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Received Oct 30, 2017; Accepted Feb 25, 2018
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1. Introduction
In the past few decades, the time-varying modal parameter identification method has attracted substantial interest in the modal analysis and testing community. The time-varying behavior is caused by the system parameters changing, such as mass properties of a flight vehicle and stiffness properties of a thermal protection system in the high temperature environment. In practice, many time-varying systems can be treated as the linear time-varying (LTV) system. Numerous methods have been developed under the LTV framework, such as time-frequency analysis method [1, 2]. Short time Fourier transform (STFT) has been used as an effective signal process tool in the modal analysis community, and the influence of Fourier analysis parameters has been studied in [3]. Compared to the Fourier analysis, the wavelet transform (WT) has an adjustable window size and location, and its effectiveness has been demonstrated in [4, 5].
Besides the time-frequency analysis method, the subspace identification method has also been widely used. Liu extended the concept of the modal parameters into LTV systems [6]. Subsequently, Liu and Deng [7] developed a subspace-based algorithm for pseudo natural frequencies (PNF) and experimentally verified it by an axially moving cantilever beam. The modal parameters, which are assumed to be changed slowly, can be extracted from a series of matrices constructed by the response data. Different from the above algorithm, Juang and Pappa [8] proposed a subspace-based identification algorithm that requires only one experiment. In this algorithm, the subspace is constructed by the singular value decomposition (SVD). For the online tracking, the SVD costs too much computational time. In order to overcome such shortage, Pang et al. [9] utilized the projection approximation subspace tracking (PAST) [10] technique instead of the SVD. Due to the problem of data saturation, PAST algorithm may lose its tracking ability. To solve this problem, Yu et al. [11] presented a finite-data-window least squares technique. Goethals et al. [12] presented a recursive method to identify the vibroacoustic behavior of an airplane utilizing the instrumental variable projection approximation subspace tracking (IV-PAST) technique. Xu et al....