Predictive Analysis of Crack Growth in Bearings via Neural Networks
Abstract
:1. Introduction
- This research work successfully developed a practical artificial neural network (ANN) model capable of predicting crack area and width in a bearing with a seeded crack.
- The model utilizes key parameters like RMS, crest factor, SNR, skewness, kurtosis, and Shannon entropy, reflecting the practical application of these metrics in bearing condition monitoring.
- This study highlights the significant influence of SNR on predicting crack propagation when using it as a single input parameter.
- The combination of kurtosis and Shannon entropy achieved an even higher accuracy, demonstrating the potential for enhancing predictive performance through the integration of multiple parameters.
- This study validates the use of ANN models for predicting crack propagation in bearings, showcasing their ability to achieve high accuracy in real-world applications.
2. Research Methodology
2.1. Data Extraction
2.2. Application of Neural Network
3. Results and Discussion
3.1. Single Parameters
Root Mean Square (RMS)
3.2. Multiple Parameters
3.2.1. RMS and Crest Factor
3.2.2. RMS and SNR
3.2.3. RMS and Skewness
3.2.4. RMS and Kurtosis
3.2.5. RMS and Shannon Entropy
3.2.6. Remaining Combinations
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Time Duration in Hours | RMS (m/s2) | Crest Factor | SNR | Skewness | Kurtosis | Shannon Entropy (107) | Input Variables | |
---|---|---|---|---|---|---|---|---|
Total Area (mm2) | Width (mm) | |||||||
0 | 8.347 | 7.1256 | 22.98 | 0.189 | 5.554 | 2.42 | 24.86 | 1.82 |
10 | 10.22 | 6.8215 | 20.77 | 0.168 | 6.492 | 3.59 | 24.86 | 1.82 |
20 | 8.087 | 6.2457 | 22.33 | 0.208 | 5.527 | 2.02 | 24.86 | 1.82 |
30 | 8.472 | 8.0384 | 21.7 | 0.184 | 5.749 | 2.27 | 24.86 | 1.82 |
40 | 8.485 | 7.0794 | 22.46 | 0.22 | 5.626 | 2.27 | 24.86 | 1.82 |
50 | 8.448 | 8.2828 | 20.71 | 0.228 | 5.913 | 2.26 | 24.8625 | 1.82 |
60 | 8.456 | 7.3888 | 23.4 | 0.229 | 5.549 | 2.26 | 24.865 | 1.82 |
70 | 8.449 | 6.5549 | 20.99 | 0.223 | 5.618 | 2.25 | 24.8675 | 1.82 |
80 | 8.365 | 7.2492 | 23.45 | 0.223 | 5.542 | 2.19 | 24.96 | 1.82 |
90 | 8.308 | 6.418 | 22.34 | 0.221 | 5.603 | 2.17 | 24.96 | 1.8286 |
100 | 8.251 | 7.0285 | 21.54 | 0.216 | 5.752 | 2.13 | 24.96 | 1.8373 |
120 | 8.3 | 6.4237 | 22.2 | 0.218 | 5.679 | 2.16 | 25.36 | 1.895 |
140 | 8.601 | 6.7204 | 21.8 | 0.225 | 6.147 | 2.37 | 25.56 | 1.92 |
160 | 9.264 | 6.8881 | 20.35 | 0.168 | 5.521 | 2.8 | 26.0445 | 2.1 |
170 | 8.79 | 6.0588 | 20.29 | 0.18 | 5.728 | 2.48 | 26.4586 | 2.4766 |
180 | 7.68 | 13.357 | 23.6 | 0.119 | 8.537 | 2.03 | 26.978 | 3.1198 |
184 | 16.9 | 11.788 | 24.1 | 0.07 | 7.43 | 13.9 | 27.609 | 3.2798 |
188 | 8.1 | 14.3845 | 22.1 | 0.17 | 9.53 | 2.07 | 27.987 | 3.4399 |
192 | 7.97 | 11.439 | 22.9 | 0.04 | 7.67 | 1.98 | 28.275 | 3.6975 |
196 | 8.24 | 14.1009 | 24 | 0.11 | 11.6 | 2.19 | 28.345 | 4.0525 |
