# 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 Multi-Steps  
The discussions in the previous sections were based on single-step prediction. In this section, a performance comparison of the models using multi-step prediction with the white dataset is provided, and the prediction steps included 1 step, 5 steps, 10 steps, and 15 steps. The _MSE_, _RMSE_, _MAE_, and \(R^{2}\) of the EEMD-based models and the single model for specific prediction steps are shown in Table 3. The results show that the accuracy of the models decreased with the increase in the prediction steps. The model prediction error accumulated as the prediction steps increased. Among all EEMD-based models, EEMD-LSTM still achieved the best performance, with smaller a _MSE_, _RMSE_, and _MAE_ and larger \(R^{2}\) compared to the other models. Figure 10: Prediction results of the traditional models and hybrid models: (**a**) comparison between LSTM and EEMD-LSTM (white dataset); (**b**) comparison between DNN and EEMD-DNN (white dataset); (**c**) comparison between BiGRU and EEMD-BiGRU (white dataset); (**d**) comparison between GRU and EEMD-GRU (white dataset). Figure 11: Predictive evaluation of hybrid EEMD-based methods with single methods: (**a**) mean squared error (_MSE_) of the different algorithms (white dataset); (**b**) root mean squared error (_RMSE_) of the different algorithms (white dataset); (**c**) mean absolute error (_MAE_) of the different algorithms (white dataset); (**d**) \(R^{2}\) of the different algorithms (white dataset). \begin{table}
\begin{tabular}{c 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** \\ \end{tabular} & \
\begin{tabular}{c} **LSTM** \\ \end{tabular} &
\begin{tabular}{c} **DNN** \\ \end{tabular} \\ \hline \multirow{8}{*}{White} & 1 & _MSE_ & 0.006 & 0.0056 & 0.0052 & 0.0101 & 0.0247 & 0.0284 & 0.0289 & 0.0325 \\  & 1 & _RMSE_ & 0.0774 & 0.0746 & 0.0722 & 0.1007 & 0.1571 & 0.1685 & 0.1699 & 0.1801 \\  & 1 & _MAE_ & 0.0585 & 0.0566 & 0.0543 & 0.0787 & 0.1243 & 0.1322 & 0.1338 & 0.1414 \\  & 1 & _R\({}^{2}\)_ & 97.92\% & 98.06\% & **98.19\%** & 96.47\% & 91.42\% & 90.13\% & 89.96\% & 88.72\% \\ \cline{2-11}  & 5 & _MSE_ & 0.0228 & 0.0237 & 0.0221 & 0.0345 & 0.116 & 0.1287 & 0.1123 & 0.1007 \\  & 5 & _RMSE_ & 0.1510 & 0.1539 & 0.1487 & 0.1857 & 0.3406 & 0.3588 & 0.3351 & 0.3173 \\  & 5 & _MAE_ & 0.1137 & 0.1129 & 0.1109 & 0.1375 & 0.2571 & 0.2714 & 0.2536 & 0.2393 \\  & 5 & _R\({}^{2}\)_ & 91.66\% & 91.34\% & **91.91\%** & 87.39\% & 57.59\% & 52.93\% & 58.93\% & 63.18\% \\ \cline{2-11}  & 10 & _MSE_ & 0.0793 & 0.0679 & 0.0675 & 0.0853 & 0.1498 & 0.1423 & 0.1459 & 0.1417 \\ \cline{2-11}  & 10 & _RMSE_ & 0.2815 & 0.2606 & 0.2599 & 0.2921 & 0.387 & 0.3772 & 0.382 & 0.3764 \\ \cline{2-11}  & 10 & _MAE_ & 0.2019 & 0.1849 & 0.1869 & 0.2183 & 0.299 & 0.2914 & 0.2954 & 0.2891 \\ \cline{2-11}  & 10 & _R\({}^{2}\)_ & 71.15\% & 75.29\% & **75.42\%** & 68.95\% & 45.48\% & 48.22\% & 46.90\% & 48.43\% \\ \hline \multirow{8}{*}{White} & 15 & _MSE_ & 0.1218 & 0.1176 & 0.1145 & 0.1462 & 0.1856 & 0.1868 & 0.1794 & 0.1764 \\  & 15 & _RMSE_ & 0.3490 & 0.343 & 0.3383 & 0.3824 & 0.4309 & 0.4322 & 0.4236 & 0.4201 \\ \cline{1-1}  & 15 & _MAE_ & 0.26 & 0.2561 & 0.2478 & 0.289 & 0.332 & 0.3335 & 0.3272 & 0.3258 \\ \cline{1-1}  & 15 & _R\({}^{2}\)_ & 57.42\% & 58.89\% & **59.99\%** & 48.90\% & 35.12\% & 34.72\% & 37.29\% & 38.33\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Multi-step prediction of the white wave. Figure 14 shows the multi-step prediction results using different algorithms on the white dataset including 1, 5, 10, and 15 steps.