## 1 Introduction  
As one kind of flexible structures, long-span bridges tend to vibrate greatly under wind load. One of the most important wind-induced vibration phenomena is the flutter since it is tightly linked to the safety of bridges. The safety margin for flutter must be carefully evaluated during the design process. Although CFD and AI-based methods can predict the wind pressure and vibration response of structures [1, 2, 3], wind tunnel tests are still the main research tool for evaluating the wind resistance performance of structures and will last for a period in the future [4]. The sectional model test is a common method of wind tunnel testing. In sectional model tests, representative models of a bridge deck with aerodynamic and geometrical similarity are elastically suspended in the wind tunnel, and their behavior in the wind flow can be extrapolated to full scale. For flutter studies, a semi-empirical model characterizing the motion-dependent self-excited forces was first introduced by [PERSON] in the 1970s [5]. In this model, the self-excited forces are functions of the flow speed, vibration frequency, and state vector, while the coefficients in front of the state vector are called flutter derivatives because they are essentially the first partial derivatives of the self-excited forces with respect to the state vector. To estimate the flutter derivatives in [PERSON]'s model, free decay vibration, forced vibration, or random vibration sectional model wind tunnel tests are usually performed. The free decay vibration method measures the bending-torsion coupled free vibration response of the sectional model under no wind and in wind flow, and then extracts the flutter derivatives from the free vibration response. The forced vibration method refers to the use of a special mechanical device to drive the model to do harmonic vibration with a controllable frequency and amplitude; directly measure the vibration signals, such as the aerodynamic force, acting on the model and displacement or acceleration of the model; and then directly perform spectral analysis or time-domain analysis on the measured aerodynamic force and vibration signals to obtain the flutter derivatives. Traditionally, flutter derivative identification is carried out in uniform flow, and the effect of turbulence is ignored. Turbulence will alter the flow pattern around the section, which will affect the identification of the flutter derivatives. The random vibration method is to identify the flutter derivatives of the bridge deck by sectional model wind tunnel test in the grid-generated turbulence field. Either traditional eight flutter derivatives related to vertical bending and torsional motion from a two-degree-of-freedom (2 DOF) sectional model or 18 flutter derivatives including additional sway motion from a 3 DOF model are obtained. Among these three kinds of flutter derivative extraction methods, the free-decay vibration approach is the simplest one; for this reason, it is widely adopted and will be the focus of the present work. This method was first proposed by [PERSON] and [PERSON] [5], using first two SDOF free-decay tests to extract the direct derivatives (\(H_{1}^{*}\), \(A_{2}^{*}\), \(A_{3}^{*}\)) and then a coupled 2 DOF free-decay test to extract cross-derivatives (\(A_{1}^{*}\), \(H_{2}^{*}\), \(H_{3}^{*}\)). [PERSON] et al. [6] proposed a system identification procedure designed to estimate eight derivatives simultaneously by a single 2 DOF free-decay test. [PERSON] et al. [7] proposed the unifying least squares (ULS) method to extract flutter derivatives, where a unified error function combining vertical and torsional motion was employed. In order to balance the vertical and torsion signals, [PERSON] et al. [8] were the first researchers who introduced weighting factors into the ULS method for flutter derivative identification. Later, [PERSON] et al. [9] proposed the weighting ensemble least-square method (WELS) to extract flutter derivatives of bridge decks. [PERSON] et al.