# Health Monitoring of Civil Infrastructures by Subspace System Identification Method:
## 4 Comparison between SSI and Other System Identification Algorithms
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Reference** & **Identification Method** & \\ \hline \hline  & SSI and ERA & \(\bullet\) Both the ERA and SSI methods are accurate and provide stable results for modal parameters. The methods are extremely sensitive to the size of the Hankel matrix. \\  & \(\bullet\) The work burden of the algorithms is large and usually needs to perform multiple analyses. \\ [PERSON] et al. [54] & PolyMAX & \(\bullet\) The PolyMAX and PolyLSCF methods are fast but the operator needs to have a high qualification. \\  & The algorithm is sensitive to the size of the Hankel matrix and sometimes needs to perform multiple analyses. \\  & PPM & \(\bullet\) PPM is a simple and less demanding algorithm. \\  & The algorithm can identify modal parameters in the pre-defined frequency range. \\  & PZM and PolyLSCF are basically similar and the obtained results can complement each other. \\  & PZM uses a non-power spectrum for modal frequencies and damping. \\  & EPD and PSDD are fast and easy for modal parameter identification under ambient excitation. \\  & EPD and PSDD & \(\bullet\) The estimation precises in these methods depend on the accuracy of the power spectral density. \\  & Both methods are sensitive to noise and leakage error. \\  & WT & \(\bullet\) The accuracy of the WT is highly high. \\  & SS & \(\bullet\) The WT is not conducive to the real-time monitoring due to analysis load. \\  & SSI & \(\bullet\) Similar performance was confirmed for the SSI and POD methods. \\  & FDD & The FDD method slightly suffered from resolution problems due to the limited number of data points. \\  & FDD & \(\bullet\) Though SS has no resolution problems, more scattered data are generated when dealing with output-only modal analysis. \\  & SSI-DATA & \(\bullet\) All three output-only methods of SSI-DATA, AR and ERA/RDRS show high robustness to modal frequency estimation in non-stationary conditions. \\  & [124] & AR \\  & [124] & \(\bullet\) By using the same methods, damping estimates were very scattered. \\  & ERA/RDS & \(\bullet\) The estimation error of modal frequency in all methods remained less than 1.5\%. \\  & & \(\bullet\) The error in estimating damping ratio ranged from 15\% (in SS6) to 50\% (in AR). \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._Table 5 shows the results of a comparison between several TD, FD, and time-frequency domain methods for damage detection and modal analysis of civil engineering structures. The obtained results confirm the reliable performance of the TD methods. It was shown that SSI is a powerful tool for modal identification, in which closely spaced frequencies are not of the same type (e.g., bending or torsion) [55]. It was reported that the identified mode shapes using SSI-DATA were the most reliable when compared to MNExT-ERA or EFDD [122]. Moreover, fewer errors were obtained in estimating the damping ratio using the SSI algorithm as compared to ARMA [124]. However, SSI has some disadvantages, such as requiring human judgment of system order for implementation [55]. On the other hand, the work burden of the SSI algorithm is large and it usually needs to perform multiple analyses [54].