## 1 Introduction  
Structural health monitoring (SHM) is an emerging multidisciplinary field for damage detection and condition monitoring of structures [1; 2]. Due to the complexity of civil structures and the associated ambient-induced uncertainty, the development of a reliable SHM is a challenging task. Vibration-based damage detection (VDD) is a promising field in SHM that deals with assessing the health state of structures using vibration parameters [3; 4; 5]. The key factor in VDD is to establish a reliable analytical model of a dynamic structure to estimate vibration parameters. Several researchers have reviewedliterature on the vibration testing and damage detection of structures. [PERSON] and [PERSON] [6] provided a comprehensive review of VDD methods. [PERSON] [7] reviewed the applicability of damage detection system using vibration behavior of structure. [PERSON] et al. [8] conducted a comparative study to evaluate different VDD methods. [PERSON] and [PERSON] [9] performed a review of VDD techniques for small to medium span bridges. System identification methods provide a powerful tool to construct an analytical model of a dynamic system [10; 11; 12; 13]. Subspace system identification aims to establish a mathematical model for resolving practical problems in various branches of science and technology, such as chemistry [14; 15], computer science [16], electrical engineering [17], industrial engineering [18], bioscience [19] and even finance [20]. Using subspace system identification for modal analysis is a well-established field in the dynamics of structures [21; 22]. VDD methods rely on observable variations in changes in modal parameters (resonant frequency, damping, and mode shape) or their derivatives as indicators of damage existence. [PERSON] et al. [23] and [PERSON] [7] reviewed subspace system identification for its use in VDD and modal analysis. Structures in VDD can be broadly divided into two categories of: (1) mechanical engineering structures, such as airplanes [24], vehicle test rig [25], ship [26], and (2) civil engineering structures, such as bridges [27], buildings [28], offshore jackets [29], and dams [30]. It is difficult to sustain any clear distinction between mechanical and civil engineering structures but, as a general idea, they could be differentiated based on their characteristics. In general, mechanical and civil engineering structure are usually subjected to different loading and boundary conditions. Civil structures are stationary, massive, and heavy [31] and they have simple structural and geometrical configuration. Civil engineering structures can be modeled in the form of simple structural elements such as beams (e.g., in bridges and wind turbines) and frames (e.g., in buildings and offshore jackets). Shells and plates are mainly used in liquid retaining and transmitting structures (e.g., in dams, and pipes). However VDD methods are not suited for structures with changing dynamic characteristics such as dams and water reservoirs. Hence, the focus of the studies on VDD of civil engineering structures is to apply their developed algorithms on beam and frame structures. Though the requirement and deployment challenges for each class of VDD structure are different, diverse techniques are essential. Subspace system identification is one of the popular methods in time-domain that was first proposed by [PERSON] and [PERSON] [32] to derive modal parameters. [PERSON] and [PERSON] [33] enhanced its computational efficiency by extending the method to handle stochastic input data. [PERSON] and [PERSON] also utilized stabilization diagram for subspace system identification to improve the quality of the identified results [34]. [PERSON] et al. [32] extended the concept of weight matrices in subspace system identification as a basis for using the column space of the extended observability matrix.