## 1 Introduction  
Modal identification is attracting growing attention in civil engineering for its wide application in the field of model updating, damage detection, structural control, and dynamic performance prediction. In the full-scale measurement of high-rise buildings or bridges, the input excitations are generally unavailable hence more efforts are devoted to developing the output-only modal identification methods. In the past decades, numerous algorithms were put forward, which could be mainly divided into two main categories (i.e., the time domain methods and the frequency domain methods). In the frequency domain, frequency decomposition and its reversions are the most representative and widely used [1, 2]. In terms of the time domain, the random decrement technique and the natural excitation [3] are utilized to obtain the free vibration response, and then the modal parameters can be obtained by some other traditional identification algorithms, including the eigensystem realization algorithm, the Ibrahim time domain, the least square complex exponential, etc. Additionally, the majority of the conventional methods are on the basis of the stationary assumption which is often violated in hazardous conditions, such as strong winds or earthquake excitations. To meet this situation, more improvements were made to overcome the limits of the stationary assumption. [PERSON] et al. [4] employed a clustering technique to expand the blind modal identification method [5] to identify the modal parameter from the seismic response. Assuming the nonstationary response is a sum of exponential functions, [PERSON] and [PERSON] [6] improved the Ibrahim time-domain method with a channel-expansion technique for a nonstationary white noise excitation. Notably, for the nonstationary signals or the time-dependent system, the Hilbert-Huang transform (HHT) is a powerful and adaptive approach to capture the time-dependent characteristics [7; 8]. The HHT contains two main procedures: the empirical mode decomposition (EMD) and the Hilbert spectrum analysis by means of the Hilbert transform. Without choosing basis functions, the EMD is data-driven and suitable to deal with the nonstationary signals: therefore, it is widely used in the field of modal identification combined with other methods, such as the random decrement technique [9; 10], stochastic subspace identification (SSI) [11] and natural excitation technique [12]. It should be noted that in the full-scale measurements, the multi-dimensional dynamic responses could be recorded synchronously by multiple sensors whereas the conventional EMD, which works only for a single signal, faces a severe problem of mode misalignment, i.e., the decomposed intrinsic mode functions (IMFs) from multiple sensors usually do not match in terms of their frequency order. More difficulties lie in the identification of mode shapes. For the IMFs derived from various signals, the number of IMFs tends to be different and usually does not match in a frequency scale; therefore, the direct usage of IMFs for mode shapes may lead to a faulty result. Subsequently, the EMD and the EMD-based modal identification algorithm might become invalid while dealing with measurements of multiple sensors or multi-dimensional signals. To overcome the limitation of EMD, the bivariate and trivariate EMD are proposed with the concept of rotating mode components [13; 14], and eventually, the multivariate empirical mode decomposition (MEMD) was developed as a generic extension of EMD which could compute the multivariate IMFs directly by projecting the signal in a multi-dimensional space [14]. Then, the MEMD was applied in many practical fields. [PERSON] et al. [15] employ MEMD to decompose downburst wind records, extract the time-varying means and carry out the time-frequency analysis. [PERSON] [16] and [PERSON] et al.