# Health Monitoring of Civil Infrastructures by Subspace System Identification Method:
## 1 Introduction
System identification is a mathematical procedure for establishing an analytical model based on experimental data. System identification is a mature field in SHM to extract modal parameters in VDD methods [24]. System identification methods in SHM can be classified into three categories based on their domains, including: time-domain (TD), frequency-domain (FD), and time/frequency domain (TFD) [25]. TD methods are more attractive for monitoring of civil structures, owing to the direct use of vibration signals. TD methods are generally classified within three groups of subspace system identification (SSI), natural excitation technique (NExT), and auto-regressive moving average (ARMA) [26]. The premise of the NExT method is that the response signals of a structure for ambient excitation and free-vibration have the same analytical form [27]. ARMA-based methods are popular statistical strategies for VDD of civil engineering structures. The auto regressive (AR) part ARMA models a linear function for the response time-history and the moving average (MA) section determines the moving average of the measurement response. The SSI algorithm presents a harmonious combination of algebraic, mathematical, statistical, and geometrical tools to identify the system parameters. SSI takes advantages of LS, angles between subspaces, QR decomposition, singular value decomposition (SVD), Kalman filter, and stochastic realization theory to deal with the problem of modal parameter identification. Subspace-based methods that are used for the parameter identification of civil structures are mainly one of the following two methods of data-driven subspace system identification (SSI-DATA) and covariance-driven subspace system identification (SSI-COV) approaches [28]. The ARMA model has the most similarity to the SSI-COV model, as both methods use the correlation function of the vibration measurement in their preprocessing stage. Recently, a large number of subspace-based methods have been applied in VDD. However, the previously conducted surveys have not kept pace with the changing environment and diversity in this field. Therefore, there is a need for a review focusing on the most important recent studies conducted in the considered area. The presented review attempts to address the available studies that employed subspace-based techniques in VDD of civil structures. This paper provides an overview of the background and new findings in SSI with a focus on both theory and practice. In addition, it describes some contributions toward the development and application of the SSI algorithm in recent years. This review study is organized, as follows. In Section 2, SHM methods are outlined and the strength and drawbacks of each class are highlighted. Section 3 evaluated vibration-based damage detection (VDD) methods. The focus is on subspace system identification in the three later sections (Sections 4-6). Section 7 introduces some commercially available software that use subspace as their main constituent. Future research directions and conclusions are provided in Sections 8 and 9, respectively.