Morales Perez2018
Morales Perez2018
Morales Perez2018
Abstract— A methodology for automatic incipient broken rotor of IMs requires the maintenance programs to be accurate
bar detection in induction motors (IMs) is presented. Sparse since faults during an operation could lead to catastrophic
representations of signals are applied as a diagnosis technique. effects, generating time, and economic losses. A common fault
The novelty of this technique is that it can analyze the fre-
quency spectra from vibration signals even when the differences in IMs involves broken rotor bars (BRBs). This fault can
among signals are small. This representation allows decompos- be attributed to different causes, ranging from manufacturing
ing or reconstructing signals through a trained dictionary that defects to operating environments and conditions, among
has learned the features of one specific group/class. The main others. Regardless of the cause, a BRB is an important fault
feature of this paper is the use of overcomplete dictionaries that should be dealt at an early stage; otherwise, the damage
trained from sets of signals with faults to be detected. In this
way, trained dictionaries perform the decomposition of signals can gradually increase until the IM becomes totally dam-
using the orthogonal matching pursuit (OMP) algorithm. The aged. In addition, bearing faults, ruptures in other bars, and
decomposition is evaluated and classified by error-based criteria increases in electrical consumption are common, and these can
and a majority decision classifier, allowing the detection of early contribute to a rapid and dramatic decrease in the structural
damage, ranging from 1 mm to one broken bar. The detection integrity of IMs.
is performed by the decomposition of vibration signals from
three axes (x, y, and z) of IMs under three load conditions A BRB is one of the most difficult faults to detect.
(unloaded, half loaded, and three-fourths loaded) and different As discussed earlier, this fault may cause other anomalies in
levels of damage (healthy or 0 mm, 1–9 mm, and one broken bar). IMs. One of the most frequently used detection techniques
These signals are processed by the Fourier transform and the is the motor current signal analysis (MCSA) [1]–[6]. Many
spectrum obtained is evaluated by the OMP algorithm. Finally, techniques based on measuring stator current have been pro-
the retrieved information is evaluated and the diagnosis is given.
All algorithms are developed in MATLAB software and the posed. Some of these include resampling [7], principal com-
detection accuracy is higher than 90% for damages as small ponent analysis [8], empirical mode decomposition [9]–[11],
as 1 mm. zero-sequence current [12]–[14], generalized likelihood ratio
Index Terms— Algorithm, broken rotor bar (BRB), fault detec- test [15], filtered parks vector approach and filtered extended
tion, induction motor (IM), orthogonal matching pursuit (OMP), park’s vector approach [16], frequency estimators [17]–[19],
signal classification, sparse representation, vibration signal. fuzzy logic [20], mutual inductances analysis [21], principal
slot harmonics tracking [22], Prony method [23], and rotor
I. I NTRODUCTION current analysis [24]. All of these use spectral information
obtained by fast Fourier transform (FFT) [25] or by one of its
N OWADAYS induction motors (IMs) are frequently used
in the industry for a number of reasons, including their
low cost, reliability, and fast installation. The extensive use
variants [26] in order to analyze information in the frequency
domain and to detect the fault.
Another technique used instead of the FFT to obtain
Manuscript September 9, 2017; revised January 23, 2018; accepted the fault diagnosis in the frequency domain is the dis-
February 22, 2018. The Associate Editor coordinating the review process was
Dr. Yuhua Cheng. (Corresponding author: Jose Rangel-Magdaleno.) crete wavelet transform [27]–[30] or Hilbert transform [31].
C. Morales-Perez and J. Rangel-Magdaleno are with the Electronics Nevertheless, the diagnosis of BRBs is not exclusively limited
Department, National Institute for Astrophysics, Optics and Electronics, to the stator current analysis. The external magnetic field
Puebla 72840, Mexico (e-mail: carlosj.morales@inaoep.mx; jrangel@
inaoep.mx). analysis [32], air-gap torque analysis [33], vibrations signals
H. Peregrina-Barreto is with the Computer Science Department, National analysis (VSA) [34]–[38], or infrared data analysis [39] can
Institute for Astrophysics, Optics and Electronics, Puebla 72840, Mexico also be applied. Although these techniques do detect BRBs,
(e-mail: hperegrina@inaoep.mx).
J. P. Amezquita-Sanchez and M. Valtierra-Rodriguez are with the ENAP- their diagnoses are limited to either one or two broken bars
Research Group, Autonomous University of Queretaro, Santiago de Querétaro and, only in very accurate cases, to partial damage [19], [40].
76806, Mexico (e-mail: jamezquita@uaq.mx; martin.valtierra@enap-rg.org). The signal decomposition analysis (SDA) [41] offers an
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org. alternative to detect accurate characteristics of the sig-
Digital Object Identifier 10.1109/TIM.2018.2813820 nals that are difficult to detect by using other techniques.
0018-9456 © 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
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MORALES-PEREZ et al.: INCIPIENT BRB DETECTION IN IMs USING VIBRATION SIGNALS AND THE OMP ALGORITHM 3
where Dk† ∈ Rk×n is the Moore–Penrose pseudoinverse argmin X − Dα s.t. α0 ≤ k (5)
α,D
of Dk . Then, under high-performance conditions r → 0,
satisfying (4). This means that the sparse representation of where X ∈ R M×n is the training set with M signals, D is
a signal can be found. the dictionary to train, α is the sparse vector, and α0 is
the pseudonorm 0 . The K-SVD applies a process known
as dictionary learning [41], which adapts a dictionary to
Algorithm 1 OMP
recognize the particular features from the X set.
