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A peer-reviewed article of this preprint also exists.
This version is not peer-reviewed
Submitted:
04 December 2023
Posted:
05 December 2023
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Parameter | Formula | Description | |
---|---|---|---|
Harmonic Features | THD | Frequency domain, measuring the distortion caused by harmonics in the signal. | |
SNR | Compares the level of a desired signal to the level of background noise. | ||
SINAD | A measure of signal quality compares the level of desired signal to the level of background noise and harmonics. | ||
Spectral Features | Peak amplitude | Represents the highest point (or peak) of the signal's waveform when viewed in the frequency domain. | |
Peak frequency | Corresponds to the frequency component that is most prominent or dominant in the signal. | ||
Band power | Quantifies the total energy within a specific frequency range, providing insights into the distribution of signal energy across the spectrum. |
Inner Race Fault Type | Outer Race Fault Type | |||
---|---|---|---|---|
Load Factor (lbs) | MeanEnergy | Mean Energy Increase % | MeanEnergy | Mean Energy Increase % |
50 | 25.549 | 347.70% | 7.699 | 35.16% |
100 | 27.547 | 383.65% | 5.431 | 4.76% |
150 | 24.915 | 337.68% | 5.573 | 2.08% |
200 | 33.742 | 491.88% | 7.604 | 33.35% |
250 | 36.147 | 533.49% | 7.178 | 25.90% |
270 | 5.7012 | 0% (baseline) | 5.701 | 0% (baseline) |
300 | 32.199 | 464.25% | 18.612 | 226.88% |
LoadFactor (lb) | Mean Energy | NormalizedEnergy | Deviation | Load-Dependent Subclasses | ||||
---|---|---|---|---|---|---|---|---|
Fault Type | Inner | Outter | Inner | Outter | Inner | Outter | Inner | Outter |
50 | 25.549 | 7.6992 | 0.14035 | 0.05758 | 0.1403 | 0.05758 | {'Mild' } | {'Mild' } |
100 | 27.547 | 5.4309 | 0.15053 | 0.023062 | 0.15053 | 0.023062 | {'Mild' } | {'Mild' } |
150 | 24.915 | 5.5728 | 0.14063 | 0.031372 | 0.14063 | 0.031372 | {'Mild' } | {'Mild' } |
200 | 33.742 | 7.6036 | 0.28444 | 0.092816 | 0.28444 | 0.092816 | {'Moderate'} | {'Mild' } |
250 | 36.147 | 7.1779 | 0.29911 | 0.061822 | 0.29911 | 0.061822 | {'Moderate'} | {'Mild' } |
270 | 5.7012 | 5.7012 | 0.00930 | 0.027659 | 0 | 0 | {'Normal' } | {'Normal'} |
300 | 32.199 | 18.612 | 0.23412 | 0.89814 | 0.23412 | 0.89814 | {'Moderate'} | {'Severe'} |
Parameter | Formula | Description |
---|---|---|
Peak or Max | The highest amplitude value is observed within a given signal or dataset. | |
Root Mean Square (RMS) | Gives a measure of the magnitude of the signal. | |
Skewness | Measures the asymmetry of the distribution about the mean. | |
Standard deviation (std) | The square root of the variance represents the average deviation from the mean. | |
Kurtosis | Indicates the "tailedness" of the distribution. A high kurtosis might indicate the presence of outliers or impulses in the signal. | |
Crest Factor | The ratio of the peak amplitude to its RMS value indicates the relative sharpness of peaks. | |
Peak to Peak | Difference between the maximum and minimum values of the signal. | |
Impulse Factor | Highlights the impulsive behaviours indicative of machinery faults. |
Inner Fault Dataset | Code | Load (lbs) | Sampling rate (Hz) |
Duration (sec) |
---|---|---|---|---|
baseline_2 | data_normal | 270 | 97656 | 6 |
InnerRaceFault_vload_2 | IRF_50 | 50 | 48828 | 3 |
InnerRaceFault_vload_3 | IRF_100 | 100 | 48828 | 3 |
