16th Mediterranean Conference on Control and Automation Congress Centre, Ajaccio, France June 25-27, 2008
Rolling Element Bearing Feature Extraction and Anomaly Detection Based on Vibration Monitoring Bin Zhang1 , Georgios Georgoulas1 , Marcos Orchard2 , Abhinav Saxena1 , Douglas Brown1 , George Vachtsevanos1 , Steven Liang3 Abstract— In this paper, an anomaly detection structure, in which different types of anomaly detection routines can be applied, is proposed. Bearing fault modes and their effects on the bearing vibration are discussed. Based on this, a feature extraction method is developed to overcome the limitation of time domain features. Experimental data from bearings under different operating conditions are used to verify the proposed method. The results show that the extracted feature has a monotonic decrease trend as the dimension of fault increases. The feature also has the ability to compensate the variation of rotating speed. The proposed structure are verified with three different detection routines, pdf-based, k-nearest neighbor, and particle-filter-based approaches.
track to allow the rolling elements to contact the raceways at a single point. The cage maintains an even and consistent spacing of rolling elements to guide them in the raceways during movement.
I. INTRODUCTION Rolling element bearings are the most essential parts in rotating machinery. The function of bearings is to permit constrained relative rotation or linear motion between two parts. During the operation, the bearings are often subject to high loading and severe conditions. Under this severe operating condition, defects are often developed on the bearing components. If no action is taken, the machine could be seriously damaged. Therefore, it is of prime importance to detect accurately the presence of faults, especially at their early stages, in bearings to prevent the sequent damage and reduce the costly downtime. In the past decades, health monitoring of critical machine bearings has attracted significant research efforts and vibration analysis has been extensively used in the fault detection and localization of bearing [3], [5], [7], [9]–[12]. Being able to measure the vibration signal, the transducers or accelerometers are mounted as close as possible to the bearings that are being monitored. Compared with signals collected from other sensors like acoustic emission or laser, the vibration signals from accelerometers have the advantage of providing a wide dynamic range and wide frequency range [5]. A rolling element bearing is composed of an inner ring, outer ring, rolling elements (balls or rollers), and a cage, as shown in Figure 1. The inner and outer rings have raceways that form a path for rolling elements. The rolling elements rotate along a path between the inner raceway and outer raceway to provide minimal friction for rotational movement. The radii of rolling elements are slightly smaller than the 1. The authors are with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA.
[email protected] 2. M. Orchard is with the Electrical Engineering Department, University of Chile, Santiago, Chile.
[email protected] 3. S. Liang is with the School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA.
978-1-4244-2505-1/08/$20.00 ©2008 IEEE
Fig. 1.
The Structure of a Bearing
The sources of bearing vibration are the external timevarying forces between the components and the transmission mechanism of the machine during the bearing operation [1]– [5]. Even a perfect bearing produces vibration because of the time-varying contact force between bearing components which is caused by the shaft rotating and the change of position of the rolling elements [5]. The bearing itself also acts as an excitation source that produces time-varying forces to induce the machinery vibration. Since the accelerometers are usually mounted on the framework, the collected vibration data also contains machinery vibration. For a healthy bearing without a fault, the contact force between bearing components is continuous. Therefore, the vibration signal shows a regular signature or characteristic, which is the baseline signature. When a defect or fault occurs on the inner/outer raceway or the rolling element, as shown in Figure 2, the interaction between the raceway and rolling elements generate time-varying and non-uniform discontinuous forces that drive vibrations. The bearing defects may be categorized into two broad classes. The first class, denoted as ‘local defects’ [4], includes cracks, pits, spalls on the raceways or rolling elements. As mentioned above, local defects result in discontinuous contact forces that generate a specific signature in the vibration signal. The second class of bearing, denoted as ‘distributed defects’ [4], involves the structure/installation of bearing, such as misaligned races, eccentric races, off-size rolling elements, and out-of-round components. Distributed defects also generate specific signatures in vibration signals and increase the chance of ‘local defects’.
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Fig. 2.
of these features may be used for the detection of a very specific fault mode, it is desirable that most of them undergo significant perturbations in the presence of several different fault scenarios. With this understanding, an anomaly detector is understood as a module that intends to recognize abnormal conditions in the operation of a monitored system. In most real applications, the anomaly detector [14] is required to perform this task while minimizing both the probability of false alarms and the detection time (time between the initiation of a fault and its detection), given a fixed threshold for false positives. A unit of these characteristics involves a comparison between the current condition of the system and the expected operational behavior. In this sense, the availability of historical data is always assumed for purposes of defining an appropriate baseline.
