Multisensor information fusion, when applied to fault diagnosis, the time-space scope, and the quantity of information are expanded compared to what could be acquired by a single sensor, so the diagnostic object can be described more comprehensively. This paper presents a methodology of fault diagnosis in rotating machinery using multisensor information fusion that all the features are calculated using vibration data in time domain to constitute fusional vector and the support vector machine (SVM) is used for classification. The effectiveness of the presented methodology is tested by three case studies: diagnostic of faulty gear, rolling bearing, and identification of rotor crack. For each case study, the sensibilities of the features are analyzed. The results indicate that the peak factor is the most sensitive feature in the twelve time-domain features for identifying gear defect, and the mean, amplitude square, root mean square, root amplitude, and standard deviation are all sensitive for identifying gear, rolling bearing, and rotor crack defect comparatively.
Typical rotating machinery systems such as water turbine, steam turbine, wind turbine, and rotary kiln are critical core equipment support of the important industries of the national economy [
At data-level fusion, all sensor data from a measured object are combined directly and features are then calculated from the fused data. Fusion of data at this level contains most information and can deliver good results. However, the sensors used in this level must be commensurate. That means the measurement has to be the same or has similar physical quantities or phenomena. During the most popular data-level fusion methodology, such as weighted fusion [
This paper proposes a feature-level fusion method for rotating machinery fault diagnosis. Generally, heterogeneous information fusion is executed at feature-level fusion for mechanical condition monitoring and fault diagnosis in the present literature. For example, Barad et al. put forward the development of an ANN based model for condition monitoring of a power turbine that blends parameters belonging to performance, vibration, and lubrication [
The SVM is a machine learning method based on the statistical learning theory and structural risk minimization principle. Given two category sample sets
The dual quadratic optimization description can be obtained by converting the problem with Kuhn-Tucker condition into the equivalent Lagrangian dual problem:
The support vector is the sample which satisfies the equation
In linear inseparable condition, the samples
The optimal classification decision function of linear inseparable samples is obtained using (
The common kernel functions include linear kernel function, poly kernel function, radial basis function (RBF) kernel function, and sigmoid kernel function.
The traditional SVM was originally designed for binary classification problems. However, many practical problems in fault diagnosis field are multiclassification. Now some effective multiclass support vector machines were proposed which include “one-against-one,” “one-against-all,” directed acyclic graph (DAG), and so on [
When the running conditions of the rotating machinery deviate from the normal condition, the time-domain statistical features of the vibration signal will be different from the normal condition. Furthermore, the time-domain statistical features will be also different under different defect models. Therefore, the time-domain statistics contain abundant defect information, and they can be used as sensitive character applied to fault diagnosis of rotating machinery. The time-domain statistical features used in this study are shown in Table
The statistic features in time domain.
Code name | Feature | Equation |
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Mean ( |
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Peak ( |
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Amplitude square ( |
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Root mean square ( |
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Root amplitude ( |
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Standard deviation ( |
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Skewness ( |
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Kurtosis ( |
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Waveform factor (SF) |
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Peak factor (CF) |
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Pulse factor (IF) |
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Margin factor (CIF) |
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The model of multisensor information fusion is used in this study and shown in Figure
The multisensor information fusion process model.
Experiments were performed on the machinery fault simulator (MFS) from SpectraQuest, Inc., shown in Figure
The machinery fault simulator.
The front view
The side view
In the vibration testing experiments for roller bearing fault diagnosis, the simulator is composed of a motor, a coupling, a testing roller bearing fitted on the left of the shaft near the motor, a working roller bearing on the other side, a bearing load, and a shaft. The MFS provides a rolling bearing fault kit consisting of one normal, one inner race defect, one outer race defect, one with ball defect, and one combination of defects for performing experiments and studying bearing fault diagnosis. The acquisition frequency rate is 10 kHz. The sensors layout is depicted schematically in Figure
In the vibration testing experiments for gear fault diagnosis, the drive from the motor transmits to the gearbox through bearing-rotor system and belt. The gearbox consists of a two-stage parallel shaft with rolling bearings, helical gears, and a magnetic brake. The simplified diagram of gearbox transmission is shown in Figure
The simplified diagram of gearbox transmission.
In the vibration testing experiments for rotor crack fault diagnosis, the rotor-bearing system is driven by the motor. In order to simulate the expanding of crack, crack faults were introduced to the test rotor by using the electrodischarge machining. The defect with crack width of 0.12 mm and crack depth of 3 mm represents slight defect, and that with crack width of 0.12 mm and crack depth of 5 mm represents serious defect. The acquisition frequency rate is 10 kHz. The sensors layout is depicted schematically in Figure
Vibration signals of gear with three fault models including normal, chipped tooth, and missing tooth are taken for analysis. A certain time-domain feature is calculated from eight sensors (
LibSVM-mat-2.9 is chosen for SVM calculation. LibSVM is developed by Lin Chih-Jen from Taiwan [
Diagnostic results of gear by using different features for fusion.