InnerRaceFault_vload_4 | IRF_150 | 150 | 48828 | 3 |
InnerRaceFault_vload_5 | IRF_200 | 200 | 48828 | 3 |
InnerRaceFault_vload_6 | IRF_250 | 250 | 48828 | 3 |
InnerRaceFault_vload_7 | IRF_300 | 300 | 48828 | 3 |
Outer Fault Dataset | Code | Load (lbs) | Sampling rate (Hz) | Duration (sec) |
---|---|---|---|---|
baseline_2 | data_normal | 270 | 97656 | 6 |
OuterRaceFault_vload_2 | ORF_50 | 50 | 48828 | 3 |
OuterRaceFault_vload_3 | ORF_100 | 100 | 48828 | 3 |
OuterRaceFault_vload_4 | ORF_150 | 150 | 48828 | 3 |
OuterRaceFault_vload_5 | ORF_200 | 200 | 48828 | 3 |
OuterRaceFault_vload_6 | ORF_250 | 250 | 48828 | 3 |
OuterRaceFault_vload_7 | ORF_300 | 300 | 48828 | 3 |
LoadFactor (lbs) |
Clearance Factor |
Crest Factor |
Impulse Factor |
Kurtosis | Mean | Peak Value |
RMS | Shape Factor |
Skewness | Std | SINAD* | SNR* | THD* |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
50 | 40.04 | 15.462 | 28.69 | 27.97 | -0.22 | 27.50 | 1.78 | 1.86 | 0.62 | 1.76 | -21.32 | -21.307 | -5.36 |
100 | 37.30 | 14.488 | 26.96 | 30.53 | -0.22 | 26.59 | 1.84 | 1.86 | 0.87 | 1.82 | -21.05 | -21.027 | -0.53 |
150 | 33.30 | 13.249 | 24.31 | 33.13 | -0.22 | 23.06 | 1.74 | 1.84 | 1.28 | 1.72 | -19.05 | -19.046 | -10.06 |
200 | 38.15 | 13.537 | 26.92 | 37.28 | -0.21 | 27.38 | 2.02 | 1.99 | 1.15 | 2.01 | -18.22 | -18.208 | -6.31 |
250 | 37.52 | 13.022 | 26.18 | 37.49 | -0.20 | 27.14 | 2.08 | 2.01 | 0.72 | 2.08 | -17.70 | -17.684 | -5.46 |
300 | 35.24 | 12.998 | 25.17 | 35.30 | -0.19 | 25.58 | 1.97 | 1.94 | 0.68 | 1.96 | -17.35 | -17.341 | -8.41 |
270** | 7.75 | 5.230 | 6.56 | 3.02 | -0.14 | 4.65 | 0.89 | 1.25 | 0.00 | 0.88 | -23.60 | -23.598 | -11.39 |
LoadFactor (lbs) |
Clearance Factor |
Crest Factor |
Impulse Factor |
Kurtosis | Mean | Peak Value |
RMS | Shape Factor |
Skewness | Std | SINAD* | SNR* | THD* |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
50 | 10.26 | 6.39 | 8.48 | 5.09 | -0.19 | 6.35 | 0.99 | 1.33 | 0.04 | 0.98 | -14.41 | -14.40 | -11.97 |
100 | 9.15 | 5.84 | 7.62 | 4.40 | -0.18 | 4.93 | 0.84 | 1.31 | -0.01 | 0.82 | -13.15 | -13.12 | -9.06 |
150 | 9.54 | 6.10 | 7.94 | 4.04 | -0.18 | 5.21 | 0.85 | 1.30 | -0.04 | 0.83 | -12.59 | -12.56 | -9.934 |
200 | 21.81 | 12.46 | 17.67 | 11.90 | -0.17 | 12.28 | 0.99 | 1.42 | 0.31 | 0.97 | -17.54 | -17.52 | -5.54 |
250 | 15.03 | 9.07 | 12.30 | 6.59 | -0.16 | 8.66 | 0.96 | 1.36 | 0.12 | 0.94 | -16.09 | -16.06 | -4.92 |
300 | 27.18 | 12.92 | 20.80 | 17.69 | -0.16 | 19.43 | 1.50 | 1.61 | 0.27 | 1.50 | -15.10 | -15.10 | -14.69 |
270** | 7.75 | 5.23 | 6.56 | 3.02 | -0.14 | 4.65 | 0.89 | 1.25 | 0.01 | 0.88 | -23.60 | -23.60 | -11.39 |
LoadFactor | PeakAmp1 | PeakAmp2 | PeakFreq1 | PeakFreq2 | BandPower | |||||
---|---|---|---|---|---|---|---|---|---|---|
Inner | Outer | Inner | Outer | Inner | Outer | Inner | Outer | Inner | Outer | |
50 | 0.00034 | 0.000109 | 0.00031 | 0.000093 | 4363.937 | 1413.267 | 13991.090 | 14179.042 | 1.474 | 0.454 |
100 | 0.00046 | 0.000075 | 0.00012 | 0.000028 | 4256.059 | 1379.739 | 13968.668 | 14258.280 | 1.476 | 0.322 |
150 | 0.00046 | 0.000080 | 0.00005 | 0.000036 | 4191.394 | 1377.111 | 14127.206 | 14462.995 | 1.330 | 0.327 |
200 | 0.00031 | 0.000063 | 0.00011 | 0.000058 | 4025.383 | 4947.698 | 10622.786 | 1391.188 | 1.663 | 0.461 |
250 | 0.00061 | 0.000058 | 0.00009 | 0.000049 | 4124.988 | 1621.552 | 10365.553 | 5212.034 | 1.807 | 0.430 |
300 | 0.00077 | 0.000302 | 0.00058 | 0.000296 | 4081.332 | 2915.517 | 748.668 | 11675.566 | 1.618 | 1.101 |
