## 4 Experimental Results
### Comparison of Computational Costs on SUSU Dataset  
For each of the five classes in SUSU dataset, 70% of the available data were used for model training and validation; the remaining 30% were used for testing. A similar experiment on this dataset was carried out by [PERSON] et al. in [33], where they used the same dataset. However, ref. [33] used a hybrid model with mixed inputs. The linear acceleration signals were turned into time-frequency images using a Hilbert-Huang transform, which were the inputs for the CNN. The magnitude of the components of the frequency spectrum around the first and the second torsional natural frequencies of the shaft were summed to find the numbers N1 and N2 from the corresponding angular signals segments, which were inputs for the Multi-Layer Perceptron branch.  
We compared the performance of our proposed LPC-NN method with the Hybrid CNN-MLP method [33] under the same conditions, and on the same data. For comparison, we also used different time-domain statistical indicators (TDSIs) as features for a neural network with two hidden layers of 30 and 20 neurons, respectively. We used six traditional TDSIs: peak, root mean square, crest factor, kurtosis, impulse factor, and shape factor. In addition to them, we used four new indicators, namely, TALAF and THIKAT [46], \"kurtosis, crest factor and root mean square (KUCR)\" [47], and INTHAR [48]. All experiments were repeated 10 times, and the average results are reported in Table 10.  
The LPC-NN method was more accurate, faster at extracting data, and quicker in model training. In [33], two components were used for feature extraction, which took over 500 times took longer than in the proposed method that uses a single acceleration component. Additionally, the training time for LPC-NN model was 15 times faster than for the hybrid model.  
The TSDIs-NN and LPC-NN methods have approximately the same training time, but TSDIs-NN is much inferior in accuracy to LPC-NN. For a detailed comparison between the methods, see Table 11, which shows the accuracy and \(f_{1}\)-score values of all approaches  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Method**} & **Average** & **Time for Feature Extraction** & **Time for Model** \\  & **Accuracy, \%** & **for Each Frame, Seconds** & **Training** \\ \hline TDSIs-NN & 76.8 & 0.038 & 25 \\ Hybrid MLP-CNN & 95.7 & 0.27 & 278 \\ LPC-NN & 98.3 & 0.00051 & 18 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Comparison of the average accuracy of the methods.  
obtained in the last run out of 10. In this run, TSDIs-NN and Hybrid CNN-MLP model achieved 78% and 96% accuracy, while LPC-NN achieved 98% accuracy.  
The \(f_{1}\)-score assesses the classification model's performance and is calculated based on precision and recall:  
\[f_{1}=\frac{2\text{-}precision\text{-}recall}{precision+recall}. \tag{14}\]  
Precision is defined as the number of true positive results divided by the number of all positive results, including those that were not identified correctly. Recall, on the other hand, is the number of true positive results divided by the total number of all samples that should have been identified as positive. The best value of \(f_{1}\)-score is 1 and the worst is 0.  
The Normal class achieved the best f1-score value for Hybrid CNN-MLP and LPC-NN models. However, this class is difficult for the TDSIs-NN model and, in general, its \(f_{1}\)-score values are worse for all classes.  
Note that all the results presented in Section 4 are available as Jupiter Notebooks [30] in the LPC-NN folder. All experiments were implemented on a computer with Intel i7-8550 K 1.80 GHz CPU, 12.0 GB RAM.