Bearing Fault-Detection Method Based on Improved Grey Wolf Algorithm to Optimize Parameters of Multistable Stochastic Resonance
<p>Potential function curve of multistable system.</p> "> Figure 2
<p>The Sobol sequence and random method to generate individual distribution maps.</p> "> Figure 3
<p>The convergence factor comparison curve.</p> "> Figure 4
<p>The pseudocode of MSGWO.</p> "> Figure 5
<p>The convergence curve of MSGWO is compared with that of standard algorithm.</p> "> Figure 5 Cont.
<p>The convergence curve of MSGWO is compared with that of standard algorithm.</p> "> Figure 6
<p>The convergence curves are compared between MSGWO and the improved algorithm.</p> "> Figure 6 Cont.
<p>The convergence curves are compared between MSGWO and the improved algorithm.</p> "> Figure 7
<p>Population diversity measurement analysis.</p> "> Figure 8
<p>The flow diagram of the proposed algorithm.</p> "> Figure 9
<p>Time domain waveform and FFT spectrum of CWRU input signal.</p> "> Figure 10
<p>The FFT spectrum of the output signal processed by the raised algorithm.</p> "> Figure 11
<p>Time domain waveform and FFT spectrum of MFPT input signal.</p> "> Figure 12
<p>The FFT spectrum of the output signal processed by the proposed algorithm.</p> "> Figure 13
<p>Crystal growing furnace and crystal lifting and rotating mechanism.</p> "> Figure 14
<p>Vibration sensor installation position.</p> "> Figure 15
<p>Original vibration signal of crystal rotating motor.</p> "> Figure 16
<p>Spectrum amplitude of motor fault.</p> ">
Abstract
:1. Introduction
2. Specific Cases of Bearing Failure
3. Basic Principles of Multistable SR
3.1. The Basic Theory of Multistable SR
3.2. System Parameters’ Range
4. Multi-Strategy Improved Grey Wolf Optimization Algorithm
4.1. The Primary Theory of Grey Wolf Optimization Algorithm
4.2. Multi-Strategy Improved Grey Wolf Optimization Algorithm
4.2.1. Sobol-Sequence Initialization Population Strategy
4.2.2. Exponential Rule Convergence-Factor Adjustment Strategy
4.2.3. Adaptive Location-Update Strategy
4.2.4. Cauchy–Gaussian Hybrid Mutation Strategy
4.3. Improved Performance Test of Grey Wolf Optimization Algorithm
4.3.1. Comparison Experiment between MSGWO and Standard Optimization Algorithm
4.3.2. Comparison Experiment between MSGWO and Improved Optimization Algorithm
4.3.3. Wilcoxon Rank Sum Test
4.3.4. Population Diversity Analysis of MSGWO
5. Bearing Fault Detection
5.1. Parameter Adaptive Multistable Stochastic Resonance Strategy
5.2. CWRU Bearing Data Set
5.3. MFPT Bearing Data Set
5.4. Bearing-Fault Diagnosis of Crystal Growing Furnace
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Function | Dim | Range | Optima |
---|---|---|---|
30 | [−100, 100] | 0 | |
30 | [−10, 10] | 0 | |
30 | [−100, 100] | 0 | |
30 | [−100, 100] | 0 | |
30 | [−30, 30] | 0 | |
30 | [−100, 100] | 0 | |
30 | [−1.28, 1.28] | 0 | |
30 | [−500, 500] | −418.98 × Dimn | |
30 | [−5.12, 5.12] | 0 | |
30 | [−32, 32] | 0 | |
30 | [−600, 600] | 0 | |
30 | [−50, 50] | 0 | |
30 | [−50, 50] | 0 | |
2 | [−65, 65] | 1 | |
4 | [−5, 5] | 0.1484 |
F | Index | WOA | GWO | BOA | GSA | PSO | ABC | MSGWO |
