Bearing Fault Diagnosis Method Based on Improved Singular Value Decomposition Package
<p>Schematic diagram of SVDP.</p> "> Figure 2
<p>Schematic diagram of ESVDP and FESVDP (the red subcomponents).</p> "> Figure 3
<p>Schematic diagram of ISVDP.</p> "> Figure 4
<p>Flowchart of ISVDP on bearing fault diagnosis.</p> "> Figure 5
<p>The simulated signal: (<b>a</b>) harmonic interference; (<b>b</b>) impulse responses excited by defects in the bearing; (<b>c</b>) the synthesis signal.</p> "> Figure 6
<p>The simulated signal: (<b>a</b>) frequency spectrum; (<b>b</b>) envelope spectrum.</p> "> Figure 7
<p>Decomposition results of SVDP with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>: (<b>a</b>–<b>f</b>) time–frequency diagram of 1st to 6th subcomponents, respectively.</p> "> Figure 8
<p>Decomposition results of FESVDP with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>: (<b>a</b>–<b>f</b>) time–frequency diagram of 1st to 6th subcomponents, respectively.</p> "> Figure 9
<p>Decomposition results of EMD with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math>: (<b>a</b>–<b>f</b>) time–frequency diagram of 1st to 6th subcomponents, respectively.</p> "> Figure 10
<p>Decomposition results of VMD with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math>: (<b>a</b>–<b>d</b>) time–frequency diagram of 1st to 4th subcomponents, respectively.</p> "> Figure 11
<p>Decomposition results of ISVDP with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>: (<b>a</b>–<b>f</b>) time–frequency diagram of 1st to 6th subcomponents, respectively.</p> "> Figure 12
<p>Decomposition results of SVDP with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>: (<b>a</b>–<b>f</b>) envelop of 1st to 6th subcomponents, respectively.</p> "> Figure 13
<p>Decomposition results of FESVDP with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>: (<b>a</b>–<b>f</b>) envelop of 1st to 6th subcomponents, respectively.</p> "> Figure 14
<p>Decomposition results of EMD with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math>: (<b>a</b>–<b>f</b>) envelop of 1st to 6th subcomponents, respectively.</p> "> Figure 15
<p>Decomposition results of VMD with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math>: (<b>a</b>–<b>d</b>) envelop of 1st to 4th subcomponents, respectively.</p> "> Figure 16
<p>Decomposition results of ISVDP with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>: (<b>a</b>–<b>f</b>) envelop of 1st to 6th subcomponents, respectively.</p> "> Figure 17
<p>The Waveform of Composite Signal.</p> "> Figure 18
<p>The Envelope Diagram of Composite Signal.</p> "> Figure 19
<p>Decomposition results of SVDP with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>: (<b>a</b>–<b>f</b>) time–frequency diagram of 1st to 6th subcomponents, respectively.</p> "> Figure 20
<p>Decomposition results of FESVDP with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>: (<b>a</b>–<b>f</b>) time–frequency diagram of 1st to 6th subcomponents, respectively.</p> "> Figure 21
<p>Decomposition results of EMD with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math>: (<b>a</b>–<b>d</b>) time–frequency diagram of 1st to 4th subcomponents, respectively.</p> "> Figure 22
<p>Decomposition results of VMD with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math>: (<b>a</b>–<b>d</b>) time–frequency diagram of 1st to 4th subcomponents, respectively.</p> "> Figure 23
<p>Decomposition results of ISVDP with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>: (<b>a</b>–<b>f</b>) time–frequency diagram of 1st to 6th subcomponents, respectively.</p> "> Figure 24
<p>Decomposition results of SVDP with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>: (<b>a</b>–<b>f</b>) envelop of 1st to 6th subcomponents, respectively.</p> "> Figure 25