Location of bearing faults
Factors that determine the bearing life include material properties, lubricant properties, bearing size, number of rolling elements, load/speed of bearing, installation, etc [5]. Material fatigue, plastic deformation and unevenly rotation cased by excessive load, wear, and lubrication are common causes of bearing faults, in which poor lubrication is the most destructive cause of bearing faults. In case of poor lubrication, the friction increases substantially, which in turn causes fatigue and wear of the surface of raceways and rolling elements. Furthermore, inadequate lubrication also leads to skidding, slip, increased friction, heat generation and sticking. All of these mentioned factors severely deteriorate the health condition of a bearing under a load. By realizing the importance of detecting bearing fault timely and accurately, our objective in this paper focuses on the development of a bearing anomaly detection structure to detect not only known bearing faults, but also unexpected faults. A feature extraction routine is developed to overcome the non-monotonic trend of most time domain features as the increase of the fault dimension [5]. The vibration signals collected from different bearings under different fault sizes, different rotating speeds, different radial loads and different axial loads are analyzed under the proposed structure. The results show good performance of the proposed structure under different anomaly detection routines. II. B EARING A NOMALY D ETECTION The concept of “coverage” - in terms of the number of fault modes that a monitoring system is capable of detecting, isolating and identifying - has recently been the subject of increased interest within the fault detection and identification (FDI) community. A diagnosis system monitors a finite number of fault modes that are conveniently ranked and selected according to a Failure Modes, Effects, and Criticality Analysis. Furthermore, it is desired that the monitoring system has the capability to detect unanticipated faults. From this standpoint, our objective is reduced to recognize the existence of deviations from the expected operation of the bearing, assuming that there is one or more features that properly characterize its most critical aspects. Although some
Fig. 3.
Bearing anomaly detection architecture
The architecture for an anomaly detector is shown in Figure 1. In this architecture, real-time measurements and information about the current operational mode are provided. Features are then extracted to monitor the bearing behavior. Note that this structure can be extended to perform failure prognosis easily. III. F EATURE E XTRACTION As mentioned above, anomaly detection depends on features that are extracted from vibration signal to reveal the fault characteristics of the bearing. In the time domain, available features are root-mean-square (RMS), peak, kurtosis, crest factor, impulse factor, shape factor, and clearance factor of vibration signals [5], [6], [15]. Some of them are good indicators for incipient fault. However, as the defect becomes severe and spreads across the bearing surface, the value of these indicators drop back to normal level. The reason is that as the damage increases, the vibration signal becomes more random and the statistical signature appear in the vibration signal with a small fault is buried again [5]. On the other hand, frequency domain features, such as energy in a frequency range, the matched filter root mean square and the RMS of the spectral difference (Rdo) [5] does indicate a fault when it exists. These features are often functioning well under steady operating conditions. However, the limitation of the frequency domain features is that they often require reliable baseline spectrum, which is difficult to obtain due to the large number of operating conditions. One of the most prominent vibration signal processing techniques for detection and diagnosis of rolling element bearing incipient failure is envelope analysis [5], [8]. The
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success of this technique is because of its ability to separate the vibration generated by a defective bearing from the vibration generated by the other machine elements. From previous analysis, we have known that when a localized defect in a rolling element bearing exists, each time the contact between rolling elements and raceway surface(s) at the defect zone under a load generates an impulse force. This impulse has a very short time duration compared to the interval between impulses. Consider in the frequency domain, this short time impulse will cause an energy distribution across a wide frequency range and, therefore, excite various resonances of the bearing and the surrounding structure. Due to the periodic characteristics of the impulse, the excitation of resonance is repetitive as well. Envelope analysis, by demodulating the vibration signals at the resonances that the impulse excited, not only detects the presence of a defect, but also localizes the component of the defect. It provides a mechanism for extracting out the periodic excitation of the resonance from vibration signals. The frequency of the extracted signal is the frequency of the impulse, i.e., the characteristic bearing defect frequency. The procedure of envelope analysis is as follows. First, the vibration measurement is band-pass filtered. The cutoff frequencies of the band-pass filter should be selected such that the filtered signal, denoted as s(t), reserves the components around the resonant frequencies that excited by impulse force while removes other components. Second, the analytic signal of s(t) is built, which is a complex time signal whose imaginary component is the Hilbert transform of s(t). The analytic signal sa (t) has the form of:
(a) Vibration signal
(b) Filtered signal and its envelope Fig. 4.
