## 1 Introduction  
Modal analysis is an experimental method used for structural parameter identification (natural frequency, damping ratio, mode shape). This method is used in vibration response calculations, the root cause analysis of vibration problems, damage detection, and virtual-acoustic simulations. In addition, it is also used for adding flexibility to multibody analyses and speeding up structural durability. Therefore, modal analysis is very effective for the evaluation of structural changes to any types of responses [1, 2]. The conventional modal analysis or the experimental modal analysis (EMA) requires a known excitation force on a system to obtain structural vibration response data, processes input and output signals to obtain the frequency response function, and finally, calculate modal parameters of the system by curve fitting [3]. This algorithm can better identify modal parameters of a system depending on its adaptability to the test environment; thus, it cannot be used under operating conditions. However, it is important to develop a method for the real-time and in situ acquisition of the state information of structures and the evaluation of their safety and residual life. In contrast, in the operational modal analysis (OMA), modal parameters of a structure are obtained only by measuring its output responses [4, 5]. [PERSON] et al. [6] found no significant difference between the modal parameters of a Plexiglas plate obtained by OMA and EMA under similar boundary conditions. Stochastic subspace identification (SSI), which was developed by [PERSON] and [PERSON] in 1991, is a powerful time-domain output-only modal parameter identification method [7, 8, 9, 10, 11]. SSI-based methods are less susceptible to prediction errors and computational efficiency [12]. Hence, continuous efforts have been made to improve the efficiency of SSI. [PERSON] et al. [13] studied the identification of user-defined parameters in a pure output, data-driven random subspace through the asymmetric partition of the Hankel matrix. [PERSON] et al. [14] proposed a sliding window-fuzzy C-means clustering algorithm in combination with deterministic-stochastic subspace identification (SC-CDSI), and reported that the proposed SC-CDSI identification algorithm could achieve the intelligent identification of online tracking of structural frequencies. [PERSON] et al. [15] improved the accuracy of modal parameter identification to determine the system matrix order of a damping ratio matrix. [PERSON] et al. [16] estimated periodic information from measured data using a non-steady-state Kalman filter, and then removed the periodic information from the original output signal by an orthogonal projection. [PERSON] et al. [17] proposed the combined use of different modal parameter identification methods, such as frequency domain decomposition, observer Kalman filter identification algorithm, and combined deterministic SSI. Dynamic displacement-based modal parameter identification methods are more useful than acceleration-based modal parameter identification methods, especially for low-frequency structures [18, 19, 20]. However, acceleration-based modal parameter identification methods are widely used because of difficulties in displacement measurement and the appearance of the trend term interference in acceleration integration [21]. Therefore, it is still a key problem to reduce the interference of the trend term drift error and low-frequency noise errors in acceleration integration. [PERSON] et al. [22] presented a displacement reconstruction method for low-frequency structures and introduced overlapping time windows to improve the reconstruction displacement accuracy and suppress low-frequency noises. However, when the target frequency was relatively low, it easily oscillated in the frequency domain. [PERSON] et al. [23] used two finite impulse response (FIR) filters to reconstruct dynamic displacements.