# An Improved Method Based on EEMD-LSTM to Predict Missing Measured Data of Structural Sensors
## 4 Comparative Analysis of the Results
### Performance Evaluation of the Proposed Models  
The performance of the different EEMD-based models was mainly compared in the second experiment. The measured and predicted values of the different methods are shown in Figure 12. The shaded parts in Figure 12 represent the missing data regions, and the common feature of these regions is that they had obvious peaks. These regions were very sensitive, and even subtle changes could significantly affect the prediction accuracy of the deep learning model here, and it was difficult for the traditional deep learning models to fully capture the features here. From the shaded parts in Figure 12, we can clearly see that the proposed model captured such microscopic changes well, and the model prediction results were basically consistent with the measured values in local variations.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Dataset** & **Point** & **Metrics** & \begin{tabular}{c} **EEMD-** \\ **BiGRU** \\ \end{tabular} & \begin{tabular}{c} **EEMD-** \\ **GRU** \\ \end{tabular} & \begin{tabular}{c} **EEMD-** \\ **LSTM** \\ \end{tabular} & \begin{tabular}{c} **EEMD-** \\ **DNN** \\ \end{tabular} & \begin{tabular}{c} **BiGRU** \\ \end{tabular} & \begin{tabular}{c} **GRU** \\ **LSTM** \\ \end{tabular} & \
\begin{tabular}{c} **LSTM** \\ \end{tabular} &
\begin{tabular}{c} **DNN** \\ \end{tabular} \\ \hline \multirow{4}{*}{White} & 1 & _MSE_ & 0.0060 & 0.0056 & **0.0052** & 0.0101 & 0.0247 & 0.0284 & 0.0289 & 0.0325 \\ \cline{2-10}  & 1 & _RMSE_ & 0.0774 & 0.0746 & **0.0722** & 0.1007 & 0.1571 & 0.1685 & 0.1699 & 0.1801 \\ \cline{2-10}  & 1 & _MAE_ & 0.0585 & 0.0566 & **0.0543** & 0.0787 & 0.1243 & 0.1322 & 0.1338 & 0.1414 \\ \cline{2-10}  & 1 & _R\({}^{2}\)_ & 97.92\% & 98.06\% & **98.19\%** & 96.47\% & 91.42\% & 90.13\% & 89.96\% & 88.72\% \\ \hline \multirow{4}{*}{El-Centro} & 1 & _MSE_ & 0.0003 & 0.0003 & **0.0003** & 0.0006 & 0.003 & 0.003 & 0.0034 & 0.0036 \\ \cline{2-10}  & 1 & _RMSE_ & 0.018 & 0.0179 & **0.0178** & 0.0244 & 0.0547 & 0.0551 & 0.058 & 0.0601 \\ \cline{2-10}  & 1 & _MAE_ & 0.0143 & 0.0144 & **0.0143** & 0.0191 & 0.0432 & 0.0436 & 0.0458 & 0.0455 \\ \cline{2-10}  & 1 & _R\({}^{2}\)_ & 98.63\% & 98.65\% & **98.66\%** & 97.49\% & 87.40\% & 87.17\% & 85.80\% & 84.78\% \\ \hline \multirow{4}{*}{RG} & 1 & _MSE_ & 0.0016 & 0.0011 & **0.001** & 0.0024 & 0.0072 & 0.0077 & 0.0072 & 0.0089 \\ \cline{2-10}  & 1 & _RMSE_ & 0.0399 & 0.0333 & **0.031** & 0.0488 & 0.085 & 0.0877 & 0.0851 & 0.0942 \\ \cline{2-10}  & 1 & _MAE_ & 0.0286 & 0.0237 & **0.0226** & 0.0358 & 0.0628 & 0.0662 & 0.0638 & 0.0698 \\ \cline{2-10}  & 1 & _R\({}^{2}\)_ & 97.80\% & 98.47\% & **98.67\%** & 96.71\% & 90.00\% & 89.35\% & 89.97\% & 87.71\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Single-step prediction.  
Figure 13 shows the evaluation metrics of different methods as the quantitative representation of missing data completion. The _MSE_, _RMSE_, and _MAE_ of EEMD-LSTM were 0.0052, 0.0722, and 0.0543, respectively, which were lower than the other three methods. The \(R^{2}\) of EEMD-LSTM was 98.19%, which was the largest among all of the methods, indicating that EEMD-LSTM had the best performance for missing data completion.