Signal and its envelope
sa (t) = s(t) + j · sh (t) where sh (t) is the Hilbert transform of s(t) and j is the complex operator. Then, the envelope signal of s(t) is simply the absolute value of the analytic signal, |sa (t)|. To illustrate this process, original signal and filtered signal and its envelope are shown in Figures 4(a) and 4(b), respectively. The next step is to Fourier transform the envelope signal to the frequency domain and calculate the spectrum. The frequency spectrum of the envelope signal |sa (t)| is shown in Figure 5. Fault components clearly appear in this spectrum. The feature extraction is illustrated in Figure 6 and elaborated as follows: 1) Retrieve the amplitude at the fault characteristic frequencies up to three (3) harmonics. The retrieved value for the first harmonic is F C1 in Figure 6, where F C means fault characteristic frequency and its harmonics, postfix 1 means the first harmonic. Three (3) harmonics are chosen based on the observation that, in most cases, the spectrum show clear fault components up to three harmonics. This way, we have F C1, F C2, and F C3. 2) Calculate the average of components sum between F C and its first sideband, the “smallest sideband”, in Figure 6. These components represent the noise level and do not change too much under the same operation condition. This value is denoted as SB11 and SB12 in Figure 6, where SB means noise components and
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Fig. 5.
The frequency spectra of the envelope signal
the postfix 1 means the first harmonics whereas the subscripts 1 and 2 mean the value on the left-handside and right-hand-side of the harmonics, respectively. That is X
ff −1
SB11 = 0.5
A(fi )
fi =ff −fsbr +1
and
X
ff +fsbr −1
SB12 = 0.5
A(fi )
fi =ff +1
where A(fi ) is the component amplitude at frequency
IV. E XPERIMENTAL RESULTS
45
40
35
Amplitude
30
A. Vibration Data
FC1 = spectra amplitude at fault characteristic frequency
The bearing used in the research is a tapered roller bearing: Timken LM501310 cup and LM501349 cone. The structure of the bearing is illustrated in Figure 7 and its main geometric parameters are listed in Table I:
smallest sideband
smallest sideband
25
20
SB11=1/2 average of spectra sum
SB12=1/2 average of
TABLE I T HE GEOMETRIC PARAMETERS OF THE BEARING
spectra sum
15
10
Pitch diameter Roller number
5
0 182
192 Frequency (Hz)
Fig. 6.
5.715cm 19
Roller diameter Contact angle
0.784cm 13.13◦
202
The calculation of features
fi , ff is the fault characteristics frequency, fsbr is the frequency range between the fault characteristics frequency and its “first sideband”. This way, we have SB11 , SB12 , SB21 , SB22 , SB31 , and SB32 available. 3) Calculate the feature value, energy ratio, denoted by ER, which is given as: P3 P2 j=1 SBij i=1 ER = P3 k=1 F Ck Remark 1: Different from time domain features, ER decreases monotonically (its reciprocal increases monotonically) with the growth of the fault dimension because the larger the fault dimension, the larger the F C while SB keeps unchanged. Remark 2: To calculate feature ER, rotating speed needs to be known. When a bearing is in service, its rotating speed always changes and has fluctuation even when it remains at a constant speed. Therefore, number of frequency components between the fault characteristic frequency and its “smallest sidebands” always changes. By calculating the average value of components between F C and “smallest sideband”, the influence of rotating speed is minimized. Remark 3: For different fault types and different rotating speeds, the number of frequency components between F C and its “smallest sideband” are different. If the fault can be identified (this can be done by the extracted feature), the position of “smallest sideband” can be localized as well. Remark 4: For a bearing with given geometric parameters, the fault components F C with inner raceway fault, outer raceway fault and rolling element fault are fid , fod and fbd , respectively. For these three potential fault types, the positions of the main fault characteristic frequencies and their “smallest sideband” can be identified as well. Then, the feature values for the three potential fault types are calculated and monitored in real-time. If the feature value of one fault type deviates from its normal value with a given confidence, we can claim the occurrence of this fault.
Fig. 7.
Tapered Roller Bearing Schematic and Photo [13]
TABLE II T HE EXPERIMENTAL T ESTS Test No. C0 C1 C2 C3 C4 C5 C6 C7 D1 D2 D3 G1 G2 G3 G4 G5 G6 G7 G8 G9
Width (micron) 0 35.33 37.67 48.33 49.33 61.00 64.00 131.3 64 64 64 297.7 0 250 423.0 364.0 442.3 37.3 425.3 64
Depth (micron) 0 2.46 10.56 2.38 4.88 5.80 11.00 1.40 11 11 11 120.0 0 70 170.7 41,5 149.8 10.6 209.3 11
Speed (rpm)
Load (psi)
800
200
1200
400
1600
600
800 1200 1600
200 400 600
1400
600
Axial load (in*lbf)
20 25 30
The bearing is under three tests, which are called CTEST, DTEST, and GTEST, respectively. These tests measure the vibration signals of bearings under different fault sizes, different radial loads, different axial loads, different rotating speeds and different sensor places. For all the tests, three accelerometers are used to measure the vibration on the x axis, y axis, and z axis and an acoustic emission sensor is used as well. The sample rate is 50KHz. Each data snapshot contains about 262154 sampling points, which is a record of
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about 5.25 seconds. The details of each test are elaborated as follows in Table II, which includes the fault size, rotating speed, radial load and axial load.
