## 2 Literature Review
### Challenges in the Practical Application
Several researchers have studied the effect of environmental variation in dynamic identification, as shown in Table 2. Hence, some researchers reported measuring externally acting agents along with measurement of the vibration response. [PERSON] et al. [116] incorporated the variance of the uncertainties caused by humidity and temperature in identification of the modal parameters using subspace system identification. Two polynomial chaos expansion and independent component analysis were conducted to isolate structural variations caused by deviation of acting agents and extraction of structural features, respectively. [PERSON] and [PERSON] [117] addressed covariance-driven recursive stochastic subspace identification (RSSI-COV) for isolating environmental effect from anomaly caused by damage. [PERSON] et al. [118] analyzed the wind-induced vibration due to typhoons with various wind speeds. [PERSON] [119] evaluated the robustness of subspace system identification method by introducing uncertainty into the FE model. It was shown that, other than the effect of externally acting agents, the inherent performance of an identification scheme plays an important role in accuracy of the estimation result. Then studying of the detectability of the dynamic parameters is of paramount importance. [PERSON] et al. [120] studied the effect of several factors, including the proximity of natural frequencies, non-proportional damping, and accuracy of the identification algorithms, on the quality of the extracted damping ratios. [PERSON] and [PERSON] [121] investigated the influence of \begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt} p{142.3 pt}} \hline \hline
**Reference** & **Test Model** & **Environmental and Operational Effect** \\ \hline [PERSON] et al. [106] & Alamosa Canyon Bridge & 5\% daily change in natural frequency due to temperature variation \\ [PERSON] and [PERSON] [107] & Real-scale bridge & 4-5\% variation in natural frequencies during spring and winter were observed. \\ [PERSON] et al. [108] & a full-scale 17-story building & Correlation between modal frequency and temperature is reported in a 24-h period. \\ [PERSON] et al. [106] & Alamosa Canyon Bridge. & 6\% variation in modal frequencies have been recorded \\ Wood [109] & Bridge beam & Damp air caused decrease in natural frequency of structures \\ [PERSON] et al. [110] & Reinforced concrete slab & 2\% increase was recorded when relative humidity was ranged from 15\% to 80\%. \\ [PERSON] et al. [74] & Alamosa Canyon Bridge and Alampalli [111] & Variation in modal parameters is entirely dependent on the targeted structure \\ [PERSON] et al. [112] & Z24 bridge & Frequency variation due to ambient, shaker and impact excitations was very small \\ [PERSON] and [PERSON] [113] & Z24-Bridge & Temperature differentials across the bridge deck as the driving forces for natural frequency variations. \\ [PERSON] et al. [114] & Ting Kau Bridge & Temperature variation changes modal frequencies with variance ranged from 0.20\% to 1.52\% in the first ten modes. \\ [PERSON] et al. [115] & Experimental model of a Euler–Bernoulli beam & Natural frequencies variation/ambient temperature from 0 \({}^{\circ}\)C to 30 \({}^{\circ}\)C was 19\%, 10\%, 13\% and 7\% for 1 st, 2 nd, 3 rd and 4 th modes, respectively. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Influence of environmental and operational condition on damage detection of structures. the number of block rows and system order on estimation accuracy in subspace system identification algorithm. The most robust identification using a subspace system identification algorithm is obtained when the number of data goes to infinity. Short-length data cause estimation bias in modal identification. The bias error is intensified when dealing with systems having high damping and high frequency. [PERSON] et al. [122] proposed a combined subspace system identification and ARX algorithms for VDD of Hammerstein systems. [PERSON] et al.