Health monitoring of cooling fan bearings based on wavelet filter

Mechanical Systems and Signal Processing ] (]]]]) ]]]–]]]

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Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp

Health monitoring of cooling fan bearings based on wavelet filter Wei He a, Qiang Miao b, Michael Azarian a, Michael Pecht a,n a

Center for Advanced Life Cycle Engineering, University of Maryland, College Park, MD 20742, USA School of Mechanical, Electronic and Industrial Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, People's Republic of China b

a r t i c l e i n f o

abstract

Article history: Received 26 July 2011 Received in revised form 24 June 2013 Accepted 1 April 2015

In this paper, a vibration-based health monitoring approach for cooling fans is proposed using a wavelet filter for early detection of faults in fan bearings and for the assessment of fault severity. To match the wavelet filter to the fault characteristic signal, a fuzzy rule is introduced to maximize the amplitudes of bearing characteristic frequencies (BCFs), which are an indicator of bearing faults. The sum of the amplitudes of BCFs and their harmonics (SABCF) is used as an index to capture the bearing degradation trend. A comparative study is conducted with commonly used time-domain indices in the degradation assessment, and performance is quantified by three measures, i.e., monotonicity, prognosability, and trendability. The analysis results of the experimental data show that the proposed method can effectively detect incipient defects and can better capture the degradation trend of fan bearings than traditional time-domain indices in vibration analysis. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Health monitoring Cooling fan bearing Wavelet Degradation assessment Fault diagnosis Time domain index

1. Introduction Increasing density in electronic products have led to an increasing number of applications that use active cooling as a means to keep the temperatures of electronic components at a level which will meet performance and reliability objectives. The most common method of active cooling is the use of forced air generated from a fan. The consequences of an unexpected fan failure to a system can be severe, as the temperature in the box can rise rapidly, causing catastrophic conditions for the electronic system. Therefore, developing an early-warning system to detect and predict fan failure can significantly improve system reliability by allowing preventive actions. Furthermore, alerting the user of a fan problem can also increase the product's marketing value. Prognostics and health management (PHM) is a methodology that evaluates a product's health by measuring the extent of deviation and degradation of the product from an expected normal operating condition and assesses the future reliability of the product based on current and historic conditions [1]. PHM generally combines sensing and interpretation of environmental, operational, and performance-related parameters to assess the health of a product and predict its remaining useful life (RUL) [2]. PHM can provide advance warning of failures and reduce the life cycle cost of a product by decreasing inspection costs, downtime, and inventory [1]. Another important application of PHM is product qualification. Traditional

n

Corresponding author. Tel.: þ1 301 405 5323; fax: þ 1 301 314 9269. E-mail address: [email protected] (M. Pecht).

http://dx.doi.org/10.1016/j.ymssp.2015.04.002 0888-3270/& 2015 Elsevier Ltd. All rights reserved.

Please cite this article as: W. He, et al., Health monitoring of cooling fan bearings based on wavelet filter, Mech. Syst. Signal Process. (2015), http://dx.doi.org/10.1016/j.ymssp.2015.04.002i