450 400 350
B. feature extraction
Fault Zone
Four sensors are used in the experimental test. To evaluate the sensor that has the best performance to indicate fault, principal component analysis technique is used. This analysis transforms the input data so that the elements of the input vectors will be uncorrelated and the size of inputs may be reduced by retaining only those components which contribute more than a specified threshold of the total variation in the data set. When this algorithm is applied to the bearing data set, the four sensors, in regard to contributing to the anomaly detection, have a sequence of [sensor 3, sensor 2, sensor 1, sensor 4]. Therefore, if only 1 sensor data is used, it should be the data from sensor 3. If two sensors are use, they should be the data from sensors 3 and 2. To utilize the data efficiently, each data snapshot is separated into 4 segments. Then, 4 feature values are generated from each data snapshot. The result of sensor 3 is shown in Figures 8. In this figure, green color is used for data from healthy bearing without fault while other colors are for data with fault.
Defect Width
300 100 250 200
50
150 0 100
0
10
20
Healthy incipient fault severe fault
50 0
30
Normal Zone
0
50
100 150 Defect Depth
Fig. 9.
200
250
Approximate detect area
be considered as a transit from healthy condition to fault. In anomaly detection, if the data under this size fault is classified as fault, there will be a high false alarm ratio. 0.7 Normal Incipient Fault Severe Fault
0.6
0.5
Sensor3; Green−Health; Red−Fault; (C0−C7)CTest; (DD)DTest; (G1−G9)GTest 2.5
0.4
feature values
2
0.3
0.2
1.5
0.1 1 0
0
0.5
1
1.5
2 2.5 Feature Value
3
3.5
4
0.5
Fig. 10. 0
Fig. 8.
C0 G2 C3 C1 C4 C5 G9 C6 C7 DD C2 G7 G1 G3 G4 G6 G8 G5 bearing conditions
The features from different bearings with different fault sizes
C. Anomaly Detection When the fault is at its incipient stage, it is difficult to detect it. More analysis shows that defect depth (F D) plays a more important role than defect width (F W ). For example, the feature values from healthy bearings are closely overlapped with those feature from tests C1 (F W = 35.33 and F D = 2.46) and C3 (F W = 48.33 and F D = 2.38), where F D is very small. Meanwhile, if F W is very large, the fault can be classified easily even F D is very small, such as test C7 (F W = 131.3 and F D = 1.4). Therefore, a rough rule is set that those defects with a depth less than 5 microns (F D < 5) and a sum of width and depth less than 60 microns ((F D + F W ) < 60) can
Anomaly detection of pdf-based approach
With this consideration, some analysis results are illustrated below. In the following figures, blue or green colors are used for healthy bearings, magenta color is used for bearing with a fault (F D < 5 and (F W + F D) < 60) and red color is for bearings with more severe faults. To make it clear, a rough detectable area is illustrated in Figure 9. Note that since only limited data sets are available, this detectable area is only a very preliminary result. Figure 10 shows the pdf of feature values obtained for sensor 3. It is clear that healthy bearing (green color) and incipient fault (magenta color) overlapped. It would be very difficult to classify them. If we combine the healthy bearing and bearing with incipient fault, the pdf of them are separated from that of bearing with severe fault. Then, the ability and confidence of anomaly detection will be greatly improved. The classification result of the k-nearest neighbor method in the sensor3-sensor2 plane with k = 3 is shown in Figure 11. In this figure, the data from bearings with incipient
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KNN classifier, k==3
for such separation is unknown.
4
V. C ONCLUSIONS
3.5
A bearing anomaly detection structure is proposed so that different types of anomaly detection methods can be applied. Since the anomaly detection is based on features, a new feature extraction is developed from the envelope signal spectrum. The advantage of this feature is that it shows a monotonic decrease trend (its reciprocal has a monotonic increase trend) as the dimension of fault increases. The proposed structure and feature extraction routine are verified on experimental data under different fault sizes and different operating conditions. The excellent performance from verification results demonstrate that the proposed method can be applied to real application.
3
Sensor 3
2.5 2 1.5 1 0.5 0
0
Fig. 11.
0.5
1
1.5 Sensor 2
2
2.5
3
Anomaly detection of k-nearest neighbor classifier
R EFERENCES
faults and no fault have been combined. It can be seen that the result is pretty good. If k is given a larger value, the separation of classes is smoother.
Fig. 12.
Anomaly detection of particle-filter-based approach
When particle-filter-based approach is used, the result is shown in Figure 12 to detect fault in the data given by test C6. In this figure, a baseline pdf (cyan) is compared to the current pdf estimate for the crack length (magenta). Given both the existence of a baseline pdf for the feature being monitored and an estimate for the current pdf of that feature, it is perfectly plausible to apply any of the fault alarm indices presented in [14] to quantify the separation between the distribution functions, even in the case when the cause
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