<p>Decomposition results of FESVDP with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>: (<b>a</b>–<b>f</b>) envelop of 1st to 6th subcomponents, respectively.</p> "> Figure 26
<p>Decomposition results of EMD with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math>: (<b>a</b>–<b>d</b>) envelop of 1st to 4th subcomponents, respectively.</p> "> Figure 27
<p>Decomposition results of VMD with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math>: (<b>a</b>–<b>d</b>) envelop of 1st to 4th subcomponents, respectively.</p> "> Figure 28
<p>Decomposition results of ISVDP with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>: (<b>a</b>–<b>f</b>) envelop of 1st to 6th subcomponents, respectively.</p> ">
Abstract
:1. Introduction
2. Singular Value Decomposition Package and Other Improved Algorithms
2.1. Singular Value Decomposition Package and Other Improved Algorithms
2.2. Extended Singular Value Decomposition Package
3. Improved Singular Value Decomposition Package
3.1. The Deficiency of SVDP and ESVDP in Bearing Feature Extraction
3.2. Improved Singular Value Decomposition Package
3.3. Parameter Selection of ISVDP
3.4. Application of ISVDP in Fault Diagnosis
4. Simulation Analysis
4.1. Simulation Parameters
4.2. Results Analysis
5. Experimental Verification
5.1. Data Description
5.2. Test Results and Analysis
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
SVDP | singular value decomposition package |
ISVDP | improved singular value decomposition package |
SVD | singular value decomposition |
MSVD | multi-resolution singular value decomposition |
ESVDP | extended singular value decomposition package |
FESVDP | fast extended singular value decomposition package |
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j | (Hz) | (s) | ||||
---|---|---|---|---|---|---|
1 | 1 | 1000 | 3100 | 0.012 | 167 | 1% |
2 | 5 | 1200 | 1400 | 0.097 | 21 | 0.5% |
3 | 5 | 1200 | 2000 | - | 3 | - |
Status | Fault Size of Samples | Motor Load | Approx. Motor Speed |
---|---|---|---|
Inner Race 1 | 0.1778 (mm) | 0 (HP) | 1797 (rpm) |
Inner Race 2 | 0.7112 (mm) | 3 (HP) | 1730 (rpm) |
Simulation | Experiment | |
---|---|---|
SVDP | 1. Reduce harmonic interference; 2. Extract fault features; 3. Mode mixing | 1. Inner race faults 1 and 2 cannot be separated; 2. Mode mixing |
FESVDP | 1. Reduce harmonic interference; 2. Extract fault features; 3. Mode mixing | 1. Inner race faults 1 and 2 cannot be separated; 2. Mode mixing |
EMD | 1. Harmonic interference exists; 2. Fault features cannot be extracted; 3. Mode mixing | 1. Inner race faults 1 and 2 cannot be separated; 2. Mode mixing |
VMD | 1. Harmonic interference exists; 2. Extract fault features; 3. Mode mixing | 1. Partial separation of inner race faults 1 and 2; 2. Mode mixing |
ISVDP | 1. Reduce harmonic interference; 2. Extract fault features; 3. Restrain modal mixing | 1. Effective separation of inner race faults 1 and 2; 2. Restrain modal mixing |
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Zhu, H.; He, Z.; Xiao, Y.; Wang, J.; Zhou, H. Bearing Fault Diagnosis Method Based on Improved Singular Value Decomposition Package. Sensors 2023, 23, 3759. https://doi.org/10.3390/s23073759
Zhu H, He Z, Xiao Y, Wang J, Zhou H. Bearing Fault Diagnosis Method Based on Improved Singular Value Decomposition Package. Sensors. 2023; 23(7):3759. https://doi.org/10.3390/s23073759
Chicago/Turabian StyleZhu, Huibin, Zhangming He, Yaqi Xiao, Jiongqi Wang, and Haiyin Zhou. 2023. "Bearing Fault Diagnosis Method Based on Improved Singular Value Decomposition Package" Sensors 23, no. 7: 3759. https://doi.org/10.3390/s23073759