# Bearing Fault Diagnosis Based on Vibration Envelope Spectral Characteristics
## 5 Conclusions  
To respond to the dramatic increase in algorithm complexity while achieving high accuracy in current fault diagnosis methods, this paper proposes a bearing fault diagnosis method based on vibration envelope spectrum features. This method utilizes the characteristic of periodic impact vibrations caused by bearing faults, which typically form periodic fault frequency peaks on the envelope spectrum. It extracts multiple peak values and their frequencies from the envelope spectrum as fault features and employs the algorithmically simple and efficient Naive Bayes classifier for fault classification. The algorithm's complexity in feature extraction and fault recognition aspects is reduced.  
The following conclusion is drawn through theoretical analysis and experimental validation based on the CWRU dataset and the MFPT dataset. Compared to current bearing fault classification methods based on deep learning, data-driven techniques, etc., the proposed method significantly reduces algorithm complexity and computational hp while ensuring accuracy. It improves classification efficiency and is more suitable for real-time industrial bearing fault diagnosis. When dealing with complex datasets, such as variable-speed conditions, the classification performance of the proposed method in this paper may not be ideal. In such cases, methods that combine multiple classifiers can be used to further improve the results, which is the focus of our future work.  
Methodology, Y.C.; Software, Q.C.; Validation, Q.C.; Formal analysis, R.W.; Writing--original draft, Q.C.; Writing--review & editing, Y.C. and R.W. All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Year** & **Acc (\%)** & **Algorithm Complexity** \\ \hline Laplacian Score, SVM [26] & 2019 & 100.00 & O(N(6144 + N)) \\ Autocorrelation, RF [10] & 2020 & 100.00 & O(N(93 + 20182 + 250 log(N))) \\ wavelet packet transform, RF [22] & 2022 & 100.00 & O(N(14,360 + 800 Nlog(N))) \\ VMD, RF [27] & 2022 & 99.67 & O(N(4096 + 150 log(N))) \\ envelope analysis, Fine KNN [3] & 2023 & 100.00 & O(N(3051)) \\ this method & & 99.90 & O(N(2280)) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparative study of fault diagnosis literature related to the current use of the CWRU.  
**Funding:** This work was supported in part by the National Natural Science Foundations of China under Grant 62301086, in part by the Natural Science Foundation of Jiangsu Province under Grant BK20230627. This research was funded by the National Natural Science Foundations of China (62301086) and the Natural Science Foundation of Jiangsu Province (BK20230627). And The APC was funded by the Research on Anti-Multi-Target Interference Technology of Signal Processing with Space and Time Domain Deconvolution Arrays (6142109180206).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data is contained within the article.  
**Conflicts of Interest:** The authors declare no conflict of interest.