200 | 25.02 | 10.2382 | 19.67 | 0.129 | 7.312 | 30.7 | 28.778 | 4.867 |
204 | 22 | 9.5045 | 19.4 | 0.09 | 7.53 | 28 | 28.835 | 5.16 |
208 | 25.4 | 9.4644 | 22.4 | 0.11 | 7.15 | 20 | 28.892 | 5.4545 |
212 | 25.7 | 12.754 | 19.5 | 0.16 | 8.63 | 26 | 28.949 | 5.7482 |
216 | 24.9 | 8.8966 | 18.18 | 0.178 | 8.017 | 30.5 | 29.007 | 6.042 |
220 | 13.8 | 9.1122 | 24.3 | 0.12 | 7.09 | 7.27 | 28.885 | 7.0116 |
224 | 16 | 10.0815 | 21.2 | 0.16 | 7.63 | 15.2 | 28.945 | 7.0983 |
229 | 15.28 | 11.0412 | 23.31 | 0.078 | 8.1 | 10.2 | 29.15 | 7.231 |
232 | 19.2 | 11.2517 | 22.5 | 0.26 | 10.2 | 15.9 | 29.172 | 7.341 |
239 | 16.28 | 7.774 | 21.91 | 0.141 | 6.48 | 11.7 | 29.202 | 7.531 |
248 | 19.21 | 9.1612 | 17.67 | 0.151 | 6.135 | 12.2 | 29.324 | 7.761 |
259 | 14.86 | 7.3411 | 18.42 | 0.1707 | 6.824 | 9.58 | 29.556 | 8.631 |
267.5 | 8.723 | 9.1705 | 21.7 | 0.14 | 4.967 | 2.66 | 29.564 | 8.987 |
274.5 | 9.15 | 8.3301 | 19.51 | 0.041 | 6.653 | 3.06 | 31.019 | 9.362 |
278.5 | 9.178 | 9.6329 | 21.2 | 0.115 | 6.682 | 13.26 | 33.372 | 9.761 |
284.5 | 9.603 | 10.247 | 19.47 | 0.014 | 7.288 | 3.09 | 36.518 | 10.401 |
285 | 9.114 | 10.4396 | 19.35 | 0.009 | 7.954 | 2.74 | 40.157 | 10.967 |
Input Parameters | Actual/Target Values | Predicted Values | Accuracy (in %) | |||
---|---|---|---|---|---|---|
Time Duration | RMS (m/s2) | Total Area (mm2) | Width (mm) | Total Area (mm2) | Width (mm) | |
0 | 8.347 | 24.86 | 1.82 | 24.8600 | 1.82 | 100.0% |
10 | 10.22 | 24.86 | 1.82 | 24.8600 | 1.82 | 100.0% |
20 | 8.087 | 24.86 | 1.82 | 24.8600 | 1.82 | 100.0% |
30 | 8.472 | 24.86 | 1.82 | 24.8600 | 1.82 | 100.0% |
40 | 8.485 | 24.86 | 1.82 | 24.8600 | 1.82 | 100.0% |
50 | 8.448 | 24.8625 | 1.82 | 24.8601 | 1.82 | 100.0% |
60 | 8.456 | 24.865 | 1.82 | 24.8604 | 1.82 | 100.0% |
70 | 8.449 | 24.8675 | 1.82 | 24.8619 | 1.8200 | 100.0% |
80 | 8.365 | 24.96 | 1.82 | 24.8708 | 1.8200 | 99.8% |
90 | 8.308 | 24.96 | 1.8286 | 24.9076 | 1.8202 | 99.7% |
100 | 8.251 | 24.96 | 1.8373 | 25.0026 | 1.8249 | 99.6% |
120 | 8.3 | 25.36 | 1.8953 | 25.3488 | 1.8787 | 99.5% |
140 | 8.601 | 25.56 | 1.92 | 25.5771 | 1.9401 | 99.4% |
160 | 9.264 | 26.0445 | 2.1 | 26.0410 | 2.0878 | 99.7% |
170 | 8.79 | 26.4586 | 2.4766 | 26.2826 | 2.4391 | 98.9% |
180 | 7.68 | 26.978 | 3.1198 | 27.6182 | 3.0798 | 98.2% |
184 | 16.9 | 27.609 | 3.2798 | 24.8600 | 3.2777 | 94.4% |
188 | 8.1 | 27.987 | 3.4399 | 27.9953 | 3.4596 | 99.7% |
192 | 7.97 | 28.275 | 3.6975 | 28.2749 | 3.6800 | 99.8% |
196 | 8.24 | 28.345 | 4.0525 | 28.1086 | 3.8432 | 96.9% |
200 | 25.02 | 28.778 | 4.867 | 24.86 | 4.8627 | 92.1% |
204 | 22 | 28.83525 | 5.16 | 24.86 | 5.1546 | 92.0% |
208 | 25.4 | 28.8925 | 5.4545 | 24.86 | 5.4346 | 91.7% |
212 | 25.7 | 28.94975 | 5.7482 | 24.86 | 5.7407 | 91.7% |
216 | 24.9 | 29.007 | 6.042 | 24.86 | 6.0431 | 91.6% |
220 | 13.8 | 28.885 | 7.0116 | 24.86 | 6.8938 | 91.1% |
224 | 16 | 28.945 | 7.0983 | 24.86 | 7.0906 | 91.7% |
