Scientific Journal of Information Engineering April 2016, Volume 6, Issue 2, PP.29-35
DWPT-Based Sub-Band Analysis for Fault Detection of Rolling Element Bearings Myeongsu Kang1, Jong-Myon Kim2, Rui Peng3*, Xiaoyang Ma3, Michael Pecht1 1. Center for Advanced Life Cycle Engineering, University of Maryland, College Park, MD 20742, USA 2. Department of IT Convergence, University of Ulsan, Ulsan 44610, South Korea 3. Donlinks School of Economics and Management, University of Science and Technology Beijing, Beijing 100083, China #Email: pengrui1988@ustb.edu.cn
Abstract To early detect symptoms of defective rolling element bearings, this paper introduces discrete wavelet packet transform (DWPT)based sub-band analysis. The objective of this analysis is to explore the impacts of multiple sub-band signals by 4-level DWPT using proper Daubechies mother wavelet on a 2.5-second acoustic emission signal. In particular, the DWPT-based sub-band analysis determines the most informative sub-band signal involving intrinsic information about bearing defects among the aforementioned multiple sub-band signals based on the ratio of spectral magnitudes at harmonics of the bearing’s characteristic frequency to those around the harmonics. This paper also verifies the efficacy of the DWPT-based sub-band analysis for seeded bearing defects (i.e., a crack on the inner race, the outer race, or a roller). Keywords: Discrete Wavelet Packet Transform; Envelope Analysis; Fault Detection; Rolling Element Bearings
1 INTRODUCTION Rotating machines have been widely utilized in heavy industries such as paper mills and wind-turbine power plants. Unfortunately, bearings, which support heavy loads with stationary rotational speed of these machines, are frequently failed due to contamination, poor lubrication, temperature extremes, poor fitting/fits, unbalance and misalignment [1]. These vulnerable bearings often cause unexpected mechanical breakdowns, resulting in significant economic losses. According to [2], for example, Siemens reported a loss of EUR 48 million for inspecting and replacing faulty bearings in offshore turbines (in the second quarter in 2014). In practice, early identification of bearings defects can support proper maintenance for bearings in a timely manner. To do this, it is significant to develop a way to well detect incipient bearing defects. In bearings, periodic impulses are produced while rolling elements pass over a defect. These impulses are highly correlated with a ball pass frequency of the inner race (BPFI), a ball pass frequency of the outer race (BPFO), a ball spin frequency (BSF), and a fundamental train frequency (FTF) [3]. Unfortunately, however, these periodic impulses are amplitude-modulated while bearings are in operation by a high frequency carrier signal (e.g., bearing resonance frequency ranging from several kilohertz to tens of kilohertz) [4]. Hence, envelope analysis, which is an efficient demodulation tool, has been widely used for detecting bearing defects [5, 6]. The fact that periodic impulses (i.e., bearing information signal) are often screened by either low-frequency components (e.g., operating frequency, misalignment, unbalance, etc) or high-frequency noise components calls for frequency analysis. To address these issues, we introduce discrete wavelet packet transform (DWPT)-based sub-band analysis. Specifically, this analysis explores the impacts of multiple sub-band signals decomposed by DWPT and determines the most informative subband signal involving intrinsic information about bearing defects. The DWPT-based sub-band analysis includes the following procedures: 4-level DWPT using Daubechies mother wavelet (db1 to db45) on an input signal; envelope power spectrum computation (i.e., 24 ď‚´ 45 envelope power spectra in this paper); and assessment of the degree of defectiveness in each envelope power spectrum. The key contribution in this analysis is to measure the degree of defectiveness (DoD) to determine the most informative sub-band signal - 29 http://www.sjie.org
that will be used for identifying bearing defects and the DoD is defined as the ratio of spectral magnitudes at harmonics of the bearing’s characteristic frequency (i.e., BPFI, BPFO, BSF, and FTF) to their neighbours around the harmonics. To verify the efficacy of this DWPT-based sub-band analysis, we use three different seeded cylindrical roller bearings. The rest of this paper is organized as follows. Section 2 introduces a self-designed fault simulator for experiments as well as a data acquisition system and Section 3 details the DWPT-based sub-band analysis for fault detection of rolling element bearings. Section 4 then carries out efficacy validation of the methodology and Section 5 finally gives conclusions.
