# Bearing Fault Diagnosis Based on Vibration Envelope Spectral Characteristics
###### Abstract
Subsequently, the model identifies and diagnoses equipment by inputting test samples into the trained fault diagnosis model. Commonly used methods include the K-Nearest Neighbor (KNN) [3], random forest (RF) [10], Support Vector Machine (SVM) [11; 12; 13], Naive Bayes (NB), convolutional neural networks (CNN) [14], Long Short-Term Memory (LSTM) [15], and recurrent neural networks (RNNs) [16; 17]. With the advancement and development of technology, fault diagnosis methods are constantly evolving. [PERSON] et al. [18] suggested using continuous wavelet transform CWT and convolutional neural networks to predict the bearing fault size diagnosis based on deep transfer learning algorithms (DTL) and time-frequency images. [PERSON] et al. [10] proposed an autocorrelation-assisted feature extraction method, which extracts the top-ranked feature vectors through dimensionality reduction and sends them to a random forest classifier for rolling bearing fault diagnosis. [PERSON] et al. [19] use VMD to decompose vibration signals into band-limited intrinsic mode functions (BLIMF), extract high-dimensional feature vectors using a high-dimensional common space pattern filter, and perform fault diagnosis using a random forest classifier. These methods achieve high-precision fault diagnosis by extracting more features or using more advanced classification algorithms. However, the complexity of the algorithms is gradually increasing. This requires more storage space, more computational resources, and more computation time, leading to an increase in hardware setup and operating costs. [PERSON] and colleagues proposed a new approach for bearing fault diagnosis using envelope analysis and machine learning methods in 2023 [3]. This method aims to detect bearing faults with minimal observational data and features, achieving high diagnostic accuracy while reducing computational complexity. The process achieved high accuracy by combining frequency-domain vibration analysis with envelope analysis and leveraging the overlap of fault harmonics and characteristic frequencies. The KernelNaive Bayes model achieved an accuracy of 94.4%, while the Decision Tree (Fine Tree) and KNN (Fine KNN) models achieved a perfect accuracy of 100% [3]. This demonstrates that frequency domain vibration analysis, especially when using envelope analysis, is the optimal technology for detecting bearing faults. However, it is noted that this method cannot diagnose faults related to the ball, as the harmonics of rolling element faults do not overlap with characteristic frequencies. As a result, the technique achieves a three-class fault diagnosis for healthy status, inner race faults, and outer race faults. Considering the above facts, this paper proposes a bearing fault diagnosis method based on vibration envelope spectrum features. Only the frequency and intensity (fai) of the fault characteristic peaks in the envelope spectrum are used as features, thereby reducing the variety of features. Meanwhile, the simple and efficient Naive Bayes algorithm is employed as the classifier to reduce the fault recognition time, ensuring accuracy while lowering algorithm complexity. In this study, evaluation is conducted using bearing fault data from both the CWRU dataset and the MFPT dataset. Firstly, the vibration signals of the bearings are demodulated using the Hilbert demodulation method to obtain the envelope spectrum. Next, multiple peaks and their frequencies are extracted from the envelope spectrum as fault features. Finally, a simple and efficient Naive Bayes classifier is utilized to classify the fault features and obtain diagnostic results.