229 | 15.28 | 29.15 | 7.231 | 24.86 | 7.2384 | 91.3% |
232 | 19.2 | 29.1725 | 7.341 | 24.86 | 7.5194 | 90.1% |
239 | 16.28 | 29.202 | 7.531 | 24.86 | 7.4396 | 90.7% |
248 | 19.21 | 29.324 | 7.761 | 24.86 | 7.7607 | 91.0% |
259 | 14.86 | 29.556 | 8.631 | 24.86 | 8.6296 | 90.5% |
267.5 | 8.723 | 29.564 | 8.987 | 24.86 | 8.9862 | 90.5% |
274.5 | 9.15 | 31.019 | 9.362 | 24.86 | 9.2226 | 86.9% |
278.5 | 9.178 | 33.372 | 9.761 | 24.86 | 9.7644 | 82.9% |
284.5 | 9.603 | 36.518 | 10.401 | 24.86 | 10.3986 | 76.5% |
285 | 9.114 | 40.157 | 10.967 | 24.86 | 10.9600 | 69.2% |
Input Parameters | Actual/Target Values | Predicted Values | Accuracy (in %) | |||
---|---|---|---|---|---|---|
Time Duration | Crest Factor | Total Area (mm2) | Width (mm) | Total Area (mm2) | Width (mm) | |
0 | 7.1256 | 24.86 | 1.82 | 24.8600 | 1.82 | 100.0% |
10 | 6.8215 | 24.86 | 1.82 | 24.8600 | 1.82 | 100.0% |
20 | 6.2457 | 24.86 | 1.82 | 24.8600 | 1.82 | 100.0% |
30 | 8.0384 | 24.86 | 1.82 | 24.8600 | 1.82 | 100.0% |
40 | 7.0794 | 24.86 | 1.82 | 24.8600 | 1.82 | 100.0% |
50 | 8.2828 | 24.8625 | 1.82 | 24.8600 | 1.82 | 100.0% |
60 | 7.3888 | 24.865 | 1.82 | 24.8600 | 1.82 | 100.0% |
70 | 6.5549 | 24.8675 | 1.82 | 24.8600 | 1.8200 | 100.0% |
80 | 7.2492 | 24.96 | 1.82 | 24.8600 | 1.8200 | 99.8% |
90 | 6.418 | 24.96 | 1.8286 | 25.6415 | 1.8200 | 98.4% |
100 | 7.0285 | 24.96 | 1.8373 | 24.9593 | 1.8200 | 99.5% |
120 | 6.4237 | 25.36 | 1.8953 | 25.7792 | 1.8200 | 97.1% |
140 | 6.7204 | 25.56 | 1.92 | 25.8987 | 1.8200 | 96.6% |
160 | 6.8881 | 26.0445 | 2.1 | 26.0445 | 1.8200 | 92.3% |
170 | 6.0588 | 26.4586 | 2.4766 | 26.4577 | 1.8200 | 82.0% |
180 | 13.357 | 26.978 | 3.1198 | 24.8600 | 3.1218 | 95.7% |
184 | 11.788 | 27.609 | 3.2798 | 24.8600 | 3.2773 | 94.4% |
188 | 14.3845 | 27.987 | 3.4399 | 24.8600 | 3.3777 | 92.8% |
192 | 11.439 | 28.275 | 3.6975 | 24.8600 | 3.6949 | 93.1% |
196 | 14.1009 | 28.345 | 4.0525 | 24.8600 | 4.0541 | 93.0% |
200 | 10.2382 | 28.778 | 4.867 | 28.7983074 | 4.9050 | 99.6% |
204 | 9.5045 | 28.83525 | 5.16 | 28.85434946 | 5.1448 | 99.8% |
208 | 9.4644 | 28.8925 | 5.4545 | 28.89521537 | 5.4927 | 99.6% |
212 | 12.754 | 28.94975 | 5.7482 | 24.86 | 5.7404 | 91.7% |
216 | 8.8966 | 29.007 | 6.042 | 28.96290978 | 6.0790 | 99.6% |
220 | 9.1122 | 28.885 | 7.0116 | 29.00115216 | 6.4209 | 95.2% |
224 | 10.0815 | 28.945 | 7.0983 | 29.04998962 | 6.8310 | 97.9% |
229 | 11.0412 | 29.15 | 7.231 | 29.10491902 | 7.2469 | 99.8% |
232 | 11.2517 | 29.1725 | 7.341 | 29.12729376 | 7.4323 | 99.3% |
239 | 7.774 | 29.202 | 7.531 | 29.18287349 | 7.5263 | 99.9% |
248 | 9.1612 | 29.324 | 7.761 | 29.20599516 | 8.0095 | 98.2% |
259 | 7.3411 | 29.556 | 8.631 | 29.5600133 | 8.6280 | 100.0% |
267.5 | 9.1705 | 29.564 | 8.987 | 29.69694264 | 8.7809 | 98.6% |
274.5 | 8.3301 | 31.019 | 9.362 | 31.01305386 | 9.3511 | 99.9% |
278.5 | 9.6329 | 33.372 | 9.761 | 32.19229614 | 9.7187 | 98.0% |