---|---|---|---|---|---|---|---|---|
F1 | mean | 4.97 × 10−74 | 1.04 × 10−27 | 4.06 × 10−4 | 98.91 | 11.65 | 3.54 | 0 |
std | 2.49 × 10−73 | 1.37 × 10−27 | 8.97 × 10−5 | 106.42 | 5.28 | 1.26 | 0 | |
F2 | mean | 2.46 × 10−52 | 9.51 × 10−17 | 4.54 × 10−9 | 4.46 | 11.69 | 0.16 | 0 |
std | 5.61 × 10−52 | 7.47 × 10−17 | 1.26 × 10−9 | 4.47 | 3.64 | 0.05 | 0 | |
F3 | mean | 3.87 × 104 | 3.15 × 10−5 | 1.25 × 10−11 | 1.31 × 103 | 7.25 × 102 | 3.37 × 104 | 0 |
std | 1.48 × 104 | 9.68 × 10−5 | 8.97 × 10−13 | 4.14 × 102 | 5.27 × 102 | 5.45 × 103 | 0 | |
F4 | mean | 59.16 | 7.78 × 10−7 | 6.15 × 10−9 | 10.07 | 6.73 | 51.08 | 0 |
std | 23.48 | 8.85 × 10−7 | 4.28 × 10−10 | 1.71 | 1.26 | 5.48 | 0 | |
F5 | mean | 27.90 | 28.44 | 28.94 | 3.26 × 102 | 1.87 × 103 | 1.40 × 105 | 27.08 |
std | 0.48 | 0.82 | 0.03 | 2.51 × 102 | 1.15 × 103 | 6.78 × 104 | 0.42 | |
F6 | mean | 0.42 | 0.90 | 5.75 | 52.25 | 9.89 | 3.96 | 0.35 |
std | 0.48 | 0.38 | 0.72 | 60.45 | 3.57 | 0.98 | 0.54 | |
F7 | mean | 2.54 × 103 | 2.07 × 103 | 1.39 × 103 | 1.36 | 0.68 | 0.25 | 6.58 × 10−5 |
std | 2.30 × 10−3 | 7.10 × 10−4 | 7.65 × 10−4 | 2.63 | 0.33 | 0.08 | 6.62 × 10−5 | |
F8 | mean | −1.04 × 104 | −5.70 × 103 | −3.77 × 104 | −2.48 × 103 | −2.22 × 103 | −4.98 × 103 | −5.47 × 1058 |
std | 1.73 × 103 | 1.18 × 103 | 3.80 × 102 | 5.29 × 102 | 5.89 × 102 | 3.55 × 102 | 1.81 × 1059 | |
F9 | mean | 0.15 | 3.63 | 6.72 | 38.94 | 92.15 | 2.33 × 102 | 0 |
std | 0.83 | 4.07 | 36.10 | 10.12 | 16.83 | 15.05 | 0 | |
F10 | mean | 5.51 × 10−15 | 1.03 × 10−13 | 5.81 × 10−9 | 0.55 | 5.43 | 1.89 | 8.88 × 10−16 |
std | 2.77 × 10−15 | 2.23 × 10−14 | 7.12 × 10−10 | 0.61 | 1.18 | 0.57 | 0 | |
F11 | mean | 0.03 | 3.02 × 10−3 | 5.22 × 10−12 | 1.01 × 103 | 0.45 | 1.02 | 0 |
std | 0.09 | 5.70 × 10−3 | 2.40 × 10−12 | 11.85 | 0.12 | 0.03 | 0 | |
F12 | mean | 0.05 | 0.07 | 0.66 | 3.12 | 4.40 | 17.54 | 0.05 |
std | 0.13 | 0.27 | 0.16 | 1.10 | 1.98 | 8.64 | 0.10 | |
F13 | mean | 0.51 | 0.71 | 2.91 | 27.43 | 22.29 | 1.49 × 104 | 0.43 |
std | 0.29 | 0.24 | 0.18 | 10.75 | 16.15 | 2.36 × 104 | 0.14 | |
F14 | mean | 2.90 | 4.53 | 1.68 | 6.66 | 2.05 | 1.69 | 1.55 |
std | 3.20 | 4.03 | 0.94 | 4.61 | 1.63 | 0 | 0.70 | |
F15 | mean | 6.13 × 10−4 | 2.47 × 10−3 | 4.39 × 10−4 | 1.17 × 10−2 | 6.15 × 10−4 | 7.04 × 10−4 | 3.46 × 10−4 |
std | 3.04 × 10−4 | 6.00 × 10−3 | 1.73 × 10−4 | 6.30 × 10−3 | 4.65 × 10−4 | 5.80 × 10−4 | 1.69 × 10−4 |
F | Index | GWO | MEGWO | mGWO | IGWO | MPSO | MSGWO |
---|---|---|---|---|---|---|---|
F1 | mean | 1.04 × 10−27 | 4.30 × 10−64 | 1.04 × 10−18 | 1.33 × 10−209 | 2.61 × 10−26 | 0 |
std | 1.37 × 10−27 | 2.09 × 10−63 | 2.97 × 10−18 | 0 | 1.12 × 10−25 | 0 | |
F2 | mean | 9.50 × 10−17 | 1.70 × 10−43 | 2.65 × 10−12 | 6.12 × 10−21 | 1.40 × 10−16 | 0 |
std | 6.40 × 10−17 | 5.77 × 10−43 | 1.99 × 10−12 | 6.67 × 10−21 | 2.86 × 10−16 | 0 | |
F3 | mean | 3.15 × 10−5 | 0.23 | 0.68 | 2.73 × 10−5 | 9.63 × 102 | 0 |
std | 9.68 × 10−5 | 0.48 | 0.81 | 9.57 × 10−5 | 4.81 × 102 | 0 | |
F4 | mean | 7.78 × 10−7 | 2.06 × 10−5 | 0.68 | 2.93 × 10−7 | 2.05 × 10−10 | 0 |
std | 8.85 × 10−7 | 5.68 × 10−5 | 0.85 | 1.78 × 10−7 | 4.81 × 10−10 | 0 | |
F5 | mean | 28.44 | 27.94 | 27.92 | 27.64 | 88.91 | 27.08 |
