# A Data Loss Recovery Technique Using EMD-BiGRU Algorithm for Structural Health Monitoring
## 3 Experimental Setting
### Description of Data Sets  
A three-story structure was selected as the damage detection test stand in the experimental procedure, as shown in Figure 5. Each layer is connected by four aluminum columns (17.7 \(\times\) 2.5 \(\times\) 0.6 cm) with aluminum plates at the top and bottom (30.5 \(\times\) 30.5 \(\times\) 2.5 cm), forming a four-degree-of-freedom system. It can be seen from Figure 5 that there was a central column (15.0 \(\times\) 2.5 \(\times\) 2.5 cm) suspended from the top level and a buffer, which can adjust the narrow space between buffer and central column. It could change the degree of nonlinearity, and the structure allowed the track to slide in the x-axis direction only.  
The shaker that provided excitation to the bottom was mounted on the substrate. A force sensor with a sensitivity of 2.2 mV/N was mounted at the end of the probe to measure the input force from the shaker. The sampling interval was set to 3.1 ms, and the sampling frequency was set to 322  
To describe the essential characteristics of the four acceleration data, four statistical indicators, including total sample size, mean, maximum and minimum values, and standard deviation, are selected for the four data sets. The result is shown in Table 1.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**data set** & **A\_1** & **A\_2** & **A\_3** & **A\_4** \\ \hline Number of samples & 8192 & 8192 & 8192 & 8192 \\ Mean & 0.000009 & 0.000073 & 0.000304 & \(-0.000018\) \\ Standard deviation & 0.5366 & 0.4556 & 0.4593 & 0.3856 \\ Min & \(-2.0286\) & \(-1.8864\) & \(-1.7249\) & \(-1.7085\) \\ Max & 1.9513 & 2.2541 & 2.1054 & 1.4282 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Statistical indicators for the four acceleration data.  
Figure 5: The three-story building structure.  
Figure 6: Position of accelerator sensor installed structure.  
In this table, A_1, A_2, A_3, and A_4 represent collected data from the accelerometer of Channel 2, Channel 3, Channel 4, Channel 5. Figure 7 shows a curve picture of collected acceleration data.  
First, each data set is divided into two parts, 80% data set is used as a training set, and the remaining 20% data set is used as a test set. As seen from Figure 8, solid boxes, as input data, are used to predict the value at the next step. Dashed boxes represent the missing data during measured signal data. For two points missing data, each input and output pair consists of 324 samples, including 322 input samples (e.g., 1 to 322) and two output samples (e.g., 323-324), namely missing data. Then, the input-output pairs are fed into the EMD-BiGRU model for training, and then a predicted model with two missing points can be achieved. When a measured signal occurs two missing points, the model can be used to predict the missing data. Similarly, EMD-BiGRU models predicting different lengths (5, 10, 20 missing data) can be achieved to tackle the problem of missing data with different lengths.  
Figure 8: Input and output of the proposed model.  
Figure 7: Acceleration data set collected from the three-story structure.