# A Data Loss Recovery Technique Using EMD-BiGRU Algorithm for Structural Health Monitoring
## 4 Analysis of Predicted Results
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**data set** & **Point** & **Metrics** & **EMD-BiGRU** & **EMD-GRU** & **BiGRU** & **GRU** & **GBR** & **RFR** & **SVR** \\ \hline \multirow{4}{*}{A\_1} & 5 & MSE & **0.0160** & 0.0311 & 0.1088 & 0.1005 & 0.1529 & 0.1652 & 0.1292 \\  & 5 & RMSE & **0.1264** & 0.1763 & 0.3298 & 0.3170 & 0.3910 & 0.4064 & 0.3595 \\  & 5 & MAE & **0.0942** & 0.1331 & 0.2525 & 0.2389 & 0.3108 & 0.3232 & 0.2825 \\  & 5 & R\({}^{2}\) & **94.33\%** & 88.97\% & 61.40\% & 64.34\% & 45.73\% & 41.39\% & 54.14\% \\ \hline \multirow{4}{*}{A\_2} & 5 & MSE & **0.0065** & 0.0097 & 0.0249 & 0.0249 & 0.0573 & 0.0669 & 0.0429 \\  & 5 & RMSE & **0.0808** & 0.0987 & 0.1579 & 0.1579 & 0.2394 & 0.2587 & 0.2070 \\  & 5 & MAE & **0.0609** & 0.0739 & 0.1175 & 0.1182 & 0.1859 & 0.2010 & 0.1595 \\  & 5 & R\({}^{2}\) & **96.85\%** & 95.30\% & 87.97\% & 87.96\% & 72.35\% & 67.72\% & 79.32\% \\ \hline \multirow{4}{*}{A\_3} & 5 & MSE & **0.0040** & 0.0055 & 0.0124 & 0.0114 & 0.0299 & 0.0321 & 0.0244 \\  & 5 & RMSE & **0.0634** & 0.0741 & 0.1115 & 0.1066 & 0.173 & 0.179 & 0.1563 \\  & 5 & MAE & **0.0458** & 0.0537 & 0.0798 & 0.0763 & 0.1329 & 0.1365 & 0.1200 \\  & 5 & R\({}^{2}\) & **98.15\%** & 97.48\% & 94.29\% & 94.78\% & 86.26\% & 85.27\% & 88.78\% \\ \hline \multirow{4}{*}{A\_4} & 5 & MSE & **0.0041** & 0.0164 & 0.0187 & 0.0180 & 0.0440 & 0.0495 & 0.0350 \\  & 5 & RMSE & **0.0644** & 0.1281 & 0.1367 & 0.1343 & 0.2097 & 0.2226 & 0.1870 \\ \cline{1-1}  & 5 & MAE & **0.0470** & 0.0912 & 0.0957 & 0.0938 & 0.1597 & 0.1690 & 0.1414 \\ \cline{1-1}  & 5 & R\({}^{2}\) & **97.26\%** & 89.14\% & 87.64\% & 88.07\% & 70.91\% & 67.21\% & 76.87\% \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison results of different models for the data set. Table 3 shows the predicted results of the A_1 data set using different models, and the predicted points include 5, 10, 15, and 20. It can be seen from Table 3 that the accuracy of most algorithms can decrease with the increasing missing points. For example, the machine learning methods GBR, RFR, and SVR drop a little faster, indicating that these algorithms are less capable of extracting temporal features of acceleration data. Moreover, the single model BiGRU GRU has better prediction than the machine learning methods, but its robustness is poor. The hybrid EMD-based models such as EMD-BiGRU, EMD-GRU are more robust and have suitable prediction results. In addition, the EMD-BiGRU has lower MSE, RMSE, MAE compared with EMD-GRU, which indicates that the predicted ability of EMD-BiGRU is more superior. To be specific, the EMD-BiGRU model only reduces by 5.76% in R\({}^{2}\) for predicting points from 5 to 20, which represents that the EMD-BiGRU has a minor loss. For A_2, A_3, and A_4 data sets, the predicted results using different models can be seen in Tables 1-3. Figure 14 shows predicted results on A_1, A_2, A_3, and A_4 by using different algorithms. It can be seen that EMD-BiGRU can better capture the characteristics of acceleration data and has a better prediction for missing points. For A_2, A_3, and A_4 data sets, the predicted results using different models can be seen in Figures A1-A3. Figure 13: Comparisons results for different data sets using various algorithms. (**a**) Comparisons of predicted results for the A_1 data set using different algorithms. (**b**) Comparisons of predicted results for the A_2 data set using different algorithms. (**c**) Comparisons of predicted results for the A_3 data set using different algorithms. (**d**) Comparisons of predicted results for the A_4 data set using different algorithms. Figure 14: Comparisons results for different data sets using various algorithms. (**a**) Comparisons of predicted results for the A_1 data set using different algorithms (points 5). (**b**) Comparisons of predicted results for the A_1 data set using different algorithms (points 10). (**c**) Comparisons of predicted results for the A_1 data set using different algorithms (points 15).