## 1 Introduction  
During the production and use of a structure, vibration is inevitable. Vibration can cause damages to the structure and endanger human health [1]. The aim of operational modal analysis (OMA) is to identify the modal parameters (modal frequencies, mode shapes, and mode damping ratios) of structures by analyzing only their vibration response signals under operating conditions, rather than in a laboratory environment [2]. Recently, this technology has become an important method for solving vibration problems in engineering and has been widely used in mechanics, especially in the aerospace, civil engineering, maritime navigation, railway, and heavy equipment industries [3; 4]. A linear structure whose system parameters (i.e., mass, stiffness, or damping) change over time is called a linear time-varying (LTV) structure. [PERSON] [5] defined a system that has much less variation in its coefficients than its solutions as a slow linear time-varying (SLTV) system. Currently, there are two main modal parameter identification studies related to LTV structures [6]. The first one is based on the time-frequency analysis of nonstationary response signals [7], including the wavelet transform [8], Hilbert-Huang transform [9], and so on. The second category is the time domain method, which can be divided into time-varying state-space model-based method [10] and time-varying autoregressive moving average model-based approaches [11]. In time domain and (time-)frequency methods, the identification of time-varying structures is achieved by \"short time invariant\"-based method [12] and online and recursive techniques. Under the assumption of \"short time invariant\", and the theories of \"time-freezing\" [13] and \"quasi-stationary\" systems, the non-stationary response signals can be regarded as stationary response time series and the LTV structures can be regarded as linear time invariant (LTI) structures over short periods of time. A representative method is the moving window technique [14]. In online and recursive techniques, when identifying newly added data, it is not necessary to re-create a new model, and only the old model is required to recursively obtain the model at this moment. The core of online and recursive techniques is the recursive algorithm. However, in recursive methods, old data, which are not relevant at the time of study, still have a large impact on the results. Therefore, forgetting factor is introduced to solve this problem. In methods based on time-frequency analysis, vibration signals are processed offline in a batch-wise manner rather than online and recursively, so the wavelet transform- and Hilbert-Huang transform-based methods cannot be applied to online vibration control, structural health diagnosis, and realtime damage detection [15; 16]. The \"short time invariant\"-based methods are computationally expensive, and their results may be somewhat delayed and only applicable to SLTV structures. These online and recursive techniques have the problems of low precision and high time and space complexity, which means it takes a lot of time and space storage to execute these algorithms and the newest acquisition signal may not to be processed in a timely manner. The complexity of the algorithm has a great impact on its performance [17; 18; 19]. Therefore, this article is dedicated to reducing space and time complexity and improving identification accuracy. PCA is a multivariate statistical technique that has been successfully applied to fault diagnosis [20], the monitoring of industrial processes [21], and operational modal parameter identification in mechanical structures [22; 23]. By applying PCA, several principal components that reflect the essential vibrational characteristics of the system are extracted from highly correlated data. In modal analysis, PCA is sometimes called proper orthogonal decomposition (POD) [24].