2 SELF-DESIGNED FAULT SIMULATOR AND DATA ACQUISITION SYSTEM A machinery fault simulator is used to conduct research on fault detection of rolling element bearings, as shown in Fig. 1. In addition, the three defective cylindrical roller bearings (FAG NJ206-E-TVP2) are used to verify the effectiveness of the developed approach, as depicted in Fig. 2: a bearing with a crack on its inner race (BCI), a bearing with a crack on its outer race (BCO), and a bearing with a crack on its roller (BCR). More details about defective bearings are presented in Table 1. To capture incipient symptoms in these three defective bearings, we use 2.5-second acoustic emission (AE) signals sampled at 1 MHz via a PCI-2 based system for each condition. This is mainly because AE is effective for early identifying bearing defects. According to [7], it can detect bearing defects before they appear on the bearing’s surface. To record AE signals, a general-purpose wide-band frequency AE sensor (WSα from Physical Acoustics Corporation) is used and attached at the top of the non-drive end bearing housing.
FIG. 1 (A) SELF-DESIGNED FAULT SIMULATOR AND (B) DATA ACQUISITION SYSTEM
FIG. 2 DEFECTIVE CYLINDRICAL ROLLER BEARINGS (A) BCI, (B) BCO, AND (C) BCR TABLE 1 DETAILED DESCRIPTION OF DEFECTIVE CYLINDRICAL ROLLER BEARINGS
Seeded bearing defects Revolutions-per-minute (RPM) Crack length
BCI
BCO
BCR
904
935
841
6 mm
Crack width
0.49 mm
Crack depth
0.5 mm
Characteristic frequency
BPFI=120.9 Hz
BPFO=78.9 Hz
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2xBSF=68.49 Hz
3 PROPOSED DWPT-BASED SUB-BAND ANALYSIS Fig. 3 illustrates the overall flow diagram of DWPT-based sub-band analysis, which ultimately yields twodimensional (2D) representation of degrees of defectiveness measured from multiple sub-band signals. In Fig. 3, fs indicates the sampling rate (fs=1 MHz in Section 2)
FIG. 3 FLOW DIAGRAM OF DWPT-BASED SUB-BAND ANALYSIS
As depicted in Fig. 3, 16 sub-band signals are achievable via decomposition and reconstruction processes of 4-level DWPT with a Daubechies mother wavelet (i.e., any of db1 from db45) and their envelope power spectra are then computed. To compute an envelope power spectrum for the given sub-band signal s(t), the Hilbert transform [6] is first performed: s t
s
1
d , t
(1)
Where, t is the time and s t is the Hilbert transform of s(t). Then, the analytical signal z(t) is defined as follows:
z t s t is t , i 1.
(2)
Finally, the envelope power spectrum of s(t) is obtained by squaring the magnitude of the fast Fourier transform of an envelope signal, in which the envelope signal is the magnitude of the complex-valued analytical signal |z(t)|. Given an envelope power spectrum, the next step in DWPT-based analysis is to measure the DoD. As stated previously, the DoD, defined as the ratio of spectral magnitudes at harmonics of BPFI, BPFO, or 2 BSF to those around the harmonics, is obtained as follows:
H DoD 20log iN1 N i 10 dB , j 1 N j h
(3)
fc
Where, Nh is the number of harmonics of the bearing’s characteristic frequency to be considered in the assessment of the DoD (i.e., Nh=3), Hi and Nfc are the spectral magnitude and the total number of frequency components at and around the ith harmonic of the bearing characteristic frequency, respectively, and Nj is the spectral magnitude of the jth frequency bin. If a defect occurs on the outer race of a bearing (i.e., BCO), high spectral magnitudes are in general observable at harmonics of BPFO (i.e., 79 Hz, 158 Hz, and 237 Hz) rather than at harmonics of BPFI or 2 BSF. Hence, the DoD in (3) can be used as a metric to assess how high spectral magnitudes at harmonics of the bearing’s characteristic frequency are achievable compared to their neighbouring spectral magnitudes. However, there is a possibility that the DoD for either BCI or BCR can be misevaluated since BFPI is closely located to multiple integers of 2 BSF, as presented in Table 1. To avoid this misevaluation, we use a new measure of the DoD (called “N-DoD”) and a NDoD is measured per failure, as follows:
DoDBCI DoD BCI N-DoDBCI DoDBCI , DoD BCO DoD BCR DoDBCO DoDBCO N-DoDBCO DoD BCO , and DoD BCI DoD BCR DoDBCR DoDBCR N-DoDBCR DoD BCR , DoD BCI DoD BCO - 31 http://www.sjie.org
(4)
Where, DoDBCI, DoDBCO, and DoDBCR are values of the DoD measured by using spectral magnitudes at and around BPFI, BPFO, and 2 BSF, respectively. According to (4), a high N-DoDBCI can be interpreted as that relatively high spectral magnitudes (meaning explicit symptoms of BCI) are revealed at harmonics of BPFI. In summary, the NDoD can be successfully used for determining the most informative sub-band signal.
4 EXPERIMENTAL RESULTS As the result of the DWPT-based sub-band analysis, we obtain 2D representation of the percentage of N-DoDBCI, NDoDBCO, and N-DoDBCR, respectively, as illustrated in Fig. 4.
