, [PERSON] et al. proposed a new method and applied it to the analysis of F-18 flutter flight test data. The method is capable of identifying the frequency and damping of the critical aircraft modes, those responsible for the flutter phenomenon [34]. [PERSON] et al. developed a novel method for moving force identification (MFI) called preconditioned least square QR factorization (PLSQR) method which seeks to reduce the impact of identification errors caused by unknown noise [35]. Some methods, such as time-frequency analysis method, can use the response signal of a vibration sensor to identify multi-modal parameters, but generally can only identify the natural frequency and damping ratio of multi-modal, but cannot identify modal shapes. Locality preserving projections (LPP) is a linear dimensionality reduction method [36], which makes it fast and suitable for practical application. In addition, LPP has several nonlinear technology data representation characteristics, which makes it more accurate in preserving data characteristics. Therefore, a method based on moving window locality preserving projections (MWLPP) is proposed to identify the operational modal parameters of linear slow-time-varying structures. LPP first calculates the transformation matrix of mapping the high-dimensional data to the low-dimensional space, and then computes the low-dimensional embedding. The primary contributions of the article can be summarized as follows:  
1. An operational modal parameter identification method based on LPP is proposed. The main idea is to find out the one-to-one correspondence between the coordinate response matrix and the low-dimensional embedded data, and the one-to-one correspondence between the modal shape matrix and the transformation matrix. The operational modal parameter identification problem can be transformed into the manifold dimension reduction problem of structural vibration response data. 2. The LPP algorithm and moving window method are combined to identify the operational modal parameters of linear slow-time-varying structures. 3. By comparing the operational modal parameter identification method based on moving window principal component analysis method, MWLPP has higher accuracy and effectively reduces the modal missing. 4. To verify the identification ability of operational modal parameters of linear slow time-varying structures based on MWLPP, a mass slow-time-varying 3-DOF (degree of freedom) structure and a density slow-time-varying cantilever beam structure were designed. The MWPCA method was used to identify the operational modal parameters of non-stationary vibration response simulation data for comparison. The remainder of this paper is organized as follows. In Section 2, The LPP algorithm is introduced to identify the operational modal parameters of linear time-invariant structures.