284.5 | 10.247 | 36.518 | 10.401 | 36.50258921 | 10.4959 | 99.5% |
285 | 10.4396 | 40.157 | 10.967 | 36.82257261 | 10.5398 | 93.4% |
S. No. | Input Parameters | Accuracy (in %) |
---|---|---|
1 | SNR | 99.2 |
2 | Skewness | 98.6 |
3 | Kurtosis | 97.1 |
4 | Shannon entropy (107) | 97.8 |
Input Parameters | Actual/Target Values | Predicted Values | Accuracy (in %) | ||||
---|---|---|---|---|---|---|---|
Time Duration | RMS (m/s2) | Crest Factor | Total Area (mm2) | Width (mm) | Total Area (mm2) | Width (mm) | |
0 | 8.347 | 7.1256 | 7.1256 | 24.86 | 1.82 | 24.862 | 99.99% |
10 | 10.22 | 6.8215 | 6.8215 | 24.86 | 1.82 | 24.860 | 100.00% |
20 | 8.087 | 6.2457 | 6.2457 | 24.86 | 1.82 | 24.865 | 99.98% |
30 | 8.472 | 8.0384 | 8.0384 | 24.86 | 1.82 | 24.869 | 99.97% |
40 | 8.485 | 7.0794 | 7.0794 | 24.86 | 1.82 | 24.875 | 99.94% |
50 | 8.448 | 8.2828 | 8.2828 | 24.8625 | 1.82 | 24.886 | 99.91% |
60 | 8.456 | 7.3888 | 7.3888 | 24.865 | 1.82 | 24.904 | 99.84% |
70 | 8.449 | 6.5549 | 6.5549 | 24.8675 | 1.82 | 24.934 | 99.73% |
80 | 8.365 | 7.2492 | 7.2492 | 24.96 | 1.82 | 24.981 | 99.92% |
90 | 8.308 | 6.418 | 6.418 | 24.96 | 1.8286 | 25.051 | 99.64% |
100 | 8.251 | 7.0285 | 7.0285 | 24.96 | 1.8373 | 25.151 | 99.24% |
120 | 8.3 | 6.4237 | 6.4237 | 25.36 | 1.8953 | 25.468 | 99.58% |
140 | 8.601 | 6.7204 | 6.7204 | 25.56 | 1.92 | 25.940 | 98.54% |
160 | 9.264 | 6.8881 | 6.8881 | 26.0445 | 2.1 | 25.753 | 98.87% |
170 | 8.79 | 6.0588 | 6.0588 | 26.4586 | 2.4766 | 26.869 | 98.47% |
180 | 7.68 | 13.357 | 13.357 | 26.978 | 3.1198 | 27.475 | 98.19% |
184 | 16.9 | 11.788 | 11.788 | 27.609 | 3.2798 | 27.437 | 99.37% |
188 | 8.1 | 14.3845 | 14.3845 | 27.987 | 3.4399 | 27.872 | 99.59% |
192 | 7.97 | 11.439 | 11.439 | 28.275 | 3.6975 | 27.986 | 98.97% |
196 | 8.24 | 14.1009 | 14.1009 | 28.345 | 4.0525 | 28.436 | 99.68% |
200 | 25.02 | 10.2382 | 10.2382 | 28.778 | 4.867 | 28.752 | 99.91% |
204 | 22 | 9.5045 | 9.5045 | 28.83525 | 5.16 | 28.785 | 99.83% |
208 | 25.4 | 9.4644 | 9.4644 | 28.8925 | 5.4545 | 28.897 | 99.98% |
212 | 25.7 | 12.754 | 12.754 | 28.94975 | 5.7482 | 28.929 | 99.93% |
216 | 24.9 | 8.8966 | 8.8966 | 29.007 | 6.042 | 28.099 | 96.77% |
220 | 13.8 | 9.1122 | 9.1122 | 28.885 | 7.0116 | 28.900 | 99.95% |
224 | 16 | 10.0815 | 10.0815 | 28.945 | 7.0983 | 29.036 | 99.69% |
229 | 15.28 | 11.0412 | 11.0412 | 29.15 | 7.231 | 29.220 | 99.76% |
232 | 19.2 | 11.2517 | 11.2517 | 29.1725 | 7.341 | 29.294 | 99.59% |
239 | 16.28 | 7.774 | 7.774 | 29.202 | 7.531 | 29.131 | 99.76% |
248 | 19.21 | 9.1612 | 9.1612 | 29.324 | 7.761 | 29.343 | 99.93% |
259 | 14.86 | 7.3411 | 7.3411 | 29.556 | 8.631 | 29.516 | 99.87% |
267.5 | 8.723 | 9.1705 | 9.1705 | 29.564 | 8.987 | 30.492 | 96.96% |
274.5 | 9.15 | 8.3301 | 8.3301 | 31.019 | 9.362 | 29.425 | 94.58% |
278.5 | 9.178 | 9.6329 | 9.6329 | 33.372 | 9.761 | 33.380 | 99.98% |
284.5 | 9.603 | 10.247 | 10.247 | 36.518 | 10.401 | 35.734 | 97.81% |
