Research on Mechanical Fault Prediction Method Based on Multifeature Fusion of Vibration Sensing Data
Abstract
1. Introduction
2. Multifeature Fusion Model Based on Vibration Sensing Data
3. Feature Extraction Method Based on Vibration Sensing Data
4. Feature-Level Fusion Based on the Use of a PSO-ANN
4.1. Artificial Neural Network and the Strategy to Obtain the Optimal Eigenvalues Combination
4.2. Optimization Principle Using the Particle Swarm Optimization Algorithm
4.3. Algorithm Principle of Feature-Level Fusion Using a PSO-ANN
Algorithm 1: PSO-ANN algorithm. |
Input: All the eigenvalues of the optimal feature combination. |
Output: The best position of the particle swarm Gbest, and the best prediction accuracy. |
01: Set the parameters {n,, , , , } 02: for i = 1 to n do /* n is the number of particles */ 03: Initialize = (), = (), 04: end for 05: Acquire training set , and test set , 06: Set the particle with best to be 07: for k = 1 do 08: Update with Equation (3) 09: Update , with Equation (4) 10: for i = 1 to n do 11: ann_model(learning_rate = , hidden_layer_ neurons = , 12: momentum_parameter = , rmsprop_parameter = ) 13: .fit(, ) /* Training ANN model */ 14: = .loss_value 15: = .score(, ) 16: if ( > fitness().loss_value and 17: < fitness().prediction_accuracy) then 18: 19: end if 20: if ( > fitness().loss_value and 21: < fitness().prediction_accuracy) then 22: 23: end if 24: for j = 1 to 4 do 25: 26: 27: end for 28: end for 29: end for |
5. Decision-Level Fusion Based on Multiple PSO-ANN Models and Dempster-Shafer Evidence Theory
5.1. Running Process of a PSO-ANN-DS
5.2. Algorithm Principle of Decision-Level Fusion Using a PSO-ANN-DS
Algorithm 2: PSO-ANN-DS algorithm. |
Input: Four single eigenvalues, and fault data with high levels of uncertainty. |
Output: Decision-level fusion result Fus(m). |
01: /* Step 1 */ 02: Train_data = {STD, Peak, RMSEE, Skewness} /* Four single eigenvalues */ 03: for i = 1 to 4 do 04: = PSO-ANN_algorithm(Input = Train_data [i]) 05: PRE[i] = (test_data = fault data with high 06: uncertainty). prediction_accuracy 07: end for 08: /* Step 2 */ 09: for i = 1 to 4 do 10: CRD[i] = PRE[i] / sum(PRE) 11: end for 12: /* Step 3 */ 13: for i = 1 to 4 do 14: MUN[i] = Calculate the value with Equation (8) and (9) 15: end for 16: /* Step 4 */ 17: for i = 1 to 4 do 18: MCRD[i] = CRD[i] * MUN[i] 19: end for 20: /* Step 5 */ 21: for i = 1 to 4 do 22: NMCRD[i] = MCRD[i] / sum(MCRD) 23: end for 24: /* Step 6 */ 25: for j = 1 to J do /* J is the number of fault types */ 26: WAE[j] = 0 27: for i = 1 to 4 do 28: WAE[j] = WAE[j] + NMCRD[i] * .prediction_result(fault_type = j) 29: end for 30: end for 31: /* Step 7 */ 32: Fus(m) = WAE 33: for i = 1 to 3 do /* There are 4 single features, which need to be merged 3 times. */ 34: Fus(m) = Fus(m) WAE /* refers to the DS fusion rule */ 35: end for |
6. Bearing Fault Prediction Experiment Based on Vibration Sensing Data
6.1. Introduction to Data Set and Experimental Environment
6.2. Using an ANN to Get Optimal Feature Combination
6.3. Feature-Level Fusion Fault Prediction Experiment Based on a PSO-ANN
6.4. Decision-Level Fusion Fault Prediction Experiment Based on PSO-ANN-DS
6.5. Comparison and Analysis of Fault Prediction Accuracy of Various Models
