# Prediction of Structural Damage Trends Based on the Integration of LSTM and SVR
## 4 Structural Damage Prediction of Engineering Vibration Signals
### Prediction of Ill-Structured Problems under an External Incentive Environment  
In order to verify the effectiveness of the proposed method in practical application, this method is used to analyze the actual engineering vibration data. The data used are Phase II IASC-ASCE, namely the second phase data of the vibration acceleration signal of the actual engineering of ASCE [44]. The actual engineering vibration data used in this section were generated with motor vibration excitation with a sampling frequency set at 200 Hz. The vibration signal collected with the acceleration sensor at the No. 6 detection point was selected as the research signal, and 3000 vibration data were used for analysis and research. Figure 8 shows the damage mode and the damage conditions. The conditions were selected as follows:1. No damage;
2. All diagonal supports on the southeast side were removed (damage mode 1);
3. When all the diagonal supports of the structure were removed, the bolts at both ends of the beams on the first and second floors on the northeast side were loose (damage mode 2).  
The collected acceleration vibration signals are shown in Figure 9. Hilbert-Huang transformation was performed on the acceleration signal, and then, the first component was taken for analysis. The transient frequency is shown in Figure 10.  
Figure 8: Three working modes. (**a**) No damage condition. (**b**) Damage mode 1. (c) Damage mode 2.  
Figure 7: Experimental model, node number, and hit position. (**a**) Steel-frame quarter-scale model structure. (**b**) Diagram of the analytical model.  
Figure 9: Acceleration vibration signals under three working conditions.  
As can be observed from Figure 10, under damage conditions, the instantaneous frequency shows a downward trend, and when there is no damage or the damage degree is slight, the overall fluctuation of the instantaneous frequency is relatively stable. As the damage degree deepens, the overall fluctuation amplitude also increases accordingly. The experimental results show that, when structural damage occurs, that is, when the structural stiffness decreases, the magnitude and amplitude of its instantaneous frequency will also change. It is further verified that instantaneous frequency can be used as a characteristic factor for structural ill-conditioned problems, and it also demonstrates the effectiveness of VMD combined with the Hilbert transform method.  
In the obtained transient frequency, 1000 data were taken for the fusion algorithm prediction. The first 700 were used as training data, and the last 300 were used as test data. The specific parameters of the fusion algorithm were set as follows: the weight coefficient w in the fusion method was 0.5, C and \(\varepsilon\) in the SVR method were 20 and 0.01, respectively, and the number of  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & **RMSE** & **MAPE(\%)** & **SDAPE** & \(\mathbf{R^{2}}\) & **RWI** & **Operation Time/s** \\ \hline LSTM & 0.8278 & 1.88 & 0.8345 & 0.9850 & 0.9431 & 103.198 \\ Integration method & 0.4973 & 0.95 & 0.7424 & 0.9960 & 0.9801 & 97.302 \\ \hline \end{tabular}
\end{table}
Table 4: Prediction performance evaluation of bolts loosening at both ends of the first and second floor beams on the northeast side without any diagonal support.  
Figure 12: Short-term prediction results after removing all the diagonal supports on the southeast side. (**a**) LSTM model. (**b**) Integration method.  
Figure 13: Short-term prediction results of bolts loosening at both ends of the first and second floor beams on the northeast side without any diagonal support. (**a**) Prediction results of LSTM. (**b**) Integration method.