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qualification tests take too much time and slow down the schedule. In the specific case of a cooling fan, the testing time is usually more than 6 months due to the high reliability of ball bearings today. PHM is a potential way to cost effectively and timely identify low reliability fans [3,4]. Because PHM can provide early warning of failure of a product, it is not necessary to run an experiment until product failure. Furthermore, when an anomaly is detected, it is possible to estimate the time-tofailure of the product, which can save time and cost [4]. The first step of PHM is to conduct the failure modes, mechanisms, and effects analysis (FMMEA) of the target system. In this step, the dominant failure mechanisms, failure sites, and parameters to be monitored can be identified. In most cases, fan failure is caused by extensive heat and mechanical wear, which results in defective bearings. Ref. [5] reported fan failure from qualification tests as well as analysis from field returns from the Hewlett-Packard Company. It was found that bearings were the dominant failure sites in mechanical failures of cooling fans. FMMEA was conducted in Ref. [6]. The potential failure mechanisms were prioritized by evaluating the occurrence and severity from the published literature. The failure mechanism with highest priority was identified as lubricant deterioration in the bearings. As shown in these articles, bearing failure is the dominant failure mechanism in cooling fans, and normally it is the failure mechanism used to define the service life of fans. Therefore, bearings are the key components that need to be monitored and evaluated in cooling fans. The second step in PHM is health monitoring, which can provide warning of a potential fault, assess the degradation level, and trigger the prognostic step. However, health monitoring of cooling fan bearings in electronic products has rarely been studied up to now. In this paper, a vibration-based method is proposed for the health monitoring of cooling fan bearings. The vibration signal is measured through an accelerometer mounted on the housing of cooling fans. The vibration signal of fans is complex, because each of the elements in a fan, such as the blade, motor, and shaft, will generate vibration signals. How to separate the bearing characteristic signal from that of other components is the key for timely detection of early faults in bearings. In this research, the wavelet filter is adopted to extract the fault characteristic signal from the noisy vibration data. The wavelet filter is the wavelet transform at a fixed scale. It is effective and efficient in signal de-noising and transient detection. Since bearing characteristic frequencies (BCFs) are a typical indicator of bearing faults [7], a fuzzy-BCF maximization rule is proposed to match the wavelet filter with the fault characteristic signal. After wavelet filtering, fast Fourier transform (FFT) is implemented into the filtered signal to identify the BCFs. Finally, an index called SABCF, which is defined as the sum of the amplitudes of the BCFs and their harmonics, is proposed to capture the bearing degradation. Case studies are presented to demonstrate the capability of the proposed methodology for the health monitoring of fan bearings. Comparative studies between SABCF and traditional time-domain indices are also provided. 2. An overview on bearing vibration signal and associated analysis techniques Bearing defects generate a series of impulses every time a running roller passes over the surface of the defects. The occurrence frequency of these fault-generated impulses is called the bearing characteristic frequency, which can be estimated based on the shaft speed, the geometry of the bearing, and the location of defects [7]. For ball bearings, there are generally four types of BCFs: bearing pass frequency of outer race (BPFO), bearing pass frequency of inner race (BPFI), ball spin frequency (BSF), and fundamental train frequency (FTF), which correspond to the defects at the outer race, the inner race, the roller, and the cage, respectively [8]. The calculation formulas for the BCFs are as follows:
 nf d BPFO ¼ r 1  cos ϕ ð1Þ D 2 BPFI ¼

FTF ¼


 nf r d 1 þ cos ϕ D 2


 fr d 1  cos ϕ D 2

(  2 ) Df r d cos ϕ 1 BSF ¼ D 2d

ð2Þ

ð3Þ

ð4Þ

where f r is the shaft speed, n is the number of rolling elements, ϕ is the angle of the load from the radial plane, d is the ball diameter, and D is the pitch diameter. In bearing degradation assessment, the amplitude of the BCFs is typically an indication of defect severity, and the presence of the harmonics of the BCFs is also another indication of degradation and spall formation [9]. However, extracting these BCFs from the vibration signal is not an easy task, which relies on the signal processing method being used, because vibration signals are often severely tainted by various noises. For the specific case of fan bearings, the noise could be the interfering vibrations generated by the shaft, the fan blade, and rotator, as well as the background noise in the measurement device. Especially in the early stage of the fault, the fault characteristic signal is much weaker than noise, which prevents the early detection of the bearing fault. In addition, because of the structural configuration of the cooling fan, the accelerometer cannot be mounted near the load zone of the bearings, which further dampens the bearing vibration signal because of the Please cite this article as: W. He, et al., Health monitoring of cooling fan bearings based on wavelet filter, Mech. Syst. Signal Process. (2015), http://dx.doi.org/10.1016/j.ymssp.2015.04.002i

