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Current Frequency Spectral Subtraction and Its
Contribution to Induction Machines’ Bearings Condition
Monitoring
El Houssin El Bouchikhi, Vincent V. Choqueuse, Mohamed Benbouzid
To cite this version:
El Houssin El Bouchikhi, Vincent V. Choqueuse, Mohamed Benbouzid. Current Frequency Spec-
tral Subtraction and Its Contribution to Induction Machines’ Bearings Condition Monitoring. IEEE
Transactions on Energy Conversion, Institute of Electrical and Electronics Engineers, 2012, 28 (1),
pp.135 - 144. �10.1109/TEC.2012.2227746�. �hal-00787316�
1
Current Frequency Spectral Subtraction and its
Contribution to Induction Machines Bearings
Condition Monitoring
El Houssin El Bouchikhi, Vincent Choqueuse, Member, IEEE and Mohamed Benbouzid, Senior Member, IEEE
Abstract—Induction machines are widely used in industrial
applications. Safety, reliability, efficiency and performance are
major concerns that direct the research activities in the field of
electrical machines. Even though the induction machine is very
reliable, many failures can occur such as bearing faults, air-gap
eccentricity and broken rotor bars. The challenge is therefore to
detect them at an early stage in order to prevent breakdowns.
In particular, stator current-based condition monitoring is an
extensively investigated field for cost and maintenance savings.
In this context, this paper deals with the assessment of a
new stator current-based fault detection approach. Indeed, it
is proposed to monitor induction machine bearings by means
of stator current spectral subtraction, which is performed using
Short Time Fourier Transform or Discrete Wavelet Transform.
In addition, it is proposed a diagnostic index based on the
subtraction residue energy.
The proposed bearing faults condition monitoring approach is
assessed using simulations, issued from a coupled electromagnetic
circuits approach-based simulation tool, and experiments on a
0.75-kW induction machine test bed.
Index Terms—Induction machines, bearing fault, fault detec-
tion, signal processing, spectral subtraction.
NOMENCLATURE
ST FT Short-Time Fourier Transform;
DW T Discrete Wavelet Transform;
P SD Power Spectral Density;
[.]
−1
Matrix inverse;
[.]
T
Matrix transpose;
[I
r
] Rotor current vector;
[I
s
] Stator current vector;
[L
rr
] Rotor windings self and mutual inductances;
[L
rs
] Mutual inductances between rotor windings and stator
ones;
[L
sr
] Mutual inductances between stator windings and rotor
ones ;
[L
ss
] Stator windings self and mutual inductances;
[R
r
] Cage resistances matrix;
[R
s
] Diagonal matrix of stator phases resistances;
[V
s
] Stator voltage vector;
d
dθ
m
[.] The derivative with respect to the angular position;
d
dt
[.] The derivative with respect to time;
E.H. El Bouchikhi, V. Choqueuse and M.E.H. Benbouzid are with
the University of Brest, EA 4325 LBMS, Rue de Kergoat, CS 93837,
29238 Brest Cedex 03, France (e-mail: El-Houssin.Elbouchikhi@univ-brest.fr,
Vincent.Choqueuse@univ-brest.fr, Mohamed.Benbouzid@univ-brest.fr).
This work was supported by Brest M
´
etropole Oc
´
eane (BMO).
J Rotating masses inertia;
Γ
C
Load torque;
Ω Rotor mechanical speed;
θ
m
rotor angular position;
f Viscous friction coefficient;
f
s
Shaft rotation frequency;
f
bd
Bearing ball fault frequency;
f
c
Bearing cage fault frequency;
f
id
Bearing inner race fault frequency;
f
od
Bearing outer race fault frequency;
D Bearing pitch diameter;
α Contact angle;
d Roller diameter;
n Roller number.
I. INTRODUCTION
Nowadays, induction machines are widely used in industrial
applications. In fact, induction machines are still the most
important rotating electric machines in industry mainly be-
cause of their low price, ruggedness, efficiency and reliability.