285 | 9.114 | 10.4396 | 10.4396 | 40.157 | 10.967 | 38.663 | 96.14% |
Input Parameters | Actual/Target Values | Predicted Values | Accuracy (in %) | ||||
---|---|---|---|---|---|---|---|
Time Duration | RMS (m/s2) | SNR | Total Area (mm2) | Width (mm) | Total Area (mm2) | Width (mm) | |
0 | 8.347 | 22.98 | 22.98 | 24.86 | 1.82 | 24.860 | 100.00% |
10 | 10.22 | 20.77 | 20.77 | 24.86 | 1.82 | 24.860 | 100.00% |
20 | 8.087 | 22.33 | 22.33 | 24.86 | 1.82 | 24.860 | 100.00% |
30 | 8.472 | 21.7 | 21.7 | 24.86 | 1.82 | 24.860 | 100.00% |
40 | 8.485 | 22.46 | 22.46 | 24.86 | 1.82 | 24.860 | 100.00% |
50 | 8.448 | 20.71 | 20.71 | 24.8625 | 1.82 | 24.860 | 99.99% |
60 | 8.456 | 23.4 | 23.4 | 24.865 | 1.82 | 24.860 | 99.98% |
70 | 8.449 | 20.99 | 20.99 | 24.8675 | 1.82 | 24.860 | 99.97% |
80 | 8.365 | 23.45 | 23.45 | 24.96 | 1.82 | 24.963 | 99.99% |
90 | 8.308 | 22.34 | 22.34 | 24.96 | 1.8286 | 24.861 | 99.60% |
100 | 8.251 | 21.54 | 21.54 | 24.96 | 1.8373 | 24.860 | 99.60% |
120 | 8.3 | 22.2 | 22.2 | 25.36 | 1.8953 | 25.359 | 100.00% |
140 | 8.601 | 21.8 | 21.8 | 25.56 | 1.92 | 25.950 | 98.50% |
160 | 9.264 | 20.35 | 20.35 | 26.0445 | 2.1 | 26.044 | 100.00% |
170 | 8.79 | 20.29 | 20.29 | 26.4586 | 2.4766 | 26.459 | 100.00% |
180 | 7.68 | 23.6 | 23.6 | 26.978 | 3.1198 | 27.960 | 96.49% |
184 | 16.9 | 24.1 | 24.1 | 27.609 | 3.2798 | 27.608 | 100.00% |
188 | 8.1 | 22.1 | 22.1 | 27.987 | 3.4399 | 27.987 | 100.00% |
192 | 7.97 | 22.9 | 22.9 | 28.275 | 3.6975 | 28.120 | 99.45% |
196 | 8.24 | 24 | 24 | 28.345 | 4.0525 | 28.344 | 100.00% |
200 | 25.02 | 19.67 | 19.67 | 28.778 | 4.867 | 24.860 | 84.24% |
204 | 22 | 19.4 | 19.4 | 28.83525 | 5.16 | 24.860 | 84.01% |
208 | 25.4 | 22.4 | 22.4 | 28.8925 | 5.4545 | 28.892 | 100.00% |
212 | 25.7 | 19.5 | 19.5 | 28.94975 | 5.7482 | 24.860 | 83.55% |
216 | 24.9 | 18.18 | 18.18 | 29.007 | 6.042 | 24.860 | 83.32% |
220 | 13.8 | 24.3 | 24.3 | 28.885 | 7.0116 | 25.148 | 85.14% |
224 | 16 | 21.2 | 21.2 | 28.945 | 7.0983 | 31.529 | 91.80% |
229 | 15.28 | 23.31 | 23.31 | 29.15 | 7.231 | 29.149 | 100.00% |
232 | 19.2 | 22.5 | 22.5 | 29.1725 | 7.341 | 29.172 | 100.00% |
239 | 16.28 | 21.91 | 21.91 | 29.202 | 7.531 | 29.569 | 98.76% |
248 | 19.21 | 17.67 | 17.67 | 29.324 | 7.761 | 24.860 | 82.04% |
259 | 14.86 | 18.42 | 18.42 | 29.556 | 8.631 | 33.783 | 87.49% |
267.5 | 8.723 | 21.7 | 21.7 | 29.564 | 8.987 | 27.384 | 92.04% |
274.5 | 9.15 | 19.51 | 19.51 | 31.019 | 9.362 | 31.018 | 100.00% |
278.5 | 9.178 | 21.2 | 21.2 | 33.372 | 9.761 | 28.197 | 81.65% |
284.5 | 9.603 | 19.47 | 19.47 | 36.518 | 10.401 | 36.518 | 100.00% |
285 | 9.114 | 19.35 | 19.35 | 40.157 | 10.967 | 31.544 | 72.69% |
Input Parameters | Actual/Target Values | Predicted Values | Accuracy (in %) | ||||
---|---|---|---|---|---|---|---|
Time Duration | RMS (m/s2) | Skewness | Total Area (mm2) | Width (mm) | Total Area (mm2) | Width (mm) | |