std | 0.82 | 9.97 | 0.58 | 0.32 | 1.89 × 102 | 0.42 | |
F6 | mean | 0.90 | 0.49 | 0.41 | 0.43 | 0.41 | 0.36 |
std | 0.38 | 1.14 | 0.25 | 0.19 | 0.22 | 0.54 | |
F7 | mean | 2.07 × 10−3 | 1.01 × 10−3 | 4.68 × 10−3 | 2.80 × 10−3 | 1.68 × 10−3 | 6.58 × 10−5 |
std | 7.10 × 10−4 | 9.10 × 10−4 | 1.90 × 10−3 | 1.10 × 10−3 | 8.87 × 10−4 | 6.62 × 10−5 | |
F8 | mean | −5.70 × 103 | −1.26 × 104 | −5.33 × 103 | −8.28 × 103 | −8.12 × 103 | −5.47× 1058 |
std | 1.18 × 103 | 2.15× 10−12 | 1.11 × 103 | 1.69 × 103 | 1.12 × 103 | 1.81 × 1059 | |
F9 | mean | 3.63 | 0 | 37.94 | 27.09 | 23.92 | 0 |
std | 4.07 | 0 | 30.01 | 22.81 | 22.64 | 0 | |
F10 | mean | 1.03 × 10−13 | 5.27 × 10−15 | 1.26 × 10−10 | 6.25 × 10−14 | 6.22 × 10−15 | 8.88× 10−16 |
std | 2.23 × 10−14 | 1.50 × 10−15 | 9.69 × 10−11 | 8.96 × 10−15 | 7.38 × 10−15 | 0 | |
F11 | mean | 3.02 × 10−3 | 0 | 3.83 × 10−3 | 3.37 × 10−3 | 0 | 0 |
std | 5.70 × 10−3 | 0 | 9.40 × 10−3 | 6.00 × 10−3 | 0 | 0 | |
F12 | mean | 0.07 | 0.05 | 0.05 | 6.58 × 10−2 | 0.42 | 0.05 |
std | 0.27 | 0.56 | 0.04 | 2.00 × 10−3 | 0.73 | 0.10 | |
F13 | mean | 0.71 | 0.46 | 0.63 | 0.66 | 0.45 | 0.43 |
std | 0.24 | 0.15 | 0.22 | 0.16 | 0.25 | 0.13 | |
F14 | mean | 4.53 | 1.78 | 2.00 | 1.70 | 1.99 | 1.55 |
std | 4.03 | 2.91 | 2.76 | 0.76 | 0.36 | 0.71 | |
F15 | mean | 2.47 × 10−3 | 3.07 × 10−4 | 1.04 × 10−3 | 8.62 × 10−4 | 5.68 × 10−4 | 3.46 × 10−4 |
std | 6.00 × 10−3 | 3.42 × 10−15 | 3.60 × 10−3 | 3.00 × 10−3 | 3.36 × 10−4 | 1.69 × 10−4 |
F | Index | MSGWO–WOA | MSGWO–GWO | MSGWO–BOA | MSGWO–GSA | MSGWO–PSO | MSGWO–ABC |
---|---|---|---|---|---|---|---|
F1 | P | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
R | + | + | + | + | + | + | |
F2 | P | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
R | + | + | + | + | + | + | |
F3 | P | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
R | + | + | + | + | + | + | |
F4 | P | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
R | + | + | + | + | + | + | |
F5 | P | 1.06 × 10−4 | 2.88 × 10−6 | 1.73 × 10−6 | 1.92 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
R | + | + | + | + | + | + | |
F6 | P | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 7.69 × 10−6 | 1.73 × 10−6 | 9.37 × 10−3 |
R | + | + | + | + | + | + | |
F7 | P | 2.13 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
R | + | + | + | + | + | + | |
F8 | P | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
R | + | + | + | + | + | + | |
F9 | P | 1.73 × 10−6 | 2.53 × 10−6 | 1.82 × 10−5 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
R | + | + | + | + | + | + | |
F10 | P | 2.57 × 10−6 | 1.61 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
R | + | + | + | + | + | + | |
F11 | P | 2.57 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
R | + | + | + | + | + | + | |
F12 | P | 1.73 × 10−6 | 1.73 × 10−6 | 1.97 × 10−5 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
R | + | + | + | + | + | + | |
F13 | P | 1.73 × 10−6 | 1.73 × 10−6 | 0.0021 | 1.73 × 10−6 | 1.92 × 10−6 | 0.0047 |
R | + | + | + | + | + | + | |
F14 | P | 1.73 × 10−6 | 1.73 × 10−6 | 4.45 × 10−5 | 4.86 × 10−5 | 1.92 × 10−6 | 0.0023 |
R | + | + | + | + | + | + | |