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transmission effect. Therefore, a proper signal processing algorithm should be developed to isolate the fault characteristic signal. The high frequency resonance technique (HFRT), also called envelope analysis, has been successfully applied to the fault detection of the ball bearings in rotating machines [8,10–12]. In this method, the vibration signal is first passed through a band-pass filter or high-pass filter to reduce the interference of irrelevant vibrations. After filtering, the signal is demodulated by an envelope detector and its frequency spectrum is derived. HFRT is robust to noise. However, the performance of it is dependent on the filter employed. It is possible to design different filters to conduct the de-noising based on noise type and application. But for a situation where the noise type and frequency range are unknown, traditional filter design could become a very challenging task [13]. Recently, time–frequency methods, such as short-time Fourier transform (STFT) [14], the Wigner–Ville transform (WVT) [15,16], wavelet transform (WT) [17–20], and Hilbert–Huang transform (HHT) [21], have been intensively investigated for vibration analysis. WT is one of the most popular time–frequency techniques because it does not contain cross-terms as in WVT, can provide a more flexible multi-resolution solution than STFT [22], and possesses a more rigorous and mature mathematical foundation than HHT. Moreover, wavelet transform is effective in detecting transients [23,24], which is useful for the monitoring of bearings. Generally, the WT can be classified as continuous WT (CWT), wavelet decomposition (WD), wavelet packet analysis (WPA), and wavelet filter (WT). Although the CWT and WPA can provide more information, it is usually difficult to explain their results because they analyze the vibration signal as a whole. Instead of being a single component, a fan is a complex system. It consists of the bearing, shaft, fan blade, and motor, each of which generates vibration signals. The WD is a binary decomposition in the frequency domain. It is prone to split a fault-related characteristic feature into two or more decomposition levels, which will weaken the fault feature and may not be robust to assess the severity of the degradation. On the other hand, the wavelet filter, which is the wavelet transform of the signal at a fixed scale or frequency band, can completely extract a target vibration component when its parameters are properly defined. In addition, it is more computationally efficient than CWT and WPA, and it is easier to interpret as it only extracts the faultrelated signal. In this study, the wavelet filter approach was adopted for early fault detection and health monitoring of fan bearings.

3. Methodology 3.1. Introduction to wavelet filter The wavelet transform of a finite energy signal xðtÞ with a wavelet basis ψ ðtÞ is defined by [25]   Z þ1 1 t τ dτ xðt Þψ n WTðs; τÞ ¼ pffiffi s s 1

ð5Þ

where ψ n ðtÞ stands for the complex conjugation of the mother wavelet function ψ ðtÞ; s and τ are the scaling parameter and time localization parameter, respectively. Based on the convolution theorem, Eq. (5) can be implemented by WTðs; τÞ ¼

pffiffi  1   n sF X ðf ÞΨ ðsf Þ

ð6Þ

where Xðf Þ and Ψ ðf Þ are the Fourier transforms of xðtÞ and ψ n ðtÞ, respectively, and F  1 denotes the inverse Fourier transform. Eq. (6) indicates that wavelet transform can be considered to be a filtering process using a filter with an impulse response pffiffi n equal to sΨ ðsf Þ. The selection of a proper wavelet function ψ n ðtÞ is the key to the application of wavelet transform. A widely accepted rule for the wavelet function selection is based on the maximum matching mechanism [26], which indicates that the wavelet transform actually calculates a “resemblance index” between the signal and the wavelet. If the resemblance is strong, then the index is large; otherwise it is slight. The indices are wavelet coefficients. If a wavelet function that best matches the fault characteristic signal is employed, then fault features will get high wavelet coefficients so that fault features can be enhanced. Meanwhile, the background noise and interfering vibrations can be suppressed since they do not resemble the wavelet function. Based on the maximum matching mechanism, we chose the Morlet wavelet, which is an impulse-like wavelet, to construct the matching filter to extract the characteristic signal of bearing faults. The Morlet wavelet is defined in the time domain as a sinusoidal wave multiplied by a Gaussian function:

σ 2 2 ψ ðt Þ ¼ pffiffiffiffie  σ t ei2π f 0 t π

ð7Þ

where σ is the shape factor, and f 0 is the wavelet center frequency. The Fourier transform of the Morlet wavelet is [27] 2 σ 2 2 ψ ðf Þ ¼ pffiffiffiffie  ðπ =σ Þðf  f 0 Þ π

ð8Þ

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According to Eq. (8), the half-power bandwidth B of the Morlet wavelet can be obtained as pffiffiffiffiffiffiffiffiffiffiffiffi 2 ln2 σ B¼