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Serial Number | Feature Name | Formula |
---|---|---|
1 | Root mean square (RMS) | |
2 | Standard deviation (STD) | |
3 | Peak | |
4 | Root mean square entropy estimator (RMSEE) | |
5 | Waveform entropy (WFE) | |
6 | Kurtosis | |
7 | Skewness | |
8 | Crest factor (CRF) | |
9 | Impulse factor (IMF) |
Noise Location | Reason | Explanation |
---|---|---|
Mechanical equipment | Eddy noise | Increased external air velocity causes eddies around machinery. |
Rotating noise | The vibration force of rotating machinery deviates easily from the normal value when encountering strong air flow. | |
Energy shortage | Energy issues (for example, oil level below average) cause large levels of noise pollution. | |
Impact noise | Large levels of noise pollution caused by impacts. | |
Other reasons | Suddenly increasing the operating power of mechanical equipment, manual operation of mechanical equipment. | |
Vibration sensor | Temperature factor | In general, the higher the temperature, the greater the measurement error. |
Resonant frequency | The closer the vibration frequency of the machine is to the value of the resonance frequency, the greater the measurement error. | |
Placement deviation | Vibration sensors generally get acceleration sensing data in three directions. The larger the deviation in the placement direction, the greater the measurement error. | |
Original error | Different types of vibration sensors have different original errors. | |
Other environmental factors | Under the condition of a strong electrostatic field, alternating magnetic field, or nuclear radiation, the measurement error may become larger. |
Fault Type | File Name |
---|---|
Normal Baseline Data | 98.mat |
48K Drive End Bearing Fault Data (Inner Race) | 110.mat |
48K Drive End Bearing Fault Data (Ball) | 123.mat |
48K Drive End Bearing Fault Data (Outer Race Orthogonal@3:00) | 149.mat |
48K Drive End Bearing Fault Data (Outer Race Centered@6:00) | 136.mat |
48K Drive End Bearing Fault Data (Outer Race Opposite@12:00) | 162.mat |
Eigenvalue | Sliding Window Size | |||||||
---|---|---|---|---|---|---|---|---|
120 | 240 | 360 | 480 | 600 | 720 | 840 | 960 | |
RMS | 31.67% | 52.11% | 77.22% | 86.11% | 88.67% | 88.11% | 91.33% | 91.89% |
STD | 30.11% | 52.11% | 76.78% | 85.89% | 88.44% | 88.00% | 91.22% | 91.78% |
Peak | 30.67% | 41.89% | 63.67% | 73.22% | 76.89% | 79.00% | 81.56% | 80.44% |
RMSEE | 23.89% | 41.78% | 46.22% | 52.33% | 53.78% | 55.44% | 56.78% | 52.78% |
WFE | 1.11% | 7.22% | 7.22% | 20.22% | 24.11% | 27.22% | 39.78% | 46.44% |
Kurtosis | 2.67% | 9.67% | 20.78% | 23.44% | 12.33% | 12.11% | 29.56% | 31.00% |
Skewness | 1.78% | 6.56% | 15.11% | 20.11% | 23.11% | 22.89% | 22.11% | 23.78% |
CRF | 0.44% | 2.89% | 1.56% | 3.56% | 10.22% | 10.67% | 10.56% | 14.22% |
IMF | 1.89% | 6.89% | 8.89% | 21.33% | 12.78% | 12.22% | 10.33% | 12.22% |
All | 48.33% | 73.00% | 86.11% | 92.33% | 94.33% | 95.78% | 97.22% | 97.89% |
Eigenvalue | RMS | STD | Peak | RMSEE | WFE | Kurtosis | Skewness | CRF | IMF |
---|---|---|---|---|---|---|---|---|---|
RMS | 79.67% | 79.00% | 80.33% | 82.78% | 83.89% | 85.11% | 86.33% | 86.11% | |
