## 4 Conclusions  
This article examined the performance of combinations of WTS with LSTM and SVM employed in the classification of unbalanced and bowed rotor systems. Additionally, changing the mass center and central axis of the shaft, respectively, allowed for the initial modeling of unbalanced and bowed coupled-rotor-disk systems using the finite element method in ABAQUS/CAE. Both methodologies present a novelty for structural health monitoring (SHM). The results of the modeled systems were compared in four simulation statuses together, i.e., the same physical properties operated in various rotational paces as well as the tantamount magnitude of unbalancing and initial bow. By applying concepts of uncertainties in model parameters, 70 different physical and operational circumstances were simulated for each of the rotating systems. Wavelet time scattering was used to perform the signal processing stage by extracting the scattered wavelet coefficients. Using a long short-term memory network as a deep learning algorithm for time series data, a hit rate of 100% was obtained running a maximum of 500 epochs in the testing phase. In the training step, the achieved accuracy was noticeable too, e.g., 99.1%. Training the LSTM network with the raw time series data, on the contrary, showed a faint performance--50% in both the training and testing stages although by adjusting the hyperparameters of the network, the accuracies in the training and testing phases developed to 62.5% and 64.3%, respectively. While considering SVM along with WTS, the training accuracy in the method was 100%, whereas, in the testing phase, 1 sample among the 28 samples (3.6%) was classified wrongly. Considering SVM without WTS, the hit rate was 83.9% and 89.3%, respectively. The results of feature extraction in the time domain and the application of SVM also \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Phase**} \\ \cline{2-5}
**Metric** & \multicolumn{2}{c}{**Training**} & \multicolumn{2}{c}{**Testing**} \\ \cline{2-5}  & \multicolumn{2}{c}{**Input**} & \multicolumn{2}{c}{**Input**} \\ \cline{2-5}  & **WTS** & **Raw Signal** & **WTS** & **Raw Signal** \\ \hline
**TP** & 55 & 38 & 14 & 10 \\
**TN** & 56 & 32 & 14 & 8 \\
**FP** & 0 & 24 & 0 & 6 \\
**FN** & 1 & 18 & 0 & 4 \\
**Accuracy (\%)** & 99.11 & 62.5 & 100 & 64.29 \\
**Precision (\%)** & 100 & 61.29 & 100 & 62.5 \\
**Recall (\%)** & 98.21 & 67.86 & 100 & 71.43 \\
**F1-Score (\%)** & 99.09 & 64.47 & 100 & 66.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Metrics for LSTM classification model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Phase**} \\ \cline{2-5}
**Metric** & \multicolumn{2}{c}{**Training**} & \multicolumn{2}{c}{**Testing**} \\ \cline{2-5}  & \multicolumn{2}{c}{**Input**} & \multicolumn{2}{c}{**Input**} \\ \cline{2-5}  & **WTS** & **Second Scenario** & **WTS** & **Second Scenario** \\ \hline
**TP** & 56 & 46 & 14 & 13 \\
**TN** & 56 & 48 & 13 & 12 \\
**FP** & 0 & 8 & 1 & 2 \\
**FN** & 0 & 10 & 0 & 1 \\
**Accuracy (\%)** & 100 & 83.93 & 96.43 & 82.29 \\
**Precision (\%)** & 100 & 85.19 & 93.33 & 86.67 \\
**Recall (\%)** & 100 & 82.14 & 100 & 92.86 \\
**F1-Score (\%)** & 100 & 83.62 & 96.55 & 89.66 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Metrics for SVM classification model. demonstrated the possibility of classifying such flawed systems in the case of setting hyperparameters and/or extracting more robust features. Ultimately, although the limited number of samples in a data set (140 overall), the methods employed in this paper showed high accuracy in classifying unbalanced and bowed rotor systems; therefore, rendering this approach a promising and useful contribution to the SHM area. Future work will focus on modeling rotor systems suffering from other prevalent defects, such as cracks, bearing faults, and misalignment, and applying the proposed benchmark in the case of multi-damaged systems.