π

ð9Þ



 Therefore, the pass-band of a Morlet wavelet filter at scale 1 is f 0  B=2; f 0 þB=2 . Since the Morlet wavelet employed in this study is a complex wavelet, the filtering result is also an analytical signal. Hence, the modulus of the wavelet coefficients will provide the envelope of the band-pass filtered signal: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi SðtÞ ¼ ½ReðWTÞ2 þ ½ImðWTÞ2 ð10Þ After obtaining the envelope, FFT can be applied to it to identify the BCFs. The envelope spectrum obtained after wavelet filtering is called a wavelet envelope spectrum in this paper. To extract fault-generated impulses, it is critical to adjust f 0 and B such that the Morlet wavelet best matches the fault features. 3.2. Optimization rule for the Morlet wavelet filter In the application of the Morlet wavelet filter, it is important to adjust the center frequency f 0 and bandwidth B of the wavelet to match the frequency respond of the fault characteristic signal so that the fault characteristic signal can be isolated. Concerning this problem, several approaches have been proposed. Kurtosis maximization is adopted in Refs. [27,28] for the simultaneous optimal selection of the wavelet parameters. An index measuring the energy of wavelet amplitude peaks is proposed in Ref. [29] as the parameter optimization criterion for the Morlet wavelet filter. However, kurtosis has been found to be sensitive to outliers [30]; the peak energy criterion may take the peaks generated by the high amplitude vibrations of other mechanical components into account. As aforementioned, the typical characteristic of ball bearing faults is the presence of BCFs in the vibration signal [7]. Since BCFs are the frequencies specifically defined by the rotating speed, the geometry of the bearing and the location of defects, it is easy to distinguish bearing vibration from the vibration of other mechanical components using BCFs. Furthermore, the amplitude of BCFs is a typical indicator of the defect severity. Therefore, an effective and intuitive rule for the selection of wavelet parameters is to maximize the amplitude of the BCFs in a wavelet envelope spectrum. A practical situation that should be taken into account is that the BCFs often slightly vary around their theoretical values due to the fluctuation of rotating speed and slippage of the rolling elements [8]. In this case, it is more reasonable to define the BCFs in a fuzzy manner rather than using the crisp values. Therefore, the BCFs are defined in a fuzzy way in this paper using Gaussian membership functions, based on the assumption that the measured BCFs follow Gaussian distributions around their theoretical values. The Gaussian membership function is defined as below [31]:

Φðf Þ ¼ e  ðf  cÞ =2σ 2

2

ð11Þ

where c is the center of the membership function and is defined by the theoretical BCFs and their harmonics; σ defines the attenuation rate of the membership function and is chosen by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ð0:01BCFÞ2 σ¼ ð12Þ 2 lnð  3 dBÞ Eq. (12) means that if a frequency f is 1% deviating from the theoretical BCF, then its membership value will attenuate to  3 dB. The fuzzy membership function indicates that the closer the frequency to the theoretical BCFs, the higher confidence that the frequency is related to a bearing fault. Fig. 1 gives a schematic diagram of the membership function. Using the membership function, the amplitude of a BCF is defined by Amp ¼ maxðΦðf Þ  F ðSðt ÞÞÞ

ð13Þ

where FðSðtÞÞ is the Fourier transform of the wavelet envelope SðtÞ, namely wavelet envelope spectrum. Then, the SABCF is defined by adding up the amplitudes of all the BCFs and their first five harmonics. The optimization rule proposed in this paper is to find out the optimal combination of the wavelet parameters f 0 and B that maximize the SABCF:

ð14Þ arg max SABCF f 0 ; B f 0 ;B

The differential evolution (DE) is employed to optimize the cost function equation (14). DE is a population based stochastic global optimization method. It has been demonstrated in various applications that DE outperforms other population based optimization algorithms, such as particle swarm optimization and evolutionary algorithm [32]. For the detailed principles of DE, refer to Ref. [33]. After identifying f 0 and B, the optimal wavelet filter can be obtained. The corresponding SABCF value is recorded as a health index to track bearing degradation. The wavelet envelope spectrum obtained by optimal wavelet filtering can be used to identify the fault location of the bearing. Fig. 2 gives the flowchart of the proposed health monitoring approach for fan bearings. Please cite this article as: W. He, et al., Health monitoring of cooling fan bearings based on wavelet filter, Mech. Syst. Signal Process. (2015), http://dx.doi.org/10.1016/j.ymssp.2015.04.002i

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5

Amplitude

0dB

−3dB

−6dB 0.99BCF

BCF

1.01BCF

Frequency Fig. 1. The Gaussian membership function.

Fig. 2. The flowchart of the proposed health monitoring approach for fan bearings.

