## 2 Literature Review
### Application of Subspace System Identification for Modal Analysis  
Subspace-based identification methods are widely used for modal parameter estimation in time-domain [73]. For most VDD methods, it has been of great interest to study the effect of damage on natural frequencies, mode shapes and damping ratios of a dynamic systems [74; 75; 76]. Table 1 shows a number of studies that have used the subspace algorithm for modal analysis.  
The methodology of calculating modal parameters from state-space parameters of subspace system identification algorithm is presented in Figure 3.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**References** & **Extraction Method** & **Test Model** & **Specification** \\ \hline \multirow{4}{*}{[PERSON] et al. [77]} & \multirow{4}{*}{RSSI-COV (SubID)} & \multirow{4}{*}{Composite beam and an CACTUS aluminium plate} & Iterative procedure is used to improve identification results. \\  & & & an CACTUS & A stabilization histogram is applied to spurious mode elimination \\ \multirow{4}{*}{[PERSON] et al. [78]} & \multirow{4}{*}{SSI-ICOV (CSI-ic)} & \multirow{4}{*}{Simulated model of an industrial process tower} & Hybrid vibration testing or OMAX model was adopted in this study. \\  & & & Numerical models of & Model identification was conducted for a system with time-varying measurement noise \\ \multirow{4}{*}{[PERSON] \& [PERSON] [49]} & \multirow{4}{*}{Recursive SSI-COV-IV} & \multirow{4}{*}{Numerical model and a small scale wind turbine tower} & The random decrement (RD) method was selected in this study for its noise reduction capabilities. \\  & & & Numerical examples and & The model is appropriate to handle incomplete measurements data and truncated mode shapes \\ \multirow{4}{*}{[PERSON] et al. [79]} & \multirow{4}{*}{RD-SSIcov} & \multirow{4}{*}{Z24 bridge benchmark structure} & Stabilization diagram is adopted for post processing of modal data combined deterministic-stochastic subspace identification is used for modal analysis using this algorithm \\  & & & Natural frequency was predicted with an average error of 3.2\% and damping ratio had average error of 2.8\% \\ \multirow{4}{*}{Urgessa [81]} & \multirow{4}{*}{CSI/ref} & \multirow{4}{*}{Ariane 5 launch vehicle} & Clear results even in the case of nonstationary data are obtained using this algorithm \\  & & & In this methodSVD algorithm is replaced by an advanced algorithm to update LQ decomposition. \\ \multirow{4}{*}{[PERSON] et al. [82]} & \multirow{4}{*}{INproved SSI} & \multirow{4}{*}{Ariane 5 launch vehicle} & \multirow{4}{*}{Ariane 5 launch vehicle} \\  & & &  using this algorithm \\ \multirow{4}{*}{[PERSON] \& Loh [83]} & \multirow{4}{*}{RSSI} & \multirow{4}{*}{3-story steel frame \&} \\  & & & \\  & & & concrete frame & algorithm to update LQ decomposition. \\ \multirow{4}{*}{[PERSON] et al. [84]} & \multirow{4}{*}{Improved SSI} & \multirow{4}{*}{A numerical example of 7 Degrees of freedom (DOF) and experimental model of (Chaotianmen bridge & Less computing time due to not having QR decomposition \\  & & & CH matrix is constructed as \\ \multirow{4}{*}{[PERSON] et al. [26]} & \multirow{4}{*}{Fast CC-SSI} & \multirow{4}{*}{Operational data from a ship} & \multirow{4}{*}{Fast multi-order computation} \\  & & FE model and & Enhanced results are achieved for \\ \multirow{4}{*}{[PERSON] et al. [85]} & \multirow{4}{*}{ECCA-based SSI algorithm} & \multirow{4}{*}{experimental wind tunnel bridge model} & \multirow{4}{*}{reshspace signal} \\ \hline \hline \end{tabular}
\end{table}
Table 1: Some examples of the schemes that use subspace algorithm for modal analysis.  
Vibration-based SHM is concurrently subject of intensive investigation. Most of the VDD methods use modal parameters to extract dynamic characteristic of structure.