F15 | P | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
R | + | + | + | + | + | + |
F | Index | MSGWO–GWO | MSGWO–MEGWO | MSGWO–mGWO | MSGWO–IGWO | MSGWO–MPSO |
---|---|---|---|---|---|---|
F1 | P | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
R | + | + | + | + | + | |
F2 | P | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
R | + | + | + | + | + | |
F3 | P | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
R | + | + | + | + | + | |
F4 | P | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
R | + | + | + | + | + | |
F5 | P | 2.88 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.92 × 10−3 |
R | + | + | + | + | + | |
F6 | P | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 9.37 × 10−3 | 1.73 × 10−6 |
R | + | + | + | + | + | |
F7 | P | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
R | + | + | + | + | + | |
F8 | P | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
R | + | + | + | + | + | |
F9 | P | 2.53 × 10−6 | 0.012 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
R | + | = | + | + | + | |
F10 | P | 1.61 × 10−6 | 3.99 × 10−7 | 1.73 × 10−6 | 1.47 × 10−6 | 1.01 × 10−7 |
R | + | + | + | + | + | |
F11 | P | 1.73 × 10−6 | 0.012 | 1.22 × 10−4 | 7.8 × 10−3 | 0.012 |
R | + | = | + | + | = | |
F12 | P | 1.73 × 10−6 | 0.012 | 1.22 × 10−4 | 1.73 × 10−6 | 2.9 × 10−3 |
R | + | = | = | + | + | |
F13 | P | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
R | + | + | + | + | + | |
F14 | P | 1.73 × 10−6 | 3.59 × 10−4 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
R | + | + | + | + | + | |
F15 | P | 1.73 × 10−6 | 1.73 × 10−6 | 1.7 × 10−3 | 3.11 × 10−5 | 1.73 × 10−6 |
R | + | + | + | + | + |
GWO | IGWO | MEGWO | mGWO | MPSO | MSGWO | |
---|---|---|---|---|---|---|
a | 0.077 | 0.080 | 0.065 | 0.101 | 0.055 | 0.033 |
b | 4.197 | 6.581 | 6.305 | 6.571 | 8.418 | 0.567 |
c | 7.206 | 2.830 | 6.028 | 7.417 | 6.160 | 0.082 |
h | 0.755 | 0.888 | 0.792 | 0.757 | 0.763 | 0.086 |
Time | 15.37 | 14.24 | 15.25 | 15.92 | 10.58 | 14.72 |
SNR | −28.35 | −28.51 | −28.27 | −28.37 | −28.32 | −26.92 |
GWO | IGWO | MEGWO | mGWO | MPSO | MSGWO | |
---|---|---|---|---|---|---|
a | 0.500 | 0.495 | 0.500 | 0.472 | 0.052 | 0.500 |
b | 10.00 | 2.173 | 8.554 | 8.247 | 8.968 | 9.571 |
c | 0.025 | 0.488 | 0.054 | 3.728 | 1.287 | 0.019 |
h | 0.328 | 0.185 | 0.257 | 0.069 | 0.122 | 0.409 |
Time | 21.51 | 25.35 | 35.52 | 34.79 | 22.91 | 19.95 |
SNR | −26.56 | −27.75 | −26.82 | −27.21 | −27.62 | −26.42 |
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Huang, W.; Zhang, G. Bearing Fault-Detection Method Based on Improved Grey Wolf Algorithm to Optimize Parameters of Multistable Stochastic Resonance. Sensors 2023, 23, 6529. https://doi.org/10.3390/s23146529
Huang W, Zhang G. Bearing Fault-Detection Method Based on Improved Grey Wolf Algorithm to Optimize Parameters of Multistable Stochastic Resonance. Sensors. 2023; 23(14):6529. https://doi.org/10.3390/s23146529
Chicago/Turabian StyleHuang, Weichao, and Ganggang Zhang. 2023. "Bearing Fault-Detection Method Based on Improved Grey Wolf Algorithm to Optimize Parameters of Multistable Stochastic Resonance" Sensors 23, no. 14: 6529. https://doi.org/10.3390/s23146529