0 | 8.347 | 0.189 | 0.189 | 24.86 | 1.82 | 24.890 | 99.88% |
10 | 10.22 | 0.168 | 0.168 | 24.86 | 1.82 | 24.911 | 99.80% |
20 | 8.087 | 0.208 | 0.208 | 24.86 | 1.82 | 24.890 | 99.88% |
30 | 8.472 | 0.184 | 0.184 | 24.86 | 1.82 | 24.894 | 99.86% |
40 | 8.485 | 0.22 | 0.22 | 24.86 | 1.82 | 24.900 | 99.84% |
50 | 8.448 | 0.228 | 0.228 | 24.8625 | 1.82 | 24.907 | 99.82% |
60 | 8.456 | 0.229 | 0.229 | 24.865 | 1.82 | 24.916 | 99.80% |
70 | 8.449 | 0.223 | 0.223 | 24.8675 | 1.82 | 24.927 | 99.76% |
80 | 8.365 | 0.223 | 0.223 | 24.96 | 1.82 | 24.942 | 99.93% |
90 | 8.308 | 0.221 | 0.221 | 24.96 | 1.8286 | 24.964 | 99.99% |
100 | 8.251 | 0.216 | 0.216 | 24.96 | 1.8373 | 24.992 | 99.87% |
120 | 8.3 | 0.218 | 0.218 | 25.36 | 1.8953 | 25.124 | 99.06% |
140 | 8.601 | 0.225 | 0.225 | 25.56 | 1.92 | 25.472 | 99.65% |
160 | 9.264 | 0.168 | 0.168 | 26.0445 | 2.1 | 26.192 | 99.44% |
170 | 8.79 | 0.18 | 0.18 | 26.4586 | 2.4766 | 26.674 | 99.19% |
180 | 7.68 | 0.119 | 0.119 | 26.978 | 3.1198 | 26.947 | 99.88% |
184 | 16.9 | 0.07 | 0.07 | 27.609 | 3.2798 | 27.845 | 99.15% |
188 | 8.1 | 0.17 | 0.17 | 27.987 | 3.4399 | 27.724 | 99.05% |
192 | 7.97 | 0.04 | 0.04 | 28.275 | 3.6975 | 28.574 | 98.95% |
196 | 8.24 | 0.11 | 0.11 | 28.345 | 4.0525 | 28.216 | 99.54% |
200 | 25.02 | 0.129 | 0.129 | 28.778 | 4.867 | 29.086 | 98.94% |
204 | 22 | 0.09 | 0.09 | 28.83525 | 5.16 | 28.815 | 99.93% |
208 | 25.4 | 0.11 | 0.11 | 28.8925 | 5.4545 | 30.963 | 93.31% |
212 | 25.7 | 0.16 | 0.16 | 28.94975 | 5.7482 | 29.157 | 99.29% |
216 | 24.9 | 0.178 | 0.178 | 29.007 | 6.042 | 28.649 | 98.75% |
220 | 13.8 | 0.12 | 0.12 | 28.885 | 7.0116 | 28.978 | 99.68% |
224 | 16 | 0.16 | 0.16 | 28.945 | 7.0983 | 28.826 | 99.59% |
229 | 15.28 | 0.078 | 0.078 | 29.15 | 7.231 | 29.602 | 98.47% |
232 | 19.2 | 0.26 | 0.26 | 29.1725 | 7.341 | 30.701 | 95.02% |
239 | 16.28 | 0.141 | 0.141 | 29.202 | 7.531 | 29.257 | 99.81% |
248 | 19.21 | 0.151 | 0.151 | 29.324 | 7.761 | 29.198 | 99.57% |
259 | 14.86 | 0.1707 | 0.1707 | 29.556 | 8.631 | 29.580 | 99.92% |
267.5 | 8.723 | 0.14 | 0.14 | 29.564 | 8.987 | 29.658 | 99.68% |
274.5 | 9.15 | 0.041 | 0.041 | 31.019 | 9.362 | 32.718 | 94.81% |
278.5 | 9.178 | 0.115 | 0.115 | 33.372 | 9.761 | 29.700 | 87.64% |
284.5 | 9.603 | 0.014 | 0.014 | 36.518 | 10.401 | 39.249 | 93.04% |
285 | 9.114 | 0.009 | 0.009 | 40.157 | 10.967 | 39.557 | 98.48% |
Input Parameters | Actual/Target Values | Predicted Values | Accuracy (in %) | ||||
---|---|---|---|---|---|---|---|
Time Duration | RMS (m/s2) | Kurtosis | Total Area (mm2) | Width (mm) | Total Area (mm2) | Width (mm) | |
0 | 8.347 | 5.554 | 5.554 | 24.86 | 1.82 | 24.860 | 100.00% |
10 | 10.22 | 6.492 | 6.492 | 24.86 | 1.82 | 24.860 | 100.00% |
20 | 8.087 | 5.527 | 5.527 | 24.86 | 1.82 | 24.860 | 100.00% |
30 | 8.472 | 5.749 | 5.749 | 24.86 | 1.82 | 24.860 | 100.00% |
40 | 8.485 | 5.626 | 5.626 | 24.86 | 1.82 | 24.860 | 100.00% |
