Methodology for the Detection of Contamination and Gradual Outer Race Faults in Bearings by Fusion of Statistical Vibration–Current Features and SVM Classifier
Abstract
:1. Introduction
2. Theoretical Background
2.1. Bearing Faults and Lubrication
2.1.1. Bearing Faults
2.1.2. Bearing Grease Lubrication
2.2. Statistical Features
2.3. Fractal Dimension
2.3.1. Higuchi’s Fractal Dimension (HFD)
- 1.
- The signal X in the time domain, with N samples, gets decomposed into new series or sequences, xkm, using Equation (20), with m as the initial time and k as the time interval.
- 2.
- The average normalized length, Lm, of each xkm is calculated with Equation (21).
- 3.
- The total length, L(k), is calculated for every k using Equation (22).
- 4.
- The value k is updated with k = k + 1. Steps 1 to 3 are repeated while k < kmax, with kmax being a selected value at which the slope of the best-fit line of the plotted diagram in the plane (ln[L(k)] versus ln[1/k]) is constant, with the slope being the value of HFD.
2.3.2. Katz’ Fractal Dimension (KFD)
- Calculate the maximum Euclidean distance, d, between the first sample, x1, and the sample xk of a signal X with N samples, with k = 1, …, N.
- Obtain the sum of the Euclidean distances between consecutive samples, L, of the signal X and its average, a, as shown in Equations (23) and (24).
- 3.
- The value of KFD is defined by Equation (25).
2.3.3. Petrosian’s Fractal Dimension (PFD)
- Take a signal, X, with N samples, and binarize it according to the criteria in Equation (26).
- 2.
- Find the total number of sign changes in the binarized signal, Z, using Equation (27).
- 3.
- Calculate the PFD as described in Equation (28).
2.3.4. Sevcik’s Fractal Dimension (SFD)
- 1.
- Considering the signal to be analyzed as a series of points (xi, yi) with length N, normalize the signals as proposed in Equation (29), with xmin and ymin as the minimum values in the series while xmax and ymax are the maximum values:
- 2.
- Obtain the length of the waveform, L, using Equation (30):
- 3.
- Calculate SFD as shown in Equation (31):
2.4. Linear Discriminant Analysis (LDA)
2.5. Support Vector Machines (SVMs)
3. Materials and Methods
3.1. Testbench
3.2. Data Acquisition Stage
3.3. Feature Extraction Stage
3.4. High-Dimensional Feature Matrices
3.5. Dimensionality Reduction and Classification Stage
4. Results
4.1. Data Preparation
4.2. Feature-Based Separation
4.3. Proposed Method
5. Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Characteristic Frequency | Equation | |
---|---|---|
Inner race defect frequency | (1) | |
Outer race defect frequency | (2) | |
Ball defect frequency | (3) | |
Cage defect frequency | (4) |
Statistical Features | Equation | |
---|---|---|
Mean | (5) | |
Maximum value | (6) | |
Root Mean Square | (7) | |
Square Root Mean | (8) | |
Standard Deviation | (9) | |
Variance | (10) | |
RMS Shape Factor | (11) | |
SRM Shape Factor | (12) | |
Crest Factor | (13) | |
Latitude Factor | (14) | |
Impulse Factor | (15) | |
Skewness | (16) | |
Kurtosis | (17) | |
Fifth Moment | (18) | |
Sixth Moment | (19) |
Proposal | Classification Model | Faults | Number of Severities | Signals | Accuracy |
---|---|---|---|---|---|
[8] | CNN | OR, IR, ball, cage, lack of lubrication | 6 | Thermal images | 99.8% |
[12] | CNN | OR and IR | 3 | Vibration | 93.97% |
[13] | RFA | OR, IR, ball | 3 | Vibration | 99.57% |
[17] | Multi-source domain information fusion network (MDIFN) | OR, IR, ball | 13 | Vibration | 98.31% |
[20] | ANN | OR, IR, ball, cage | 16 | Vibration | 91.6% |
[23] | SVM and CNN | Contamination | 3 | Vibration | 100% and 98.33% |
Proposed Method | Linear SVM | OR and Contamination | 5 | Vibration and current | 97.1% |
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Díaz-Saldaña, G.; Cureño-Osornio, J.; Zamudio-Ramírez, I.; Osornio-Ríos, R.A.; Dunai, L.; Sava, L.; Antonino-Daviu, J.A. Methodology for the Detection of Contamination and Gradual Outer Race Faults in Bearings by Fusion of Statistical Vibration–Current Features and SVM Classifier. Appl. Sci. 2024, 14, 5310. https://doi.org/10.3390/app14125310
Díaz-Saldaña G, Cureño-Osornio J, Zamudio-Ramírez I, Osornio-Ríos RA, Dunai L, Sava L, Antonino-Daviu JA. Methodology for the Detection of Contamination and Gradual Outer Race Faults in Bearings by Fusion of Statistical Vibration–Current Features and SVM Classifier. Applied Sciences. 2024; 14(12):5310. https://doi.org/10.3390/app14125310
Chicago/Turabian StyleDíaz-Saldaña, Geovanni, Jonathan Cureño-Osornio, Israel Zamudio-Ramírez, Roque A. Osornio-Ríos, Larisa Dunai, Lilia Sava, and Jose A. Antonino-Daviu. 2024. "Methodology for the Detection of Contamination and Gradual Outer Race Faults in Bearings by Fusion of Statistical Vibration–Current Features and SVM Classifier" Applied Sciences 14, no. 12: 5310. https://doi.org/10.3390/app14125310
APA StyleDíaz-Saldaña, G., Cureño-Osornio, J., Zamudio-Ramírez, I., Osornio-Ríos, R. A., Dunai, L., Sava, L., & Antonino-Daviu, J. A. (2024). Methodology for the Detection of Contamination and Gradual Outer Race Faults in Bearings by Fusion of Statistical Vibration–Current Features and SVM Classifier. Applied Sciences, 14(12), 5310. https://doi.org/10.3390/app14125310