# Health Monitoring of Civil Infrastructures by Subspace System Identification Method:
## Vibration-Based Damage Detection (VDD)
### Covariance-Driven Stochastic Subspace Identification (SSI-COV) Method  
SSI-COV is a parametric output-only method that is used for modal analysis. The method use the vibration response time-history to extract the state-space model of a dynamic system. SSI-COV is a two-step procedure that utilizes the correlation function of vibration time-history. The system order is the only user defined parameter in SSI and it must be carefully chosen to obtain meaningful results. In these methods, the applied excitation is considered as white noise and it is equal to the covariance of the measured response time-history.  
Table 4 shows some SSI-COV algorithms that are applied for the damage detection of civil engineering structures. The damage indices in these methods are either modal parameters or a novel indicator for detecting changes that are caused by damage. In the previous two subsections, the application of SSI-DATA and SSI-COV algorithms for the damage detection of civil engineering structures was presented. In the following section, a comparison between the SSI algorithm and other key system identification methods in TD and FD is presented.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method/Reference** & **Damage Feature** & **Pattern Recognition** & **Test Model** & **Specification** \\ \hline SSI-DATA [94] & Eigensolutions & Statistical local approach & Analytical model & Application of a combined SSI \\ \hline SSI-DATA [95] & Residual error & Statistical process control & Aircraft model and real bridge structure & Kalman model is extracted to represent the reference state of the structure. \\ \hline Null-space based algorithm [96] & Residue matrix of orthomorality between subspaces & Statistical process control & Aircraft model and steel lighting device & Subspace analysis of the Hankel matrices is used for extracting features. \\ \hline CSI/ref [97] & Modal parameters & - & Z24 bridge benchmark structure & Stabilization diagram is adopted for post processing of modal data. \\ \hline McKelvey FD SSI [98] & Modal parameters & - & Uncontrolled cantilever plate & Natural frequency was predicted with an average error of 3.2\% and damping ratio had an average error of 2.8\% \\ \hline KPCA subspace based damage detection [99] & Subspace angles & Through mapping the Subspace angles & A beam with non-linear stiffness & KPCA performs damage detection problem without modal identification. \\ \hline CC-SSI [100] & Modal parameters & - & Ariane 5 launch vehicle & Clear results even in the case of non-stationary data obtained using this algorithm \\ \hline RSSI [101] & Modal parameters & - & 3-story steel frame and 2-story reinforced concrete frame & In this method the SVD algorithm is replaced by an advanced algorithm to update LQ decomposition. \\ \hline Improved SSI [102] & Modal parameters & - & \begin{tabular}{c} A numerical example \\ of 7 DOF and an \\ experimental model of \\ Chaotianmen bridge \\ \end{tabular} & Less computing time due to not having QR decomposition \\ \hline SSA [103] & Subspace-based and nullspace-based damage indices & \begin{tabular}{c} A numerical example \\ of 7 DOF and an \\ experimental model of \\ Chaotianmen bridge \\ \end{tabular} & 6-story steel frame & SSA algorithm uses SVD for change-point change-point detection \\ \hline Fast CC-SSI [104] & Modal parameters & - & \
\begin{tabular}{c} Operational data from \\ a ship \\ \end{tabular} & Fast multi-order computation \\ \hline ECCA-based SSI algorithm [105] & Modal parameters & - &
\begin{tabular}{c} FE model and \\ experimental wind \\ tunnel bridge model \\ \end{tabular} & Enhanced results are achieved for weakly excited modes and noisy response signals \\ \hline \hline \end{tabular}
\end{table}
Table 3: Some examples of schemes that use data-driven subspace system identification (SSI-DATA) in their damage identification process.