Healthy 270 | 0.00003 | 0.000028 | 0.00003 | 0.000028 | 5490.855 | 5490.855 | 14478.764 | 14478.764 | 0.279 | 0.302 |
Dataset Segmentation | CSV files | Code | Load Factor | Subfiles Count |
---|---|---|---|---|
Example on baseline(Normal) with Matlab code. The segment is based on ratio, i.e., each segment in inner and outer fault contains 2500 samples, and each sample in normal condition contains 5000 data points. | IRF_50 | {'IRF_50' } | 58 | |
IRF_100 | {'IRF_100'} | 58 | ||
IRF_150 | {'IRF_150'} | 58 | ||
IRF_200 | {'IRF_200'} | 58 | ||
IRF_250 | {'IRF_250'} | 58 | ||
IRF_300 | {'IRF_300'} | 58 | ||
ORF_50 | {'ORF_50' } | 58 | ||
ORF_100 | {'ORF_100' } | 58 | ||
ORF_150 | {'ORF_150'} | 58 | ||
ORF_200 | {'ORF_200'} | 58 | ||
ORF_250 | {'ORF_250'} | 58 | ||
ORF_300 | {'ORF_300'} | 58 | ||
Normal | {'Normal' } | 117 |
No. of features used in classifier training | Top 13 >20 |
Top 8 >345 |
Top 7 >373 |
Top 2 >629 |
---|---|---|---|---|
Classifier name | Boosted Trees | Narrow Neural Network | Bilayered Neural Network | Fine Gaussian SVM |
Accuracy score on the testing dataset | 74.1% | 72.8% | 73.5% | 59.9% |
Number of selected features from ANOVA ranking | Top 19 >20 |
Top 14 >72 |
Top 13 >129 |
Top 11 >171 |
Top 8 >345 |
---|---|---|---|---|---|
Classifier | Bagged trees | Cubic SVM | Quadratic SVM | Quadratic Discriminant | Quadratic SVM |
Accuracy score on the testing dataset | 86.4% | 86.4% | 83.3% | 84.6% | 76.5% |
Features Color Code | |||
Features (ANOVA Rank) | Features Histogram | Features (ANOVA Rank) | Features Histogram |
1. Shape Factor | 2. Peak Value | ||
3. ClearanceFactor | 4. Impulse Factor | ||
5.Mean | 6.CrestFactor | ||
7. Kurtosis | 8.RMS | ||
9.Standard deviation | 10.Band Power | ||
11.Peak Amplitude1 | 12.Peak Frequency4 | ||
13.Peak Amplitude 2 | 14.PeakFrequency3 |
Health State | Inner | Outter | Healthy |
---|---|---|---|
Dataset | InnerRaceFault_vload_1 | 'OuterRaceFault_3.mat' | 'baseline_1.mat' |
2D time-frequency diagrams | |||
Bump | |||
Morse | |||
Amor |
Health State Training set | Code | Morse | Bump | Amor | |
---|---|---|---|---|---|
Healthy | baseline_1 | data_normal | 2.236 | 1.483 | 5.381 |
baseline_2 | data_normal2 | 2.836 | 1.600 | 15.830 | |
WSE Avg. for 0.1 sec | 2.536 | 1.541 | 10.603 | ||
Inner | InnerRaceFault_vload_1 | datat_inner | 0.011 | 0.017 | 0.009 |
InnerRaceFault_vload_2 | datat_inner2 | 0.023 | 0.040 | 0.019 | |
WSE Avg. for 0.1 sec | 0.017 | 0.028 | 0.014 | ||
Outer | OuterRaceFault_3 | data_outer | 2.311 | 2.028 | 0.611 |
OuterRaceFault_1 | data_outer_2 | 2.225 | 1.743 | 2.653 | |
WSE Avg. for 0.1 sec | 2.268 | 1.886 | 1.632 |
Classifier | ANOVA ranking | TTime 1 | Validation dataset | Testing Dataset | ||||
---|---|---|---|---|---|---|---|---|
(sec) | VA2 | HA3 | MA4 | MoA5 | SA 6 | Overall Accuracy | ||
RUSBoostedTrees | Top 20 >26 |
11.539 | 92.6% | 100% | 92.4% | 91.2% | 100% | 93.8% |
Fine Tree | Top 17 >58.6 |
4.393 | 92.6% | 100% | 95.7% | 82.4% | 100% | 93.8% |
Wide neural network | Top 10 >161 |
18.155 | 91.2% | 100% | 97.8% | 88.2% | 100% | 96.3% |
Cubic SVM | Top7 (a) >215 |
8.1055 | 93.1% | 100% | 96.7% | 82.4% | 100% | 94.4% |
Medium Gaussian SVM | Top 7 (b) | 5.8059 | 91.6% | 100% | 96.7% | 82.4% | 100% | 94.4% |
Fine Gaussian SVM | Top 5 >240 |
12.711 | 92.9% | 100% | 97.8% | 82.4% | 100% | 95.1% |
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