STD | 79.67% | 79.00% | 80.33% | 82.78% | 83.89% | 84.67% | 86.33% | 86.00% | |
Peak | 79.22% | 79.44% | 80.00% | 82.89% | 83.89% | 84.56% | 85.67% | 85.11% | |
RMSEE | 79.67% | 81.33% | 79.78% | 82.89% | 83.78% | 85.33% | 86.00% | 86.22% | |
WFE | 81.78% | 82.33% | 83.11% | 83.22% | 84.00% | 84.33% | 85.44% | 86.00% | |
Kurtosis | 82.44% | 84.11% | 82.89% | 83.00% | 84.00% | 83.89% | 85.00% | 85.56% | |
Skewness | 82.22% | 82.56% | 83.22% | 83.44% | 84.44% | 84.44% | 85.44% | 85.00% | |
CRF | 81.33% | 80.44% | 81.11% | 81.44% | 82.33% | 84.89% | 85.33% | 85.00% | |
IMF | 82.33% | 83.67% | 82.11% | 82.44% | 83.00% | 83.89% | 84.78% | 86.22% |
Sliding Window Size | Optimal Feature Combination | Accuracy | |
---|---|---|---|
All | Optimal Combination | ||
120 | {Kurtosis,RMS,STD,Peak,RMSEE,WFE,Skewness,CRF} | 48.33% | 50.44% |
240 | {RMS,STD,Peak,RMSEE,WFE,Kurtosis,Skewness,CRF,IMF} | 73.00% | 73.00% |
360 | {RMS,STD,Peak,RMSEE,WFE,Kurtosis,Skewness,CRF} | 86.11% | 86.33% |
480 | {WFE,RMS,STD,Peak,RMSEE,Kurtosis,Skewness,CRF,IMF} | 92.33% | 93.00% |
600 | {RMS, STD,Peak,RMSEE,WFE,Kurtosis,Skewness,CRF,IMF} | 94.33% | 94.33% |
720 | {IMF,RMS,STD,Peak,RMSEE,WFE,Kurtosis,Skewness} | 95.78% | 96.44% |
840 | {Skewness,RMS,STD,Peak,RMSEE,WFE,Kurtosis,CRF,IMF} | 97.22% | 97.67% |
960 | {RMS,STD,Peak,RMSEE,WFE,Kurtosis,Skewness,CRF,IMF} | 97.89% | 97.89% |
Parameter | Range Interval/Value |
---|---|
Number of hidden layers | 1 |
Number of hidden layer units | [10, 100] |
Learning rate | [0.0001, 0.1] |
Momentum parameter | [0.001, 0.999] |
RMSprop parameter | [0.001, 0.999] |
Number of Particles | Learning Rate | Momentum Parameter | RMSprop Parameter | Number of Hidden Layer Neurons | Loss Value | Accuracy |
---|---|---|---|---|---|---|
10 | 0.021404 | 0.999 | 0.999 | 100 | 0.372830 | 89.22% |
20 | 0.007614 | 0.609325 | 0.658986 | 58 | 0.479214 | 89.44% |
30 | 0.006649 | 0.573852 | 0.966601 | 81 | 0.464076 | 89.89% |
40 | 0.008156 | 0.467269 | 0.989776 | 77 | 0.467528 | 89.22% |
50 | 0.014367 | 0.998993 | 0.999 | 90 | 0.347928 | 90.11% |
60 | 0.010740 | 0.999 | 0.999 | 81 | 0.349434 | 89.67% |
Eigenvalue | Sliding Window Size | |||||||
---|---|---|---|---|---|---|---|---|
120 | 240 | 360 | 480 | 600 | 720 | 840 | 960 | |
RMS | 40.00% | 58.89% | 78.33% | 87.11% | 89.22% | 88.78% | 91.56% | 92.00% |
STD | 41.22% | 64.22% | 78.00% | 86.44% | 89.22% | 88.56% | 91.78% | 92.11% |
Peak | 42.67% | 58.11% | 68.00% | 76.33% | 77.44% | 81.11% | 82.22% | 81.78% |
RMSEE | 33.00% | 47.67% | 59.44% | 62.44% | 70.89% | 70.89% | 72.44% | 75.33% |
WFE | 7.33% | 10.67% | 20.56% | 30.33% | 32.33% | 42.56% | 47.44% | 49.89% |
Kurtosis | 5.89% | 11.44% | 24.33% | 25.67% | 21.00% | 23.11% | 41.44% | 47.00% |
Skewness | 3.22% | 11.44% | 19.78% | 20.44% | 23.56% | 24.11% | 23.56% | 30.22% |
CRF | 1.11% | 4.89% | 7.89% | 20.11% | 21.78% | 11.44% | 12.56% | 15.67% |
IMF | 4.11% | 10.33% | 20.00% | 23.89% | 14.78% | 14.22% | 34.78% | 32.56% |
All | 54.67% | 78.44% | 90.11% | 93.11% | 96.22% | 97.22% | 97.89% | 98.67% |
PSO-ANN Model | Fault Type | |||||
---|---|---|---|---|---|---|
Normal State | Inner Race Fault | Rolling Element Fault | Outer Race Orthogonal@3:00 Fault | Outer Race Centered@6:00 Fault | Outer Race Opposite@12:00 Fault | |
