## 3 Case Study
### On-Site Measurement Campaign before Damage
#### 3.2.2 Data Processing and Feature Extraction  
The MACEC toolbox [53] was used to analyse all of the measurement data. First, the data needed to be pre-processed. A measuring grid was created on the MACEC system. The measuring points were assigned and numbered, corresponding to the actual measuring points. Input parameters, such as sensor label, sensitivity, data, and distance to each measuring point, were assigned. Such measured signal data are often skewed and do not coincide with the balance axis; the remove-offset function removes these components from the measurement data. The obtained dynamic signal was taken from the time domain and represented in the frequency domain using the Fast Fourier Transform (FFT) algorithm (Figure 6).  
Based on input data, as well as data obtained from pre-processing (noise removal, and data classification into corresponding nodes), a model with complete data for measurement points was formed. System identification was accomplished using the covariance-based  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Setup** & **Reference Point** & & & & **Moving Point** & & \\ \hline Setup 1 & 103 z & 103 y & 100 y & 100 x & 200 y & 200 x & 101 y & 101 z \\ Setup 2 & 103 z & 103 y & 102 y & 102 z & 104 y & 104 z & 201 z & 202 z \\ Setup 3 & 103 z & 103 y & 105 y & 105 z & 106 y & 106 z & 204 z & 205 z \\ Setup 4 & 103 z & 103 y & 107 z & 107 z & 108 y & 108 z & 205 z & 206 z \\ Setup 5 & 103 z & 103 y & 109 y & 109 z & 110 y & 110 z & 207 z & 208 z \\ Setup 6 & 103 z & 103 y & 111 y & 111 x & 211 y & 211 x & 209 z & 210 z \\ Setup 7 & 103 z & 103 y & 1001 y & 1001 x & 1002 y & 1003 y & 1003 x & 1004 y \\ Setup 8 & 103 z & 103 y & 1005 y & 1006 y & 1007 y & 1008 y & 1009 y & 1010 y \\ \hline \hline \end{tabular}
\end{table}
Table 1: DOF at measuring points.  
Figure 6: Dynamic response sensor in: (**a**) time domain and (**b**) frequency domain.  
stochastic subspace identification (SSI-COV) technique. Based on knowledge from numerous similar constructs, the following criteria were selected to concretise and characterise the modality: frequency stabilisation (1%), damping ratio stabilisation (5%), and mode shape stabilisation (1%). The stabilisation diagrams (Figure 7) were then constructed.  
The choice of stable poles (marked by the dashed red lines) was based on their obvious appearance in the eight setups (Figure 8). The corresponding frequency and mode shape could be determined for each selection via MACEC.  
After data processing, the shape of the seven identified modes were identified from the campaigns. Figure 9 displays mode shapes from eight setups:  
Figure 8: Stabilisation diagram in an interval from 1 to 8.5 Hz.  
Figure 9: _Cont._  
Figure 9: Mode shapes of Chuong Duong bridge in the campaigns: (**a**) Mode 1: f = 1.79 [Hz] (1 st vertical bending); (**b**) Mode 2: f = 2.25 [Hz] (1 st lateral); (**c**) Mode 3: f = 3.57 [Hz] (2 nd torsion); (**d**) Mode 4: f = 4.30 [Hz] (2 nd vertical bending); (**e**) Mode 5: f = 4.60 [Hz] (lateral movement); (**f**) Mode 6: f = 5.03 [Hz] (2 nd lateral bending); (**g**) Mode 7: f = 8.09 [Hz] (3 rd vertical bending).  
From these different setups, seven modes could be identified. Their natural frequencies and damping ratios can be found in the Table 2.  
The standard deviation of the natural frequency was calculated to assess the defined modes' effectiveness. Because these standard deviation of natural frequency values were low, each setting's system recognition quality was high. Modal phase alignment (MPC) measured the mode shape's departure from actual values, with MPC = 1 corresponding to the pure real mode. Every MPC value was higher than 0.998. A structure with light and/or proportional damping physics modes was likely to be realistic, so the elevated MPC result typically indicated a mode that had been precisely defined.