Feature | The best parameter | Diagnostic accuracy (%) | ||||
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Normal | Chipped tooth | Missing tooth | All testing samples | |
Mean | 26.5 | 215 | 98 | 82 | 84 | 88.00 |
Peak | 21 | 28 | 98 | 86 | 66 | 83.33 |
Amplitude square | 212 | 20 | 98 | 82 | 88 | 89.33 |
Root mean square | 214 | 23 | 98 | 78 | 86 | 87.33 |
Root amplitude | 211.5 | 211.5 | 100 | 88 | 76 | 88.00 |
Standard deviation | 27.5 | 29.5 | 98 | 78 | 86 | 87.33 |
Skewness | 28 | 2−1 | 98 | 30 | 58 | 62.00 |
Kurtosis | 22.5 | 2−3 | 94 | 68 | 40 | 67.33 |
Waveform factor | 2−1.5 | 29 | 92 | 42 | 30 | 55.33 |
Peak factor | 20.5 | 2−1 | 94 | 92 | 94 | 93.33 |
Pulse factor | 2−0.5 | 2−2 | 96 | 64 | 60 | 73.33 |
Margin factor | 20 | 2−3 | 96 | 57 | 55 | 69.33 |
It can be found from Table
It also can be found from Table
In order to compare with single sensor for gear fault diagnosis, take eight features from a single sensor to constitute an eight-dimensional vector as a fault sample. The eight features are the peak factor, amplitude square, root amplitude, mean, root mean square, standard deviation, peak, and pulse factor, which are the first eight sensitive features for identifying gear defect selected on the basis of the above analysis result. In order to avoid the orders of magnitude difference of different features, normalized eigenvector is processed before inputting SVM. In fact, during the proposed multisensors information analysis, the fault sample is constituted by the same feature from multisensors, so the orders of magnitude difference are nonexistent and normalized eigenvector is not needed. The sensors
Diagnostic results of gear by using different single sensors.
Sensor | The best parameter | Diagnostic accuracy (%) | ||||
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Normal | Chipped tooth | Missing tooth | All testing samples | |
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25.5 | 28 | 40 | 28 | 86 | 51.33 |
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23.5 | 213.5 | 22 | 94 | 100 | 72.00 |
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21 | 24 | 84 | 82 | 76 | 80.67 |
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23 | 28.5 | 54 | 80 | 94 | 76.00 |
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215 | 20.5 | 64 | 90 | 100 | 84.67 |
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213.5 | 26.5 | 92 | 96 | 56 | 81.33 |
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211.5 | 27.5 | 90 | 96 | 64 | 83.33 |
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215 | 24 | 78 | 86 | 58 | 74.00 |
Comparing with Tables
Vibration signals of rolling bearing with four fault models including normal, inner race defect, outer race defect, and ball defect are taken for analysis. A certain time-domain feature is calculated from eight sensors (
LibSVM-mat-2.9 is chosen for SVM calculation. Gaussian kernel function is chosen as kernel function. The cross-validation combination with network search method is used to search the parameters
Diagnostic results of rolling bearing by using different features for fusion.
Feature | The best parameter | Diagnostic accuracy (%) | |||||
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Normal | Inner race defect | Outer race defect | Ball defect | All testing samples | |
Mean | 2−3 | 215 | 100 | 100 | 100 | 100 | 100 |
Peak | 23 | 27 | 94.29 | 94.29 | 100 | 100 | 97.14 |
Amplitude square | 2−3 | 25 | 100 | 100 | 100 | 100 | 100 |
Root mean square | 24.5 | 215 | 100 | 100 | 100 | 100 | 100 |
Root amplitude | 2−2 | 215 | 100 | 100 | 100 | 100 | 100 |
Standard deviation | 24.5 | 215 | 100 | 100 | 100 | 100 | 100 |
Skewness | 22 | 24 | 65.71 | 84.29 | 62.86 | 80 | 73.21 |
Kurtosis | 26 | 2−2 | 90.00 | 72.86 | 82.86 | 97.14 | 85.71 |
Waveform factor | 22 | 29 | 81.43 | 70.00 | 80.00 | 98.57 | 82.50 |
Peak factor | 23 | 2−3 | 64.29 | 64.29 | 78.57 | 95.71 | 75.71 |
Pulse factor | 22 | 2−3 | 71.43 | 64.29 | 81.43 | 95.71 | 78.21 |
Margin factor | 25 | 2−4.5 | 71.43 | 68.57 | 80 | 95.71 | 78.93 |
It can be found from Table
In order to compare with single sensor for rolling bearing fault diagnosis, take eight features from a single sensor to constitute an eight-dimensional vector as a fault sample. The eight features are the mean, amplitude square, root mean square, root amplitude, standard deviation, peak, kurtosis, and waveform factor, which are the first eight sensitive features for identifying rolling bearing defect selected on the basis of the above analysis result. In order to avoid the orders of magnitude difference of different features, normalized eigenvector is processed before inputting SVM. The sensors
Diagnostic results of rolling bearing by using different single sensors.