3.3. Compare the wavelet filter with the wavelet decomposition and the continuous wavelet transform The most intensively investigated wavelet approaches for bearing fault diagnosis are continuous wavelet transform (CWT) and wavelet decomposition (WD). CWT is a redundant representation of a signal in a time–frequency map. It is effective for singularity detection and can effectively extract the fault feature. However, CWT might be too computationally expensive for real-time monitoring. In addition, the CWT map contains so much information that it is hard to interpret sometimes. On the other hand, the wavelet filter only focuses on the scale in which the fault feature is most significant. So it is more computationally efficient than the CWT while preserving the important fault information. A comparative study between the wavelet filter and WD is presented in Ref. [13]. The results showed that the wavelet filter is better than WD for bearing fault detection. In addition, it should be noticed that WD is a binary decomposition method in the frequency domain. If the fault feature lies in the transition zone of the frequency band of two adjacent decomposition levels, then the Please cite this article as: W. He, et al., Health monitoring of cooling fan bearings based on wavelet filter, Mech. Syst. Signal Process. (2015), http://dx.doi.org/10.1016/j.ymssp.2015.04.002i

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Fig. 3. The continuous wavelet transform of the simulated signal x(t).

0.09 0.08 0.07

Amplitude

0.06 0.05 0.04 0.03 0.02 0.01 0

0

2000

4000 6000 8000 Frequency (Hz)

10000

12000

Fig. 4. The frequency spectrum of the simulated impulsive signal x2 ðtÞ.

fault feature will be split into two parts, and the split signal will be further masked by noise and other frequencies in the same decomposition level. To illustrate these points, a simulation study was conducted. The simulated signal is defined as xðtÞ ¼ x1 ðtÞ þx2 ðtÞ þ x3 ðtÞ

ð15Þ

where x1 ðtÞ is a combination of harmonic signals to simulate the interferences of the rotating speed (66.7 Hz) and an irrelevant high frequency (4400 Hz) signal defined by x1 ðtÞ ¼ cos ð2π 66:7tÞ þ cos ð2π 4400tÞ

ð16Þ

x2 ðtÞ is a series of exponentially decaying pulses designed to simulate the vibration signal of a bearing with an outer race defect. The BPFO is 143 Hz, which excites a resonance frequency of 6500 Hz. The impulsive function in one period is x2 ¼ 0:1e  50t cos ð2π 6500tÞ

ð17Þ

x3 ðtÞ is Gaussian noise with a standard deviation of 0.1. The sampling frequency is 100 kHz. Fig. 3 presents the CWT result of the simulated signal xðtÞ. The wavelet scale was converted to pseudo-frequency in the plot. The harmonic signal at around 4400 Hz can be seen clearly, and some vague impacts with a period of 7 ms (corresponding to 143 Hz) can be detected at around 6500 Hz. But it should be noted that in case one does not know the frequency range of the impulses, it may be hard to identify these impulses. In the WD, a 6-level decomposition was conducted. The wavelet function employed here was a “db12” wavelet. According to the WD theory, the frequency ranges of the detailed signals of 3rd and 4th level are 6400–12 800 Hz and 3200–6400 Hz, respectively. As shown in Fig. 4, the spectrum of the impulsive signal x2 ðtÞ spreads across the frequency range of the two levels. Hence, the fault characteristic Please cite this article as: W. He, et al., Health monitoring of cooling fan bearings based on wavelet filter, Mech. Syst. Signal Process. (2015), http://dx.doi.org/10.1016/j.ymssp.2015.04.002i

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7

−3

x 10

4.5

143

4 3.5

Amplitude

3 286

2.5 2

429

1.5

572

1 0.5 0

0

200

400 600 Frequency (Hz)

800

1000

Fig. 5. The wavelet envelope spectrum obtained by wavelet filtering.

Amplitude

0.015

0.01 143

0.005

0

0

100

200

300

400

500

600

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800

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3

x 10

Amplitude

2.5 2 1.5 1 0.5 0

0

100

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300

400

500

600

Frequency (Hz)

Fig. 6. The envelope spectrum obtained by wavelet decomposition: (a) level 3; (b) level 4.

component will be decomposed into two parts by WD. On the other hand, using the optimization rule proposed in this paper, the wavelet filter can be adapted to match the characteristic frequency band of the fault feature. The central frequency and bandwidth found by the optimization rule were 6535 and 1053 Hz, respectively. The envelope spectrum obtained by wavelet filtering is shown Fig. 5. The impulsive repetition frequency and its harmonics can be clearly identified. The envelope spectrum obtained by WD is shown in Fig. 6. Although 143 Hz can be detected in Fig. 6(a), its harmonics are not observed in Fig. 6(a). However, harmonics of BCF provide important diagnostic information on the impulsiveness of the signal. This simulation study demonstrated that the wavelet filter is more feasible and robust than CWT and WD in impulsive feature extraction.