FIG. 4 2D REPRESENTATION OF THE PERCENTAGE OF THE N-DODBCI (LEFT), N-DODBCO (MIDDLE), N-DODBCR (RIGHT)
An interesting observation in Fig. 4 is that high N-DoDBCO is mainly measured in low-frequency sub-band signals, whereas high N-DoDBCI is yielded in high-frequency sub-band signals. This is highly correlated with signal attenuation. In general, as we capture AE signals for BCR, signal attenuation occurs much more rapidly due to the greater distance from the source compared to BCO. As a consequence, intrinsic information about BCI can exist relatively in higher frequency sub-band signals, resulting in an opposite pattern in N-DoDBCO distribution. This causes a sub-band selection problem because any of these bearing defects can randomly occur. That is, it is necessary to select a sub-band signal involving intrinsic information about all of these bearing defects. To address this issue, we modify the 2D representation based on the N-DoDmodified, defined as: N-DoDmodified
Where, SN-DoD and DN-DoD
S N-DoD , DN-DoD
(5)
N-DoDBCI N-DoDBCO N-DoDBCR 3
N-DoDBCI N-DoDBCO + N-DoDBCO N-DoDBCR + N-DoDBCR N-DoDBCI 3
,
respectively. In (5), the N-DoDmodified is defined as the ratio of SN-DoD and DN-DoD, where SN-DoD is the average of the N-DoDs for all the bearings (i.e., BCI, BCO, and BCR) and DN-DoD is the average of N-DoD absolute differences. Based on the N-DoDmodified, the DWPT-based sub-band analysis determines the most informative sub-band signal with a Daubechies mother wavelet, as shown in Fig. 5. That is, we use the sub-band13 by 4-level DWPT with db1 for identifying incipient symptoms in cylindrical roller bearings. To verify the efficacy of the presented methodology, we compare envelope power spectra obtained by our and Jiang’s methods. In 2013, Jiang et al. introduced a bearing defect diagnosis methodology that accumulates envelope power spectra calculated from all of sub-band signals by 4-level DWPT [6]. As illustrated in Fig. 6, despite the fact that Jiang’s method shows satisfactory performance for identifying defects in BCI and BCO, it suffers from highly dominant low-frequency components (see Fig. 6 for BCR) due to its nature that accumulates all envelope power spectra computed from sub-band signals. On the other hand, our methodology can be a promising candidate for addressing this issue by exploiting an envelope power spectrum computed from the most informative sub-band signal. - 32 http://www.sjie.org
FIG. 5 2D REPRESENTATION OF THE PERCENTAGE OF THE N-DODMODIFIED
FIG. 6 COMPARISON OF ENVELOPE POWER SPECTRA OBTAINED BY THE DEVELOPED (TOP) AND THE JIANG’S (BOTTOM) METHODS
5 CONCLUSIONS The fact that symptoms of bearing defects can be revealed anywhere in frequency domain calls for frequency analysis. To deal with this issue, we developed DWPT-based sub-band analysis, which determines the most informative sub-band signal that will be used for early identifying bearing defects. This analysis yielded satisfactory results for three seeded bearing defects (i.e., BCI, BCO, and BCR), showing high spectral magnitudes (explicit symptoms) at harmonics of BPFI for BCI, BPFO for BCO, and 2 BSF for BCR, respectively. In particular, the DWPT-based sub-band analysis was more effective than the Jiang’s DWPT-based envelope analysis, especially resulting in 7% higher N-DoDs for BCO and BCR. The key contribution in the developed DWPT-based analysis was to measure the degree of defectiveness. Although the presented metric (i.e., N-DoD) was effective for assessing the degree of defectiveness in each sub-band signal, it needs enhancement. This was because sidebands (explicit symptoms for BCI and BCR) were not properly considered as their symptoms in calculation of the degree of defectiveness. In addition, sub-band analysis should meet real-time requirements. Unfortunately, however, the presented sub-band analysis is computationally cumbersome. Hence, we will find a way to accelerate it via parallel processing techniques that can exploit massive parallelism inherent in the analysis. - 33 http://www.sjie.org
ACKNOWLEDGMENT This research was supported by the National Research Foundation of Korea funded by the Ministry of Education, Science, and Technology of Korea under grant NRF-2013R1A2A2A05004566 and NSF-2015K2A1A2070866, by the over 100 CALCE members of the CALCE Consortium, and by the NSFC under grant number 71420107023.