50 | 8.448 | 5.913 | 5.913 | 24.8625 | 1.82 | 24.860 | 99.99% |
60 | 8.456 | 5.549 | 5.549 | 24.865 | 1.82 | 24.860 | 99.98% |
70 | 8.449 | 5.618 | 5.618 | 24.8675 | 1.82 | 24.860 | 99.97% |
80 | 8.365 | 5.542 | 5.542 | 24.96 | 1.82 | 24.860 | 99.60% |
90 | 8.308 | 5.603 | 5.603 | 24.96 | 1.8286 | 24.860 | 99.60% |
100 | 8.251 | 5.752 | 5.752 | 24.96 | 1.8373 | 24.863 | 99.61% |
120 | 8.3 | 5.679 | 5.679 | 25.36 | 1.8953 | 25.170 | 99.25% |
140 | 8.601 | 6.147 | 6.147 | 25.56 | 1.92 | 25.858 | 98.85% |
160 | 9.264 | 5.521 | 5.521 | 26.0445 | 2.1 | 25.981 | 99.76% |
170 | 8.79 | 5.728 | 5.728 | 26.4586 | 2.4766 | 26.438 | 99.92% |
180 | 7.68 | 8.537 | 8.537 | 26.978 | 3.1198 | 26.913 | 99.76% |
184 | 16.9 | 7.43 | 7.43 | 27.609 | 3.2798 | 28.375 | 97.30% |
188 | 8.1 | 9.53 | 9.53 | 27.987 | 3.4399 | 28.002 | 99.95% |
192 | 7.97 | 7.67 | 7.67 | 28.275 | 3.6975 | 29.446 | 96.02% |
196 | 8.24 | 11.6 | 11.6 | 28.345 | 4.0525 | 27.283 | 96.11% |
200 | 25.02 | 7.312 | 7.312 | 28.778 | 4.867 | 28.935 | 99.46% |
204 | 22 | 7.53 | 7.53 | 28.83525 | 5.16 | 28.846 | 99.96% |
208 | 25.4 | 7.15 | 7.15 | 28.8925 | 5.4545 | 28.966 | 99.75% |
212 | 25.7 | 8.63 | 8.63 | 28.94975 | 5.7482 | 28.864 | 99.70% |
216 | 24.9 | 8.017 | 8.017 | 29.007 | 6.042 | 28.957 | 99.83% |
220 | 13.8 | 7.09 | 7.09 | 28.885 | 7.0116 | 29.168 | 99.03% |
224 | 16 | 7.63 | 7.63 | 28.945 | 7.0983 | 28.889 | 99.81% |
229 | 15.28 | 8.1 | 8.1 | 29.15 | 7.231 | 29.104 | 99.84% |
232 | 19.2 | 10.2 | 10.2 | 29.1725 | 7.341 | 30.250 | 96.44% |
239 | 16.28 | 6.48 | 6.48 | 29.202 | 7.531 | 29.092 | 99.62% |
248 | 19.21 | 6.135 | 6.135 | 29.324 | 7.761 | 29.297 | 99.91% |
259 | 14.86 | 6.824 | 6.824 | 29.556 | 8.631 | 29.299 | 99.12% |
267.5 | 8.723 | 4.967 | 4.967 | 29.564 | 8.987 | 26.822 | 89.78% |
274.5 | 9.15 | 6.653 | 6.653 | 31.019 | 9.362 | 31.452 | 98.62% |
278.5 | 9.178 | 6.682 | 6.682 | 33.372 | 9.761 | 31.975 | 95.63% |
284.5 | 9.603 | 7.288 | 7.288 | 36.518 | 10.401 | 36.292 | 99.38% |
285 | 9.114 | 7.954 | 7.954 | 40.157 | 10.967 | 39.883 | 99.31% |
Input Parameters | Actual/Target Values | Predicted Values | Accuracy (in %) | ||||
---|---|---|---|---|---|---|---|
Time Duration | RMS (m/s2) | Shannon Entropy (107) | Total Area (mm2) | Width (mm) | Total Area (mm2) | Width (mm) | |
0 | 8.347 | 2.42 | 2.42 | 24.86 | 1.82 | 24.861 | 100.0% |
10 | 10.22 | 3.59 | 3.59 | 24.86 | 1.82 | 24.862 | 99.99% |
20 | 8.087 | 2.02 | 2.02 | 24.86 | 1.82 | 24.861 | 100.0% |
30 | 8.472 | 2.27 | 2.27 | 24.86 | 1.82 | 24.862 | 99.99% |
40 | 8.485 | 2.27 | 2.27 | 24.86 | 1.82 | 24.863 | 99.99% |
50 | 8.448 | 2.26 | 2.26 | 24.8625 | 1.82 | 24.863 | 100.0% |
60 | 8.456 | 2.26 | 2.26 | 24.865 | 1.82 | 24.865 | 100.0% |
70 | 8.449 | 2.25 | 2.25 | 24.8675 | 1.82 | 24.867 | 100.0% |
80 | 8.365 | 2.19 | 2.19 | 24.96 | 1.82 | 24.871 | 99.64% |
90 | 8.308 | 2.17 | 2.17 | 24.96 | 1.8286 | 24.877 | 99.67% |