Despite its robustness, this machine can be subjected to various
failures that can broadly be classified as follows [1]:
- Stator faults; opening or shorting of one or more of a
stator phase winding;
- Broken rotor bar or cracked rotor end-rings;
- Static and/or dynamic air-gap irregularities;
- Bent shaft;
- Bearing and gearbox failures.
The distribution of these failures within the machine subassem-
blies is reported in many reliability survey [2], [3]. Depending
on the type and size of the machine, bearing faults distributions
among all faults vary from 40% to 90% from large to small
machines.
Therefore, a permanent condition monitoring of the induc-
tion machine is of high interest since it contributes to minimize
the downtime and improves its reliability and availability.
Early diagnosis of these faults is an extensively investigated
field for cost and maintenance savings. Traditionally, the
machine state can be supervised using different strategies
such as vibration monitoring, temperature measurements, flux
monitoring, model and artificial intelligence based techniques
[4], [5]. Motor current signature analysis for incipient fault
detection has received much attention in recent years [2].
These techniques are based on the use of three-phase currents
that are already measured in the drive system for other
purposes such as control and protection.
2
Previous works have focused on the use of signal processing
tools for stator current post-processing in order to detect a
characteristic fault frequencies in both stationary (steady-state)
and non-stationary (transient, variable speed, load oscillation,
etc.) operating conditions. In stationary environment, most
studies perform stator current spectral analysis using the
periodogram and its extensions based on the Fourier Transform
[1], [6]–[8]. In order to improve the frequency resolution
many high resolution techniques have been used such as the
MUSIC algorithm [9], [10]. In non-stationary conditions, time-
frequency [11]–[13] and time scale [14] techniques were pro-
posed. Although these techniques lead to good representations,
they require a feature extraction and a classification steps in
order to distinguish a faulty machine from a healthy one and
afterwards measure fault severity.
This paper proposes then a fault detection technique that
takes into account some of the above discussed aspects [15].
The proposed technique is based on stator current frequency
spectral subtraction. More precisely, the proposed approach
is based on the ST FT and allows to directly derive a fault
criterion. The fault criterion is of high interest since it conveys
the information about the presence of the fault and its severity.
The major contributions of this paper are:
- An intuitive stator current-based fault detection approach.
- A reliable and robust fault criteria for bearing faults
detection.
It is organized as follows: The proposed technique is presented
in section II. In section III, a short overview of bearing fault
types and their effects on induction machine stator current
is given. Then, the performances of the proposed approach
on simulated data, issued from a coupled electromagnetic
circuits approach-based simulation tool, are discussed. Finally,
experimental results for several bearing faults are reported in
section IV to validate the feasibility of the STFT-based spectral
subtraction, which is compared with DWT−based spectral
subtraction. Section V concludes this paper and gives some
prospects for further investigations.
II. SPECTRAL SUBTRACTION
A. Fault Detection Algorithm
Spectral subtraction is broadly used in audio data pro-
cessing in order to remove acoustic noise and for speech
enhancement [16]–[18]. Up to now, for fault detection, the
spectral subtraction was only used as a denoising method. This
preprocessing step allows to improve robustness against noise
of failure indicators in electrical drives [19], [20]. Afterwards,
advanced signal processing techniques are used to detect
electrical machine abnormal operating conditions. Figure 1
shows flowcharts illustrating the main differences between
the classical technique [20] (Fig. 1(a)) and the proposed one
(Fig. 1(b)). In fact, in this paper, we propose to use spectral
subtraction as the main tool for induction machines fault
diagnosis. In particular, it is used for bearing faults detection
using stator current. The proposed technique is well-suited for
steady-state and constant speed induction machine operating
conditions. It is only applied on stationary signals which
means time independent frequency content. In this context, the
proposed strategy allows the fault effect extraction from the
stator current by subtracting the PSD of the healthy machine
from the faulty machine one for each time step.
