## 1 Introduction  
The dynamic characteristics of a structural system, such as natural frequencies, damping ratios, and mode shapes, can be investigated through numerical and experimental analysis. The response of a structural system is measured with a known excitation in modal testing, which is usually performed under well-controlled laboratory conditions. However, performing experimental modal analysis in real operating conditions may be possible, even for large and complex mechanical systems with real boundary conditions [1, 2]. The modal parameters obtained theoretically under the free boundary condition can be calculated by mathematical modeling to obtain the characteristics under arbitrary boundary constraints [3]. However, experimental results obtained under specified boundary conditions cannot be converted to other dynamic characteristics under the constraints of other boundaries. Therefore, it is difficult to perform modal testing under practical boundary conditions. The hammer excitation testing method is generally used to measure the frequency response function of the structural system, and then parametric estimation is performed to understand the dynamic characteristics of the structural system [4]. The system-identification methods described above are generally used to systematically determine or improve a mathematical model for a physical system and are implemented by measuring both observed structural excitation and corresponding response data. However, an obvious difference exists between the operating conditions of realistic structures in practical work and a controlled-environment laboratory in modal testing [5]. Dynamic characteristics cannot fully represent the system mode under real-world operating conditions; thus, it is necessary to study how to perform modal identification of systems in authentic operating environments [6]. Operational modal analysis [7], which is also called \"ambient modal analysis\", or \"output-only modal analysis\" [8], is extensively used in modal estimation of large structures under environmental and operational loads [9], such as vehicle suspension systems [10], offshore wind power facilities [11], and stadium structures [12]. Many identification methods have been extensively employed for modal extraction based on ambient response. In 1993, the so-called natural excitation technique (NExT) was proposed and initially used for modal estimation of structures in wind engineering, by assuming that ambient excitation is stationary white noise [13]. It was employed to replace free or impulse response in conventional modal estimation methods in the time domain. Subsequently, if ambient excitation can be expressed as a product model of stationary white noise and an envelope function describing the same variation of time history as excitation amplitude, the corresponding response of a structural system can be converted approximately into free response through the correlation technique [14] or random decrement technique [15]. Modal estimation can then be carried out, using the parametric estimation technique in the time domain. In addition, by introducing the correlation matrix between ambient response data to the procedure of ERA/DC, the ERA/DC can be effectively applied to modal identification of structures subjected to stationary white excitation, even to the practical recorded excitation of an earthquake [16]. In recent years, Stochastic Subspace Identification (SSI), applied with NExT, has been widely employed to modal estimation of structures under ambient vibration [17]. The SSI method is a time-domain modal-estimation method under the assumption of stationary white noise for ambient excitation and can be directly applied to modal estimation from ambient response records only [18]. There is no need for excitation measurement; thus, it is suitable for the analysis of ambient vibration.