4. Experimental data analysis 4.1. Experimental setup In the experiment, three cooling fans with the name convention 102, 104 and 110 were tested. They are axial type brushless direct current (BLDC) fans, as shown in Fig. 7, which have two grease-lubricated ball bearings. The geometrical specifications of the bearing are shown in Fig. 8. Most fan bearing failures are caused by the loss of lubricant. To simulate the Please cite this article as: W. He, et al., Health monitoring of cooling fan bearings based on wavelet filter, Mech. Syst. Signal Process. (2015), http://dx.doi.org/10.1016/j.ymssp.2015.04.002i

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lubricant starvation [3,34], the grease inside the bearings was completely removed by putting the bearing in acetone for several days. Bearing run-to-failure tests were performed under free airflow conditions, and the rotating speed was 4000 rpm. Based on the geometry and the rotating speed of the bearing, the theoretical BPFI, BPFO, BSF and FTF are 257, 143, 212, and 24 Hz, respectively. A PCB 352A42 accelerometer was attached to the fan housing near the bearing to acquire vibration data. Data collection was conducted using the National Instruments LabVIEW program. The sampling frequency was 102.4 kHz and the sampling length was 100k points for each measurement. A condenser microphone was set up 10 cm

Fig. 7. BLDC fan and accelerometer location.

SABCF

Fig. 8. Geometrical specification of the fan bearing.

10

3

10

2

10

1

10

0

Bearing #110

Bearing #102

Bearing #104

10

-1

0

8

16

24

48 Time (Hour)

72

Fig. 9. The evolution of SABCF.

Please cite this article as: W. He, et al., Health monitoring of cooling fan bearings based on wavelet filter, Mech. Syst. Signal Process. (2015), http://dx.doi.org/10.1016/j.ymssp.2015.04.002i

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−3

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x 10

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773

2 0

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0.03 0.02 258

0.01 0

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Fig. 10. The wavelet envelope spectrum of the three fan bearings at 8 h: (a) bearing 102; (b) bearing 104; (c) bearing 110.

away from the cooling fan to record the acoustic noise emission of the cooling fan. The test was ended and the bearings were considered to be failed when the acoustic noise increased 3 dB from the initial value, which is the failure criterion defined in the IPC-9591 standard [34]. After the testing, the bearings were dissembled. Cracks and dents were founded in the outraces, inner races and rolling elements of the bearings. 4.2. Degradation assessment based on wavelet filter To track the degradation of fan bearings, the SABCF is used as an indicator in this study. The evolution of the SABCF for the three bearings is shown in Fig. 9. The trends for all the three bearings presented significant increases at 8 h, which can be considered to be an anomaly. Further analysis was conducted by using wavelet envelope spectrum. The results are shown in Fig. 10. It can be seen that BPFI is clear in the wavelet envelope spectrum of bearing 102 and 110, and BSF is obvious in the spectrum of bearing 104. These observations indicate that the bearings had defects at 8 h. Therefore, advance warning of bearing failure can be achieved using SABCF. Further examining the SABCF, it can be found that the overall SABCF trends of the three bearings were similar, which means that the degradation trends of the three bearings can be roughly described by the same function based on SABCF. This is a desirable property for PHM, because it facilitates the construction of data-driven models for degradation assessment and prognostics. Moreover, the SABCF shows a statistical monotonically increasing trend, which corresponds to the physical fact that the degradation of bearings is irreversible. 4.3. Comparison with traditional time-domain indices Traditional time domain indices proposed to characterize vibration signals include root mean square (RMS), kurtosis (KU), peak value (PV), and crest factor (CF). A comparative study between the traditional time domain indices and SABCF is conducted in this section to compare their performance in bearing fault detection and degradation trending. First, a brief review of the traditional time domain indices is provided below. The RMS is a measure of the power included in the waveform of the signal. It estimates the overall vibration level of a mechanical system. The RMS value of a discrete signal xðiÞ; i ¼ 1; 2; …; n, is defined by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 i ¼ n ½xðiÞ RMS ¼ ð18Þ n PV is the maximum absolute amplitude of the vibration signal. However, the maximum absolute amplitude is sensitive to outliers or noise. Commonly, the 99% PV is used, which is defined by the np -th largest absolute amplitude of the signal, where np is defined by np ¼ n  roundð99%  nÞ

ð19Þ

where n is the sample length of the signal. Please cite this article as: W. He, et al., Health monitoring of cooling fan bearings based on wavelet filter, Mech. Syst. Signal Process. (2015), http://dx.doi.org/10.1016/j.ymssp.2015.04.002i

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#102 #110

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#104

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#102 #110 0

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#102

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72

0

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48 Time (Hour)

72

Fig. 11. The evolution of traditional time-domain indices of the experimental data.