NOISE SIGNAL
Learning noise
spectrum
MACHINE CURRENT
Computing current
spectrum
−
Subtraction
Denoised signal
Detection
algorithm
Fault indicators
Decision
algorithm
MACHINE STATE
FAULT DETECTION
(a) Spectral subtraction for denoising aims.
HEALTHY MACHINE
CURRENT
Computing a
spectrum
MACHINE CURRENT
ACQUISITION
Computing a
spectrum
−
Subtraction
Fault signature
Fault indicators
computation
Fault indicators
Decision
algorithm
MACHINE STATE
FAULT DETECTION
(b) The proposed approach.
Fig. 1 . Spectral subtraction flowchart for fault detection approach.
The proposed technique is based on the following steps:
1) Spectral estimation of the healthy signal x
h
[n] (baseline
data) based on the (ST FT ). The ST FT of x
h
[n] is
3
Stator
Current
Normalization
Segmentation
windowing
Sensors or estimation
based on stator current
Operating
condition
FFT
Spectral
subtraction
Phase
Baseline
data
Combine phase
and magnitude
Fault Detection
Criteria r[n]
ST F T
x(t) x
n
(t)
Amplitude
Searching the appropriate data
Fig. 2 . Block diagram of the proposed FFT-based spectral subtraction faults detection algorithm.
defined as
X
h
(m, ω) =
N−1
X
n=0
x
h
[n]w[n − m]e
−jωn
(1)
where w[n] is the window function and N is the number
of samples. m ∈ Ω corresponds to the time index.
Finally, the spectrum of the healthy signal is computed
by averaging the ST FT with respect to time i.e.(2).
µ(ω) =
1
|Ω|
X
m∈Ω
|X
h
(m, ω)| (2)
where|Ω|denotes the cardinal of the set Ω. This first
step is equivalent to the computation of the Welch
periodogram [21].
2) Spectral estimation of the supervised machine stator
current signal x
s
[n] using ST FT (3). The ST FT of
x
s
[n] is defined as
X
s
(m, ω) =
M−1
X
n=0
x
s
[n]w[n − m]e
−jωn
(3)
where w[n] has been defined previously and M is the
number of samples.
3) Subtraction of the current spectrum of the healthy case
from the monitored machine current spectrum at each
time m (4);
R(m, ω) = ||X
s
(m, ω)| − µ(ω)| e
ϕ(m,ω)
∀m (4)
where ϕ(m, ω) = ∠(X
h
(m, ω)) and ∠ is the angle of
the complex number X
h
.
4) Performing the inverse ST FT to reconstruct the tem-
poral signal r[n] from R(m, ω) with the Overlap and
Add algorithm [22].
5) Computation of the fault indicator.
The spectral subtraction for fault detection is an easy way
to extract the fault effect on the stator current. Figure 2
shows then the proposed FFT-based spectral subtraction faults
detection algorithm. It clearly illustrates the importance of
the operating condition measurement in order to chose the
appropriate healthy state condition signal from the database.
Ones the healthy state signal is obtained, it is subtracted from
the acquired signal in order to diagnose the machine condition.
Furthermore, the proposed approach is simple to implement
since it is based on the Fourier transform which makes it very
attractive for industrial applications. In fact, most DSP-boards
include functions for DFT computation. Moreover, the DFT
can be efficiently computed using the FFT.
The next subsection deals with the criteria chosen as fault
indicator.
B. Fault Detection Criteria
For an automatic fault detection, we propose two criteria
based on the results of the stator current spectral subtraction.
These criteria are the fault signature energy E and the fault
signature energy to healthy case energy ratio R.
(
E =
1
N
P
N−1
n=0
|r[n]|
2
R =
P
N −1
n=0
|r[n]|
2
P
N −1
n=0
|x
h
[n]|
2
(5)
In addition, to highlight the machine healthy state, the above
criteria have also been used to estimate the fault severity
degree.
Figure 3 summarizes the proposed fault severity estimation
algorithm.
III. SIMULATION RESULTS
This section reports on the performance of the proposed
approach on simulated data. Simulation were performed using
a coupled electromagnetic circuits induction machine model.
