## 5 Discussion  
This study developed a novel approach for rolling bearing diagnosis, which relies on the spectrum estimation of the signal, using an LPC algorithm. The LPC coefficients are used as input vectors for a simple NN that can predict the fault type with high precision. The benefits of the proposed LPC-NN approach are as follows: (1) it is easy to implement, (2) the feature vector size is small, containing only 50 values, and (3) the NN used is simple, containing only one hidden layer. The performance of LPC-NN was verified under different operating conditions and on two experimental datasets CWRU and SUSU.  
In our experimental studies, the LPC-NN method outperformed the powerful method CNN-gcForest for single-load CWRU data. The LPC-NN method demonstrated good robustness under changing operating conditions, surpassing the robustness of methods such as SVM, MLP, DNN, and WDCNN. Although the proposed method LPC-NN was sometimes inferior in accuracy to the extremely powerful method Ensemble TICNN, it showed comparable results. Given approximately the same accuracy values, the relative simplicity of the LPC-NN method should be noted.  
The LPC-NN method also outperformed the Hybrid MLP-CNN method in terms of accuracy and computational costs when tested on the SUSU dataset. Compared to the TDSIs-NN method with a similar running time, LPC-NN demonstrated significantly greater accuracy.  
Further research will focus on determining whether the features extracted using the LPC algorithm can also serve as input for another classifier (such as SVM and Logistic Regression) and on testing the method's performance under conditions of data imbalance and high noise.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **TDSIs-NN** & **Hybrid CNN-MLP** & **LPC-NN** \\ \hline Normal & 0.70 & 1.00 & 1.00 \\ Inner & 0.86 & 0.96 & 0.96 \\ Outer & 0.78 & 0.96 & 1.00 \\ Ball & 0.70 & 0.92 & 1.00 \\ Comb & 0.84 & 0.95 & 0.96 \\
**Accuracy** & **0.78** & **0.96** & **0.98** \\ \hline \hline \end{tabular}
\end{table}
Table 11: \(f_{1}\)-score comparison.  
The methods being developed for diagnosing rotating equipment are becoming more reliable, efficient, accurate, and superior over time, often combined with artificial intelligence algorithms. However, they are also becoming increasingly computationally expensive and deep, requiring a large set of labeled data for training. In reality, such methods are unlikely to be implemented in industrial enterprises; therefore, effective methods suitable for practical applications are needed. The development of these methods will be the focus of many scientific researchers in the future.  
Conceptualization, O.I., M.M. and V.E.; methodology, V.S. and O.I.; investigation, M.M., V.E. and O.I.; resources, V.E. and V.S.; writing--original draft preparation, M.M.; writing--review and editing, O.I.; project administration, V.S.; funding acquisition, V.S. All authors have read and agreed to the published version of the manuscript.  
This work was financially supported by Ministry of Science and Higher Education of the Russian Federation (FENU-2023-0010).  
Not applicable.  
The SUSU dataset and the codes with experimental results are available at [[https://github.com/susu-cm/bearings-dataset/](https://github.com/susu-cm/bearings-dataset/)]([https://github.com/susu-cm/bearings-dataset/](https://github.com/susu-cm/bearings-dataset/)), accessed on 19 January 2025.  
The authors declare no conflicts of interest.