The CF is calculated from the peak value of the waveform divided by the RMS value of the waveform: CF ¼

PV RMS

ð20Þ

The CF gives a quick idea of how much impacting is occurring in a waveform. Impacting is often associated with ball bearing defects. Kurtosis is a statistical indicator that measures the impulsive character of a signal. It is given by the formula 1 Pn 4 i ¼ 1 ðxðnÞ x Þ KU ¼  n 2 1 Pn 2 i ¼ 1 ðxðnÞ  x Þ n

ð21Þ

where x is the mean of the signal. The kurtosis, RMS, PV, CF, and KU for the three bearings were estimated and presented in Fig. 11. It can be seen that the performance of time-domain indices is not satisfactory. For example, the RMS and PV fluctuate around their 0 h values before 48 h so that initial bearing faults cannot be identified. In addition, the kurtosis trend of bearing 104 is quite different from that of the bearing 102 and 110. This will add difficulty to the construction of the prognostic models. Moreover, the time domain indices are greatly divergent in the final failure values under the same loading condition, which may add difficulty to define a failure threshold. 4.4. Quantify the performance of the degradation indices Identification of an appropriate indicator facilitates the degradation assessment and prognostics. Ref. [35] proposed three metrics to quantify the suitableness of the indicators: monotonicity, prognosability, and trendability. They are defined as follows: (1) Monotonicity characterizes the underlying positive or negative trend of the indicator. This is an important feature of a degradation indicator because the degradation of bearings is considered to be an irreversible process. The monotonicity of a population of indicators is given by the average difference between the number of positive and negative growth for each Please cite this article as: W. He, et al., Health monitoring of cooling fan bearings based on wavelet filter, Mech. Syst. Signal Process. (2015), http://dx.doi.org/10.1016/j.ymssp.2015.04.002i

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Table 1 Indices performance metrics. Index

Monotonicity

Prognosability

Trendability

Total suitability

SABCF Kurtosis Crest factor RMS Peak value

0.47 0.33 0.33 0.33 0.33

0.69 0.56 0.67 0.45 0.50

0.99 0.08 0.21 0.71 0.73

2.15 0.97 1.21 1.49 1.56

path:

  positiveðdiffðxi ÞÞ negativeðdiffðxi ÞÞ  Monotonicity ¼ mean   n1 i ¼ 1; 2; …; m

ð22Þ

where n is the number of measurement time points and m is the number of systems monitored. In this study, m ¼ 3, since 3 fans were tested. (2) Prognosability is calculated as the deviation of the final failure values for each path divided by the mean range of the path. This is exponentially weighted to give the desired zero to one scale: ! stdðfailurevaluesÞ 

 ð23Þ Prognosability ¼ exp  mean failurevalue startingvalue This measure encourages well-clustered failure values. Ideally, failure should occur at a crisp, well-defined degradation level. A wide spread in critical failure values can make it difficult to define a failure threshold. (3) Trendability indicates the degree to which the indicators of a population of systems have the same underlying shape and can be described by the same function form. This will facilitate the development of an accurate degradation or prognostic model. Trendability is calculated by the smallest absolute correlation in a population of the indicators: 



