## 1 Introduction  
The modal estimation theory uses free response or impulse response data to identify modal parameters, or uses excitation and response data simultaneously for parametric estimation of structures. However, in many actual engineering structures, the structures are often subjected to ambient excitation, which is difficult to be available. Therefore, how to estimate the modal parameter of structural systems without excitation data for structural control, damage detection, or analysis, and model updating is an important issue in structural engineering. The output-only modal identification can be implemented by multiple time-domain or frequency-domain methods. In 1965, [PERSON] and [PERSON] [1] proposed the minimum realization algorithm, using the Markov parameter composed of the impulse response function to obtain the minimum-order state-space representation. This method could describe the system accurately but disregarded effective estimation of impulse response with noise. In 1974, [PERSON] and [PERSON] [2] proposed the concept of Singular Value Decomposition (SVD) in conjunction with the minimum realization algorithm. In 1986, [PERSON] and [PERSON] [3] developed the eigensystem realization algorithm (ERA) based on SVD and the minimum realization algorithm. The ERA is mathematically reasonable, but improper optimum dimension and size of the Hankel matrix will result in incorrect modal parameter estimation [4]. In 1988, [PERSON] et al. [5] proposed the improved method of ERA, that is, the eigensystem realization algorithm using data correlation (ERA/DC), which reduces the effect of noise on modal estimation using the characteristics of a correlation matrix to increase the accuracy of identification. In 1993, [PERSON] et al. [6] assumed the ambient excitation to be a white noise and calculated the autocorrelation and cross-correlation functions of the response signal. They found that the mathematical version of the correlation function was identical to that of free response and impulse response and the modal parameter of the structure was obtained. [PERSON] and [PERSON] [7] used the correlation between structural system response signals corresponding to stationary white noise to redefine the Markovparameter and built the generalized Hankel matrix with SVD to obtain the system modal parameter. In recent years, the ERA has been extensively used in output mode estimation [8; 9]; this method has been effective in identifying the modal parameter of large-scale structures, such as offshore structural systems [10] and roof overflow powerhouses [11]. In 2011, [PERSON] et al. [12] studied the Hankel matrix of the ERA and found that a larger Hankel matrix made the decomposition of noise much easier. The numerical calculations may be erroneous if the difference between values of rows and columns is too large. [PERSON] [13] used a four-layer rectangular steel structure (benchmark structure) for the experiment in which the ambient vibration was measured; six modes were identified successfully by using the natural excitation technique in conjunction with eigensystem realization algorithm (NExT-ERA), including a group of similar modes. It was indicated that the number of sampling points of the correlation matrix would influence the identification result directly. [PERSON] and [PERSON] et al. [14] measured the rail vibration signals induced by impulse and actual train running and used the ERA for identification. The impulse and ambient vibration results were close to the computer-aided analysis result. [PERSON] and [PERSON] [15] used this method for output mode estimation of a suspension bridge. They identified low-frequency closely spaced modes effectively, but the high-frequency closely spaced modes could not be identified due to noise interference. [PERSON] et al. [16] used the method for mode estimation for the flat plate with similar modes and the pulley with repetition frequency mode.