## 1 Introduction
### Literature Survey  
To date, a number of vibration-based system identification and damage detection methods have been developed, and review articles with different emphases can be also found [2; 3; 4]. In general, structural parameters identification can be performed in three different paradigms: (i) time domain (e.g., [5; 6; 7; 8; 9; 10]), (ii) frequency domain (e.g., [11; 12; 13; 14]), and (iii) time-frequency domain (e.g., [15; 16; 17]). To identify structural parameters and their variations caused by damages, time domain analyses have been studied extensively. In particular, research on system identification based on least-squares estimation (LSE) has been carried out for a relatively long time, and much progress has been made. [PERSON] et al. [18] first proposed a time domain identification method by using recursive LSE in 1970s. By using the recursive LSE-based algorithm to upgrade the diagonal elements of the adaptation gain matrix at each time step, [PERSON] et al. [19] proposed an on-line parametric identification algorithm for the identification of non-linear hysteretic structures. By using LSE for the coefficient estimation, [PERSON] et al. [20] developed a system identification approach for non-linear restoring force identification. Based on the LSE approach, [PERSON] and [PERSON] [21] proposed an adaptive tracking technique to identify and track the system parameter variations due to damages. [PERSON] et al. [22] further developed a sequential non-linear LSE approach for the on-line identification of structural parameters by employing the proposed adaptive tracking technique. [PERSON] et al. [23] presented an adaptive system identification approach with the aid of the least mean square algorithm and least mean fourth algorithm. [PERSON] and [PERSON] [24] proposed a fast iterative recursive LSE algorithm for identifying non-linear systems with output colored noise. Although the aforementioned LSE-based approaches are capable of accurately identifying structural parameters, the external excitations in these approaches are all assumed to be available. However, in many cases, the excitations are unmeasurable or difficult to be precisely measured. Thus, the development of LSE-based algorithms for parameters identification under unknown loadings is required. Based on recursive LSE and the extended Kalman filter (EKF), [PERSON] and [PERSON] [25] proposed a system identification approach for the estimation of structural parameters under unknown excitations. Using the Taylor series approximation to transform a set of non-linear equations to linear equations, [PERSON] and [PERSON] [26] developed a modified iterative LSE approach for the element-level system identification in consideration of Rayleigh damping under unknown input. Based on the LSE technique and partially known input information, [PERSON] and [PERSON] [27] presented a time domain method for the simultaneous identification of the structural parameters and the time history of the unknown external excitations. A recursive least-squares estimation with unknown inputs (RLSE-UI) approach was proposed by [PERSON] et al. [28] for the identification of the structural parameters and the unmeasured excitations. To reduce the number of sensors required, [PERSON] and [PERSON] [29] further proposed a sequential non-linear LSE method for damage identification of structures with unknown inputs and unknown outputs. With the aid of a weighted positive definite matrix and a learning coefficient, [PERSON] et al. [30] proposed a weighted adaptive LSE approach for the identification of structural parameters and partially unknown loadings. This method was further extended for the identification of large-scale structures [31] and non-linear structures [32]. By sequentially using the EKF for the parameters identification of the concerned structure and LSE for its unknown external excitations, [PERSON] et al. [33] proposed an approach for estimating structural parameters with limited input and output measurements. Based on the fluctuating properties of wind, [PERSON] et al.