Require: D, x, k, and .
Ensure: αk , Sk , rk , and e.
Algorithm 2 K-SVD
1: r0 = x, D0 = ∅, and j = 0.
2: while ( j < k and s j = s j −1 ) do
Require: D0 , X, and K .
3: j = j +1 Ensure: Dk .
1: for k = 1 to K do
4: s j = argmax |r j −1 di |
i=1,...,m 2: Use OMP to obtain α
5: S j = S j −1 ∪ s j 3: for j = 1 to m do
6: D j = [D j −1 ds j ] 4: ω = {l ∈ 1, 2, . . . , M, αk [ j, l] = 0}
7: argmi nx − D j α j 5: αω [ j, ω] = 0
αj
8: rj = x − Djαj 6: R = X ω − Dk αω
9: end while 7: [U V ] = SV D(R)
rk
10: e = x
8: d j ∈ Dk = u 1
9: α j ∈ αk = v 1 (1, 1)
10: end for
The steps to obtain the sparse representation of a signal are 11: end for
described in Algorithm 1. First, it is necessary to provide a
dictionary (D), the signal to decompose (x), and the maximum The steps to perform the K-SVD are shown in Algorithm 2.
number of atoms (k) to decompose the signal, and then to This process uses an initial dictionary of random values D0 ,
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Fig. 4. Methodology. (a) Used for the dictionary training process. (b) Used for the SDA.
MORALES-PEREZ et al.: INCIPIENT BRB DETECTION IN IMs USING VIBRATION SIGNALS AND THE OMP ALGORITHM 5
Fig. 6. IM setup. (a) Rotor damage. (b) Coupling for mechanical load.
TABLE I TABLE II
V IBRATION S IGNALS P ER A XIS AVERAGE P ERCENTAGES OF C LASSIFICATIONS FOR THE x-A XIS
TABLE III
AVERAGE P ERCENTAGES OF C LASSIFICATIONS FOR THE y-A XIS
MORALES-PEREZ et al.: INCIPIENT BRB DETECTION IN IMs USING VIBRATION SIGNALS AND THE OMP ALGORITHM 7
TABLE V
AVERAGES P ERCENTAGES OF C LASSIFICATIONS FOR M AJORITY D ECISION
Fig. 10. ROC curves for classifier under different load conditions and based
on (a) 1 and (b) 2 .
TABLE VI
Q UALITATIVE C OMPARISON B ETWEEN THE P ROPOSED M ETHODOLOGY P ERFORMANCE AND
THE O THER P REVIOUS M ETHODS P RESENTED IN THE L ITERATURE
where an effectiveness percentage of 99% is obtained; never- when it is supported by a classifier such as the majority
theless, the methodology proposed in this paper is capable of decision (Algorithm 3), a better classification is achieved.
identifying the BRB fault in an earlier stage to different load On the other hand, as the proposed methodology makes use
levels: 0%, 50%, and 75%, i.e., from 1 mm to the consoli- of the FFT, the analysis has to be focused on the stationary
dation of the failure, making it a more attractive tool for the vibration signals, else the accuracy of the detection is not
industry. guaranteed. Although the obtained of a sparse representation
is a time-consuming process given that the dictionaries may
VII. C ONCLUSION have higher dimensions (overcomplete dictionaries), the results
A methodology to detect BRBs based on sparse representa- show that the diagnosis is obtained rapidly (1.463 s) if we take
tion was presented. The accuracy for detecting faults from into account the amount of data analyzed.
1 to 10 mm in an unloaded condition, a one-half loaded With the OMP and the K-SVD algorithms, early BRBs,
condition, and a three-fourths loaded condition (90%, 96%, starting from 1 mm, are possible to detect. The results
and 94%, respectively) are high, mainly considering the chal- make possible to start a hardware implementation design.
lenge that represents the detection of a partially cracked bar This methodology will be performed and tested on field-
(from 1 mm) using both vibration signals and loads lower than programmable gate array in a future work.
the rated load. Also, the efficiency of the sparse representation
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MORALES-PEREZ et al.: INCIPIENT BRB DETECTION IN IMs USING VIBRATION SIGNALS AND THE OMP ALGORITHM 11
Juan Pablo Amezquita-Sanchez received the B.Sc. Martin Valtierra-Rodriguez (M’14) received
and M.Sc. degrees in electronic engineering from the B.E. degree in mechatronics engineering and
the University of Guanajuato, Guanajuato, Mexico, the M.E. degree in electrical engineering from the
in 2007 and 2009, respectively, and the Ph.D. University of Guanajuato, Guanajuato, Mexico,
degree in mechatronics from the Autonomous Uni- in 2008 and 2010, respectively, and the Ph.D.
versity of Queretaro, Santiago de Querétaro, Mexico, degree in mechatronics from the Autonomous
in 2012. University of Queretaro, Santiago de Querétaro,
From 2013 to 2014, he was a Post-Doctoral Mexico, in 2013.
Visiting Scholar with The Ohio State University, He is currently a Professor with the Faculty of
Columbus, OH, USA. He is currently a Full Engineering, Autonomous University of Queretaro.
Time Professor with the Faculty of Engineering, His current research interests include power quality
Autonomous University of Queretaro. He has authored or co-authored in the analysis, expert systems, and signal processing.
areas of structural health monitoring, signal processing, and mechatronics. Dr. Valtierra-Rodriguez is a member of the Mexican National Research
Dr. Amezquita-Sanchez is a member of the Mexican National Research System (Sistema Nacional de Investigadores), level 1.
System (Sistema Nacional de Investigadores), level 1.