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Lacey, S. J. “An Overview of Bearing Vibration Analysis.” Maintenance & Asset Management 23 (2008): 32-42. Accessed January 19, 2016
[2]
Smith, P. “Siemens Wind Makes Quarterly Loss.” Wind Power Monthly, May 7, 2014. Accessed January 19, 2016. http://www.windpoweroffshore.com/article/1293200/siemens-wind-makes-quarterly-loss
[3]
Bediaga, I., Mendizabal, X., Arnaiz, A., and Munoa, J. “Ball Bearing Damage Detection Using Traditional Signal Processing Algorithms.” IEEE Instrumentation and Measurement Magazine 16 (2013): 20-25. Accessed January 22, 2016. doi: 10.1109/MIM.2013.6495676
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Kang, M., Kim, J., Wills, L. M., and Kim, J. –M. “Time-Varying and Multiresolution Envelope Analysis and Discriminative Feature Analysis for Bearing Fault Diagnosis.” IEEE Transactions on Industrial Electronics 62 (2015): 7749-7761. Accessed January 19, 2016. doi: 10.1109/TIE.2015.2460242
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Borghesani, P., Ricci, R., Chatterton, S., and Pennacchi, P. “A New Procedure for Using Envelope Analysis for Rolling Element Bearing Diagnostics in Variable Operating Conditions.” Mechanical Systems and Signal Processing 23 (2013): 23-35. Accessed January 19, 2016. doi: 10.1016/j.ymssp.2012.09.014
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Jiang, R., Liu, S., Tang Y., and Liu, Y. “A Novel Method of Fault Diagnosis for Rolling Element Bearings Based on the Accumulated Envelope Spectrum of the Wavelet Packet.” Journal of Vibration and Control 21 (2015): 1580-1593. Accessed January 22, 2016. doi: 10.1177/1077546313499391
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Widodo, A., Kim, E. Y., Son, J. –D., Yang, B. –S., Tan, A. C. C., Gu, D. –S., Choi, B. –K., and Mathew, J. “Fault Diagnosis of Low Speed Bearing Based on Relevance Vector Machine and Support Vector Machine.” Expert Systems with Applications 36 (2009): 7252-7261. Accessed January 22, 2016. doi: 10.1016/j.eswa.2008.09.033
AUTHORS 1
Myeongsu Kang received the B.E. and
M.S. degrees in computer engineering and information technology and the Ph.D. degree in electronical, electronic, and computer engineering from the University of Ulsan, Ulsan, South Korea, in 2008, 2010, and 2015, respectively.
Atlanta, GA, USA, in 2005. He is currently a Professor with the Department of IT Convergence and also a Vice-President of the Foundation for Industry Cooperation at the University of Ulsan, Ulsan, South Korea. His research interests include multimedia-specific processor architecture, fault diagnosis and condition monitoring, parallel processing, and embedded systems.
He is currently a Research Associate with the Center for Advanced Life Cycle Engineering, University of Maryland, College Park, MD, USA. His current research interests include
Prof. Kim is a member of the Institute of Electrical and Electronics Engineers. 3
Rui Peng received the B.S degree in
data-driven prognostics and health management using signal processing, data mining, and machine learning techniques, and
Physics from University of Science &
high-performance computing.
Technology of China, Hefei, Anhui, China, in 2007, and the Ph. D degree in
2
Jong-Myon Kim received the B.S.
Industrial & Systems Engineering from
degree in electrical engineering from the
National
Myongji University, Yongin, South Korea,
University
of
Singapore,
Singapore, in 2011.
in 1995, the M.S. degree in electrical and computer engineering from the University
He is currently an Associate Professor in Donlinks School of
of Florida, Gainesville, FL, USA, in 2000,
Economics
and the Ph.D. degree in electrical and
Technology Beijing, Beijing, China. His research interests
computer engineering from the Georgia Institute of Technology,
include system reliability, maintenance, and defense strategies.
- 34 http://www.sjie.org
&
Management,
University
of
Science
&
He has published 30 SCI Journal papers.
Advanced Life Cycle Engineering, University of Maryland, College Park, MD, USA, which is funded by over 150 of the
3
Xiaoyang Ma received the B.S. degrees
world’s leading electronics companies at more than U.S. $6
in information and computing science in
million/year. He is also a George E. Dieter of applied
2011 and is currently a PhD candidate in Donlinks
School
of
Economics
mathematics with the University of Maryland. He has authored
&
more than 20 books on electronic product development, use, and
Management, University of Science & Technology
Beijing.
Her
supply chain management and over 500 technical articles.
research
interests include reliability, maintenance
Prof. Pecht is a Fellow of the Institute of Electrical and
and stochastic processes.
Electronics Engineers.
1
Michael Pecht received the M.S. degree
in electrical engineering and the M.S. and Ph.D. degrees in engineering mechanics from
the
University
of
Wisconsin-
Madison, WI, USA. He is the Founder of the Center for
- 35 URL