Trendability ¼ min corrcoef xi ; xj  i ¼ 1; 2; …; m; j ¼ 1; 2; …; m ð24Þ

4.5. Results and discussion Table 1 gives the performance metrics for each of the degradation indices. The total suitability (given by the sum of the three performance metrics) of SABCF is the highest among the five indices. SABCF avoids the effect of noise by using the optimal wavelet filtering, so it is more robust than time-domain indices. In addition, it only takes the vibration generated by bearing defects into account, so it can better correlate with the severity of bearing degradation. RMS and PV are poor in monotonicity and prognosability, due to their unpredictable fluctuation between 0 and 48 h and the divergence in final failure values. In addition, RMS and PV measure the overall vibration level of a signal and tend to be affected by noise. At the early stage of bearing faults, the vibration of bearing fault has little impact on the overall vibration level of the whole fan system. As a result, RMS and PV may be not sensitive to incipient bearing faults. KU and CF are sensitive to the impulsive components in the signal, and they have the capability to detect early bearing faults. The KU and CF of the three bearings show increasing trends at the early stage of operation in Fig. 11, indicating the early degradation of the bearings. However, the total suitability of KU and CF are the lowest two among the five indices. This is mainly caused by their poor performance in trendability. In Fig. 11, the KU and CF of the bearing 104 exhibit a quite different trend from other two bearings, which results in their low scores in trendability. The KU and CF of the bearing 104 first increase, and then decrease to the value at normal stage and then increase again. One possible interpretation for this kind of trend could be the localized deformation or defective groove on the ball surface wears out to a larger and smoother fatigue area as the bearing rotates, resulting in the decrease in the peakiness of the vibration signal of bearing 104, and as a result the KU and CF decrease. Then, with the further evolution of the damage, more and more debris spall from the fatigue surface, so that the irregularity of the ball surface increases and the debris will also cause the defect of other bearing components. As the result, the KU and CF increase again after some time. In sum, the comparative study shows that the SABCF is more effective than time-domain indices. It not only can timely detect the early fault of fan bearings, but also provide better degradation trending for fan bearings than time-domain indices. 5. Conclusions This paper presents a health monitoring approach for cooling fan bearings. This approach relies on monitoring the vibration signal by mounting an accelerometer on the surface of the fan housing. A wavelet filter based method is presented to extract the bearing characteristic vibration from the noisy vibration signal. A health index is calculated as the sum of the Please cite this article as: W. He, et al., Health monitoring of cooling fan bearings based on wavelet filter, Mech. Syst. Signal Process. (2015), http://dx.doi.org/10.1016/j.ymssp.2015.04.002i

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amplitudes of bearing characteristic frequencies (SABCF) to assess the degradation severity of fan bearings. Accelerated tests were conducted to simulate the lubricant starvation of bearings. The measured vibration signals were used to validate the proposed method. It was demonstrated that SABCF can provide early warning of bearing defects and assess the bearing degradation. Comparative studies were conducted to compare the performance of SABCF and traditional time-domain indices, i.e. root mean square (RMS), peak value (PV), kurtosis (KU) and crest factor (CF), in the early defect detection and degradation trending. It was found that RMS and PV failed to detect early faults, since they measure the overall vibration level of the signal and are sensitive to noise. KU and CF are able to detect early faults. But when defects reach an advanced stage, they may return back to the values under normal condition. On the other hand, SABCF not only can provide early warning of bearing fault, but also can better capture the bearing degradation. As shown in the case study, SABCF detected the bearing fault at 8 h, and a further step of wavelet envelope spectrum analysis identified the fault type. In addition, the SABCF for the three bearings show similar increasing trends with time, which would facilitate the development of a data-driven prognostic model, since they could be roughly depicted by a similar function. The better performance of SABCF compared to traditional time-domain indices can be attributed to the following reasons: first, an optimal wavelet filtering is used as the preprocessing step before the SABCF computation. The wavelet filter is designed to match the characteristic vibration of bearing faults. After filtering, the energy of noise and the vibration of other components of the fan can be significantly trimmed down, and the bearing vibration signal can be enhanced. Second, BCFs and their harmonics are generated by the bearing vibration. Their amplitudes can reflect the severity degree of the bearing degradation. SABCF only takes the bearing vibration into account and thus further avoids the impact of noise. Hence, SABCF can better track the bearing degradation than traditional time-domain indices. This paper has addressed the problem of health monitoring of cooling fan bearings. The aim of this study is to propose an approach to provide advanced fault warning and capture the degradation trend of fan bearings. The benefits of the proposed approach can be expressed in terms of the prevention of unexpected bearing failure, the increase of fan reliability, and the reduction of downtime and maintenance cost. In the product qualification process, it is possible to timely identify low reliable fan bearings in the accelerated testing using the proposed approach, which can save time and cost.

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Please cite this article as: W. He, et al., Health monitoring of cooling fan bearings based on wavelet filter, Mech. Syst. Signal Process. (2015), http://dx.doi.org/10.1016/j.ymssp.2015.04.002i