In particular, eccentricity fault introduced by bearing failures
have been simulated and stator current signal has been sampled
and processed according to the above presented algorithm.
A. Coupled Electromagnetic Circuits Machine Modeling
Briefly
The coupled electromagnetic circuits approach combined
with the arbitrary reference frames theory is the theoreti-
cal groundwork for modeling induction machines [24]. An
induction machine is considered as a highly symmetrical
electromagnetic system. Any fault will therefore induce a
certain degree of asymmetry [25]. In this context, a Matlab-
Simulnik
R
-based tool of faulty induction machines has been
developed to generate a fault database and therefore allow
testing different stator current-based fault detection technique
[26].
In this modeling context, the representation of an induction
machine with a cage rotor is fundamentally the same as one
4
BEGIN
Learn the healthy induction machine stator current
spectrum based on (1) and (2)
Extract M-data samples x[n]
from the monitored induction machine.
Compute the stator current ST FT
using (3).
Perform the spectral subtraction
with (4).
Perform the Overlap and Add algorithm
to rebuild the temporal residue signal [23].
Compute the criteria
with (5)
STOP
Fig. 3 . Spectral subtraction-based fault severity criteria algorithm.
with a phase wound rotor, where it is assumed that the cage
rotor can be replaced by a set of mutually coupled loops as
shown by Fig. 4.
The dealt with approach is based on the induction machine
analytical models. Inductances are calculated from the actual
geometry and winding layout of the machine.
The induction machine electrical and mechanical equation
system is given by (6).
d
dt
[I] = −[L]
−1
[R] + Ω
d
dθ
m
[L]
[I] + [L]
−1
[V ]
d
dt
Ω =
1
2J
[I]
T
d
dθ
m
[L]
[I] −
f
J
Ω −
1
J
Γ
C
d
dt
θ
m
= Ω
(6)
where:
[V ] =
[V
s
]
[0]
[I] =
[I
s
]
[I
r
]
[R] =
[R
s
] [0]
[0] [R
r
]]
[L] =
[L
ss
] [L
sr
]
[L
rs
] [L
rr
]
All the relevant inductances matrices [L] are calculated using
the winding function method [27].
B. Bearing Faults Detection
1) Bearing Fault Impact on Induction Machine Stator Cur-
rent: Vibration analysis is one of the most extended condition
R
b
L
b
L
e
R
e
i
R
q
-
2
i
R
q
-1
i
R
q
i
R
1
i
R
2
i
R
3
i
e
L
e
L
e
L
e
L
e
L
e
L
e
L
e
L
e
L
e
L
e
L
e
R
e
R
e
R
e
R
e
R
e
R
e
R
e
R
e
R
e
R
e
R
e
R
b
R
b
R
b
R
b
R
b
R
b
L
b
L
b
L
b
L
b
L
b
L
b
Fig. 4 . Equivalent circuit of a cage rotor showing rotor loop and
circulating end-ring current.
Cage
Outer race
Ball
Inner race
α
D
d
Fig. 5 . Bearing structure with main dimensions.
monitoring techniques for bearing fault diagnosis. Bearings
defects have been typically categorized as distributed or local.
Local defects cause periodic impulses in vibration signals.
Amplitude and frequency of such impulses are determined by
shaft rotational speed, fault location, and bearing dimensions
(Fig. 5). The frequencies of these impulses are given in (7).
f
c
=
f
s
2
1 −
d
D
cos(α)
f
bd
=
D
d
f
s
1 −
d
2
D
2
cos
2
(α)
f
id
=
nf
s
2
1 −
d
D
cos(α)
f
od
=
nf
s
2d
1 −
d
D
cos(α)
(7)
In [28], [29], it has been demonstrated that the characteristic
bearing fault frequencies in vibration can be reflected on stator
currents. Since ball bearings support the rotor, any bearing
defect will produce a radial motion between the rotor and the
stator of the machine (air-gap eccentricity) which may lead
to anomalies in the air-gap flux density. As the stator current