STD | 0 | 0.2979 | 0.0053 | 0.1500 | 0.2961 | 0.2507 |
Peak | 0 | 0.267 | 0.0608 | 0.1630 | 0.2214 | 0.2878 |
RMSEE | 0 | 0.2763 | 0.0846 | 0.1170 | 0.2759 | 0.2462 |
Skewness | 0.0926 | 0.0674 | 0.1257 | 0.2928 | 0.227 | 0.1945 |
Parameter Name | PSO-ANN Trained by a Single Feature | |||
---|---|---|---|---|
STD | Peak | RMSEE | Skewness | |
PRE | 0.2941 | 0.2623 | 0.2672 | 0.1789 |
CRD | 0.2934 | 0.2616 | 0.2665 | 0.1785 |
MUN | 7.3255 | 8.8422 | 8.9058 | 11.2462 |
MCRD | 2.1493 | 2.3132 | 2.3734 | 2.0073 |
NMCRD | 0.243 | 0.2616 | 0.2684 | 0.227 |
Fusion Times of DS | Fault Type | |||||
---|---|---|---|---|---|---|
Normal State | Inner Race Fault | Rolling Element Fault | Outer Race Orthogonal@3:00 Fault | Outer Race Centered@6:00 Fault | Outer Race Opposite@12:00 Fault | |
0 | 0.021 | 0.2317 | 0.0684 | 0.1769 | 0.2555 | 0.2465 |
1 | 0.002 | 0.2484 | 0.0217 | 0.1448 | 0.302 | 0.2811 |
2 | 0.0001 | 0.249 | 0.0065 | 0.1109 | 0.3338 | 0.2997 |
3 | 0 | 0.2435 | 0.0019 | 0.0828 | 0.36 | 0.3118 |
Method | Sliding Window Size | |||||||
---|---|---|---|---|---|---|---|---|
120 | 240 | 360 | 480 | 600 | 720 | 840 | 960 | |
Basic DS | 67.89% | 82.00% | 92.44% | 95.89% | 97.44% | 97.89% | 98.89% | 98.89% |
Literature [30] | 67.56% | 82.56% | 92.44% | 96.22% | 97.44% | 97.89% | 98.89% | 98.78% |
Literature [31] | 68.44% | 81.78% | 92.33% | 96.22% | 97.44% | 98.00% | 98.78% | 98.89% |
Literature [32] | 68.22% | 81.67% | 92.33% | 96.22% | 97.33% | 98.00% | 98.78% | 98.89% |
We Proposed | 68.33% | 82.67% | 92.44% | 96.44% | 97.44% | 98.22% | 99.00% | 99.00% |
Model | Sliding Window Size | |||||||
---|---|---|---|---|---|---|---|---|
120 | 240 | 360 | 480 | 600 | 720 | 840 | 960 | |
KNN | 57.78% | 74.45% | 84.33% | 90.11% | 93.11% | 94.67% | 95.44% | 96.44% |
Decision tree | 57.22% | 75.44% | 86.89% | 91.44% | 94.00% | 95.67% | 97.11% | 98.22% |
Random forest | 61.89% | 78.00% | 89.33% | 94.00% | 96.44% | 97.33% | 97.78% | 98.44% |
Naive Bayes | 62.11% | 76.33% | 83.67% | 90.56% | 93.78% | 95.00% | 97.44% | 98.11% |
ANN | 50.44% | 73.00% | 86.33% | 93.00% | 94.33% | 96.44% | 97.67% | 97.89% |
SVM | 63.67% | 78.89% | 88.00% | 92.67% | 95.11% | 96.78% | 97.78% | 98.00% |
LSTM | 57.89% | 72.89% | 80.11% | 84.22% | 88.33% | 91.56% | 93.00% | 96.11% |
PSO-ANN | 54.67% | 78.44% | 90.11% | 93.11% | 96.22% | 97.22% | 97.89% | 98.67% |
PSO-ANN-DS | 68.33% | 82.67% | 92.44% | 96.44% | 97.44% | 98.22% | 99.00% | 99.00% |
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Huang, M.; Liu, Z. Research on Mechanical Fault Prediction Method Based on Multifeature Fusion of Vibration Sensing Data. Sensors 2020, 20, 6. https://doi.org/10.3390/s20010006
Huang M, Liu Z. Research on Mechanical Fault Prediction Method Based on Multifeature Fusion of Vibration Sensing Data. Sensors. 2020; 20(1):6. https://doi.org/10.3390/s20010006
Chicago/Turabian StyleHuang, Min, and Zhen Liu. 2020. "Research on Mechanical Fault Prediction Method Based on Multifeature Fusion of Vibration Sensing Data" Sensors 20, no. 1: 6. https://doi.org/10.3390/s20010006
APA StyleHuang, M., & Liu, Z. (2020). Research on Mechanical Fault Prediction Method Based on Multifeature Fusion of Vibration Sensing Data. Sensors, 20(1), 6. https://doi.org/10.3390/s20010006