## 4 Experimental Case Study  
The benchmark vibration data from Alamosa Canyon Bridge in New Mexico,USA is adopted for the experimental study. The experimental procedure for implementation and instrumentation of the vibration tests as well as the obtained response signals are made accessible through the Los Alamos National Laboratory's (LANL) website [46]. The benchmark dataset includes response signals extracted from the structure under artificial and natural excitation. These benchmark data have been used as experimental case study for many outstanding researches [47; 48; 49]. Figure 8 illustrates the ambient vibration test on the Alamosa Canyon Bridge. Dynamic load is applied to the structure by direct passing of a cesar across the bridge deck and also by the traffic-induced ground vibration.  
A direct vibration load was introduced by passing a typical car over the bridge. The car and the van containing the test instrumentation are shown in Figure 9a. In order to introduce the ground-induced vibration into the structure a truck passing over the adjacent bridge was used as shown in Figure 9b. The robustness of the subspace algorithms against the environmental and operational noise are evaluated using pole analysis. The acceleration response signals for the evaluation process are obtained from the accelerometers mounted on the bridge structure. A total of 30 accelerometers were installed within six rows in the widths of each deck and one accelerometer was mounted on the girder. The acceleration response time-histories are shrunk into groups of 1024 samples with the frequency of 50 Hz. The obtained signals are rearranged into 100 sets of five distinctive rows for the identification purpose [50]. Unlike the numerical test in Section 2 there is no access to the noise-free reference state of the real-world structures so, the optimum choice of the weight matrix is selected from the densest distribution of pole values in the complex plane plot.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & **Elapsed Time (s)** \\ \hline PC & 10.8 \\ UPC & 5.2 \\ CVA & 11.3 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The average elapsed time for identification of the dynamic model using different subspace algorithms.  
Figure 10 illustrates the results obtained for the comparison of the noise-robustness in subspace algorithms using pole analysis in the experimental model. Poles of the bridge structure lie inside a zero one plane. The scatteration of the conjugate poles is symmetric to real axes. The scatteration of poles in UPC algorithm (Figure 10a,b) are more aggregated particularly in the 1 st, 2 nd, and 4 th order. It means that the UPC algorithm is more robust to the noise variation compared to the other algorithms. Pole values obtained by PC algorithm (Figure 10c,d) are more aggregated compared to CVA algorithm. The CVA (Figure 10e,f) algorithm has the highest scatteration among all subspace algorithms.  
Figure 10: The estimated poles of the numerical model for: (**a**) 1 st and 2 nd and (**b**) 3 rd and 4 th orders in PC algorithm. (**c**) 1 st and 2 nd and (**d**) 3 rd and 4 th orders in UPC algorithm. (**e**) 1 st and 2 nd and (**f**) 3 rd and 4 th orders in CVA algorithm.  
Figure 9: The ambient testing of the Alamosa Canyon Bridge. (**a**) Crossing of vehicles over the bridge. (**b**) Passing vehicle from the adjacent bridge [46].  
The obtained result for the noise robustness of the subspace algorithms show that the PC is least affected by the noise inclusion.