100 | 8.251 | 2.13 | 2.13 | 24.96 | 1.8373 | 24.891 | 99.72% |
120 | 8.3 | 2.16 | 2.16 | 25.36 | 1.8953 | 24.987 | 98.51% |
140 | 8.601 | 2.37 | 2.37 | 25.56 | 1.92 | 25.438 | 99.52% |
160 | 9.264 | 2.8 | 2.8 | 26.0445 | 2.1 | 26.614 | 97.86% |
170 | 8.79 | 2.48 | 2.48 | 26.4586 | 2.4766 | 27.025 | 97.90% |
180 | 7.68 | 2.03 | 2.03 | 26.978 | 3.1198 | 27.324 | 98.73% |
184 | 16.9 | 13.9 | 13.9 | 27.609 | 3.2798 | 28.520 | 96.81% |
188 | 8.1 | 2.07 | 2.07 | 27.987 | 3.4399 | 27.707 | 98.99% |
192 | 7.97 | 1.98 | 1.98 | 28.275 | 3.6975 | 27.821 | 98.37% |
196 | 8.24 | 2.19 | 2.19 | 28.345 | 4.0525 | 27.875 | 98.31% |
200 | 25.02 | 30.7 | 30.7 | 28.778 | 4.867 | 28.516 | 99.08% |
204 | 22 | 28 | 28 | 28.83525 | 5.16 | 28.975 | 99.52% |
208 | 25.4 | 20 | 20 | 28.8925 | 5.4545 | 28.973 | 99.72% |
212 | 25.7 | 26 | 26 | 28.94975 | 5.7482 | 29.006 | 99.81% |
216 | 24.9 | 30.5 | 30.5 | 29.007 | 6.042 | 28.798 | 99.27% |
220 | 13.8 | 7.27 | 7.27 | 28.885 | 7.0116 | 27.910 | 96.51% |
224 | 16 | 15.2 | 15.2 | 28.945 | 7.0983 | 28.516 | 98.49% |
229 | 15.28 | 10.2 | 10.2 | 29.15 | 7.231 | 28.898 | 99.13% |
232 | 19.2 | 15.9 | 15.9 | 29.1725 | 7.341 | 28.486 | 97.59% |
239 | 16.28 | 11.7 | 11.7 | 29.202 | 7.531 | 29.349 | 99.50% |
248 | 19.21 | 12.2 | 12.2 | 29.324 | 7.761 | 29.495 | 99.42% |
259 | 14.86 | 9.58 | 9.58 | 29.556 | 8.631 | 30.125 | 98.11% |
267.5 | 8.723 | 2.66 | 2.66 | 29.564 | 8.987 | 29.749 | 99.38% |
274.5 | 9.15 | 3.06 | 3.06 | 31.019 | 9.362 | 32.180 | 96.39% |
278.5 | 9.178 | 13.26 | 13.26 | 33.372 | 9.761 | 33.544 | 99.49% |
284.5 | 9.603 | 3.09 | 3.09 | 36.518 | 10.401 | 37.427 | 97.57% |
285 | 9.114 | 2.74 | 2.74 | 40.157 | 10.967 | 38.142 | 94.72% |
S. No. | Input Parameters | Accuracy (in %) |
---|---|---|
1 | Crest Factor and SNR | 96.51% |
2 | Crest Factor and Skewness | 97.64% |
3 | Crest Factor and Kurtosis | 98.87% |
4 | Crest Factor and Shannon Entropy | 97.36% |
5 | SNR and Skewness | 98.17% |
6 | SNR and Kurtosis | 97.81% |
7 | SNR and Shannon Entropy | 96.08% |
8 | Skewness and Kurtosis | 98.41% |
9 | Skewness and Shannon Entropy | 97.45% |
10 | Kurtosis and Shannon Entropy | 99.39% |
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© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Singh, M.; Gopaluni, D.T.; Shoor, S.; Vashishtha, G.; Chauhan, S. Predictive Analysis of Crack Growth in Bearings via Neural Networks. Machines 2024, 12, 607. https://doi.org/10.3390/machines12090607
Singh M, Gopaluni DT, Shoor S, Vashishtha G, Chauhan S. Predictive Analysis of Crack Growth in Bearings via Neural Networks. Machines. 2024; 12(9):607. https://doi.org/10.3390/machines12090607
Chicago/Turabian StyleSingh, Manpreet, Dharma Teja Gopaluni, Sumit Shoor, Govind Vashishtha, and Sumika Chauhan. 2024. "Predictive Analysis of Crack Growth in Bearings via Neural Networks" Machines 12, no. 9: 607. https://doi.org/10.3390/machines12090607