# Health Monitoring of Civil Infrastructures by Subspace System Identification Method:
## 6 Application of Subspace Identification in Civil Engineering Structures  
Currently, stochastic subspace methods are widely accepted tools in civil engineering communities. Large number of SHM methods is operating in structures that are subjected to dynamic vehicular, seismic, wind, or impact loading. In this study, the application of the SSI algorithm in civil engineering structures is investigated in the following three categories:  
1. beams and two dimensional (2D) frames;
2. three dimensional (3D) frames and building structures; and,
3. bridges and other structures. Beams and two-dimensional (2D) models attempt to explain the performance of the SHM algorithm while using numerical FE or laboratory-scale models [153]. Many of the studies on these structures are generally academic in nature. Three-dimensional (3D) frames and building structures are generally used to investigate the practical aspects of SHM. Bridges are spectacular due to their specific loading conditions when compared to building-type structures [154]. Vehicular and pedestrian loading, together with exposure to environmental variations due to temperature and wind precipitation, have been the focus of the analysis of bridge structures in many pioneering studies of SHM [155]. Tables 7-9 show some application of SSI algorithms for damage detection of 2D frames, 3D frames, and buildings and bridges, and other structures, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Reference** & **Applied Damage Detection Technique** & **Test Structure** & **Damage Configuration** & **Damage Identification** \\ \hline [PERSON] et al. & Subspace theory and & Laboratory-scale & (1) 30\% and 50\% sew cut in the & \\
[156] & RSVD & aluminum beam & middle & Reliable results were obtained \\  & & & (2) A beam with fatigue crack & by applying the introduced \\  & & & & under several geometrical and & RSVD method. \\  & & & damping conditions. & \\ [PERSON] et al. & Theory of subspaces & Three simulations & Reduction in Young’s & \\  & and Kernel & of 1D and 2D case & modulus ranging from 10\% to & Most single and multiple \\  & parallelization & studies & 30\% correlated with the extent & damage scenarios \\  & & & of the damage & \\  & & & The crack-like damage & \\  & & (1) Numerical & simulated by the loosened 3 to & All damage cases were clearly \\  & & simulations & 7 number of bolts, which & detected under variable \\  & & (2) A 1D steel & correlates with a reduction of & excitation using the new test \\  & & frame structure & bending stiffness from 3\% to & method \\  & & & 30\%, respectively. & \\ Banan and & Concept of subspace & A simulation & Single damage case with a & \\ Mehdi-Pour, [159] & & rotation and Monte & 25\%, 50\%, and 95\% reduction & \\  & & Carlo simulation & structure & in Young’s Modulus & results were unreliable for all \\  & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Application of SSI algorithms for damage detection of beams and two-dimensional (2D) frames. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Reference** & **Applied Damage Detection Technique** & **Test Structure** & **Damage Configuration** & **Damage Identification Results** \\ \hline \multirow{3}{*}{[PERSON] et al. [160]} & Statistical & & & \\  & subspace-based & & & \\  & algorithm & & & \\  & & & & \\ \hline \multirow{3}{*}{[PERSON] and [PERSON] [114]} & \multirow{3}{*}{SSI and IV} & Numerical model of a & & & \\  & four-story, ASCE benchmark & & & \\  & steel frame & & & \\  & & & & \\  & & & & \\  & & & & \\ \hline \multirow{3}{*}{[PERSON] et al. [161]} & \multirow{3}{*}{SSI and DLV} & Numerical model and & & \\  & laboratory-scale of a & & & \\  & five-story steel frame & & & \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\ \hline \multirow{3}{*}{[PERSON] and [PERSON] [162]} & \multirow{3}{*}{SSI algorithms} & Laboratory scale of a & & \\  & single-bay six-story steel & & & \\  & frame structure & & & \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\ \hline \multirow{3}{*}{[PERSON] et al.