Sensor | The best parameter | Diagnostic accuracy (%) | |||||
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Normal | Inner race defect | Outer race defect | Ball defect | All testing samples | |
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214.5 | 2−1.5 | 85.56 | 88.89 | 100 | 98.89 | 93.33 |
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211 | 25.5 | 58.89 | 58.89 | 100 | 100 | 79.44 |
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23.5 | 24 | 96.67 | 78.89 | 100 | 98.89 | 93.67 |
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214.5 | 20.5 | 100 | 85.56 | 83.33 | 98.89 | 91.94 |
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22 | 27.5 | 100 | 96.67 | 100 | 100 | 99.17 |
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22 | 27.5 | 97.7 | 96.67 | 100 | 91.11 | 96.39 |
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211 | 23.5 | 98.89 | 90 | 100 | 88.89 | 94.44 |
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210 | 2−1.5 | 61.11 | 51.11 | 53.33 | 87.78 | 63.33 |
Comparing with Tables
Vibration signals of rotor crack with three fault models including normal, crack depth of 3 mm, and crack depth of 5 mm are taken for analysis. A certain time-domain feature is calculated from four sensors (
LibSVM-mat-2.9 is chosen for SVM calculation. Gaussian kernel function is chosen as kernel function. The cross-validation combination with network search method is used to search the parameters
Diagnostic results of rotor crack by using different features for fusion.
Feature | The best parameter | Diagnostic accuracy (%) | ||||
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Normal | Crack depth of 3 mm | Crack depth of 5 mm | All testing samples | |
Mean | 24.5 | 212 | 98 | 94 | 100 | 98.67 |
Peak | 20 | 29.5 | 72 | 86 | 88 | 85.33 |
Amplitude square | 27 | 22 | 100 | 96 | 94 | 96.67 |
Root mean square | 26 | 24 | 100 | 98 | 100 | 99.67 |
Root amplitude | 25.5 | 23 | 100 | 92 | 100 | 97.33 |
Standard deviation | 24 | 28 | 98 | 96 | 98 | 98.67 |
Skewness | 25 | 2−2 | 58 | 44 | 46 | 58.00 |
Kurtosis | 23.5 | 2−1 | 44 | 74 | 84 | 71.00 |
Waveform factor | 22 | 23 | 34 | 80 | 84 | 72.33 |
Peak factor | 22.5 | 2−1.5 | 42 | 46 | 62 | 69.33 |
Pulse factor | 2−3 | 2−1 | 28 | 74 | 76 | 64.00 |
Margin factor | 21 | 2−3 | 32 | 72 | 74 | 64.67 |
It can be found from Table
In this paper, a feature-level information fusion methodology is proposed that all the features are calculated using vibration data in time domain to constitute fusional vector and the SVM is used for classification. Only a vibration testing system is needed for raw signal collected in this method, so the process is simpler. The effectiveness of the proposed methodology is tested with examples of gear, rolling bearing, and rotor crack fault diagnosis. Sensitivities of the twelve time-domain features are discussed in each case study. The analyzed results indicate that the peak factor is the most sensitive feature in the twelve time-domain features for identifying gear defect, but it is not very sensitive for identifying rolling bearing and rotor crack defect. The mean, amplitude square, root mean square, root amplitude, and standard deviation are all sensitive for identifying gear, rolling bearing, and rotor crack defect comparatively.
The features used and discussed in this paper are all in time domain; however, features in frequency domain also can be used for fault diagnosis of rotating machinery and the sensibilities of the features for identifying rolling bearing, gear, and rotor defect are also worth studying in the future.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is supported by the National Natural Science Foundation of China (51105138 and 51175169), the National High Technology Research and Development Program Items (2012AA041805), the Pre-research Project (813040302), the CEEUSRO special plan of Hunan province (2010XK6066), and the Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan province.