Toward Embedded Broken Rotor Bars
Detection in Induction Machines
Daniele Angelosante, Abhisek Ukil, and Andrea Andenna
ABB Corporate Research Center
Integrated Sensor Systems
Dättwil, Baden, Segelhofstrasse 1K, 5405
Emails: daniele.angelosante@ch.abb.com, abhisek.ukil@ch.abb.com, andrea.andenna@ch.abb.com
Abstract—Low-complexity broken rotor bar detection methods
amenable to an embedded implementation are dealt in this paper.
A novel method based on zoom-FFT has been developed, and
compared to an existing method based on zero-crossing time
(ZCT) processing using real data from faulty and healthy motors.
Numerical tests show that both methods can reliably detect
broken rotor bars. ZCT processing entails better performance
than zoom-FFT for low load and low current, but zoom-FFT is
easier to tune, thus being preferable for embedded systems such
as motor controllers, softstarters and drives that have to operate
with a vast variety of motors.
I. I NTRODUCTION
Induction machines (IM) are the industry workhorses due
to their robustness and reliability, and are responsible for consumption of almost half of the generated electrical power [11].
Therefore, IM diagnostic and monitoring has sparked a lot of
attention since more than two decades. Operators are asked
to minimize the maintenance costs and avoid unscheduled
downtimes to due IM faults. In fact, approximately 10% of
the total faults in squirrel cage IMs is due to broken rotor
bars (BRB) and end-rings [11]. The major causes of BRBs
are:
c1)
Direct online starting duty cycles;
c2)
Pulsating mechanical loads; and
c3)
Manufacturing defects.
While c1) and c3) can be limited by resorting to motor
softstarters, and improved production processes, respectively,
c2) is unavoidable.
After two decades of intensive research activity, it is widely
accepted that faults due to BRBs can be detected at an early
stage using online, non-invasive techniques based of motor
current signature analysis (MCSA) [11]. The crux of classical
MCSA for BRB detection is [11]:
• A current transformer to sense the absorbed current
(typically one phase only);
• A spectrum analyzer (and, eventually, a PC for further
processing); and
• An operator that, basing on judiciously measured spectral
signatures, decides whether the motor is healthy or faulty.
Typically, the difference (in dB) between the peak of the
spectrum at the rated frequency and some peaks at selected
frequencies that are due to BRBs is evaluated. For healthy
motors, it is expected that this difference is large (e.g., larger
than 45-50 dB), while, for faulty motors, this difference
decreases as the side peak amplitudes are expected to increase
(e.g., the difference with the main peak might become less
than 35-40 dB) [6]. For motor under low load conditions,
performing this analysis is challenged by the fact that the side
peaks due to BRBs are in the proximity of the main peak at the
rated frequency, therefore, computationally intensive spectral
analysis is required.
Recently, advanced signal processing techniques have been
applied to overcome the spectral resolution limitations of
classical fast Fourier transform (FFT). In [5], Prony’s analysis
is applied to improve spectral resolution and shorten the
analysis time. Parametric super-resolution spectral methods
have been applied as well [1], [2] along with non-parametric
methods based on Wavelet, neural networks, and support
vector machines [10]. An excellent review of signal processing
techniques for condition monitoring in IMs is given in [8].
One limitation of most of the existing techniques for BRB
detection in IMs is the computational complexity and, thus, the
high cost required, which makes MCSA practical for larger
IMs only. Indeed, the cost of an IM can be as low as few
hundreds USD, which makes classical conditioning monitoring
often cost-ineffective. These motors can be substituted periodically or if the operator notices un-expected vibrations and
acoustic noise. Nevertheless, the lack of condition monitoring
increases the risk in hazardous environment since BRBs can
degrades into more severe faults and also produce sparking.
However, a significant percentage of IMs is equipped with
low-cost motor controllers, softstarters, and drives which,
for different applications (e.g., thermal overload protection),
posses a current sensor. The goal of this paper is to propose
new low-complexity BRB detection methods that can be
embedded in these low-cost devices, which posses a low-end
microcontroller and/or digital signal processor (DSP), and a
limited memory.
To this end, a novel BRB detection method is developed
based on zoom-FFT wherein the number of FFT-points is
reduced by means of signal conditioning aimed at filtering
out portions of spectrum that are not required for MCSA. This
method is compared to the existing zero-crossing time (ZCT)
method [3], [4], wherein only the inter-arrivals of the zerocrossing are processed instead of the full current waveform.
Numerical tests on real motor data have been carried out, and
100% Nominal current, 2 BRB, s = 5.7%, 2sf0 = 5.7 Hz
120
50 Hz,
109.5 dB
110
100
Amplitude [dB]
90
44.36 Hz,
78.1 dB
80
Fig. 2.
70
Zoom-FFT processing scheme.
60
50
40
30
20
0
10
20
30
Frequency [Hz]
40
50
60
Fig. 1. Signal spectrum in presence of BRBs. The FFT has been normalized
by the number of samples. Data from motor S1 described in Sec. IV-A are
used.
both methods are able to reliably detect BRBs.
The outline of the paper is as follows. Section II is devoted
to preliminaries, while, in Sec. III, the novel BRB diagnostic
method based on zoom-FFT is presented, and the ZCT method
developed in [3], [4] is recalled. Numerical tests are sketched
in Sec. IV, while concluding remarks are provided in Sec. V.
II. P RELIMINARIES
AND PROBLEM STATEMENT
Let ik (t) denote the (analog) current waveform for the kth
phase, where k = 1, 2, 3, and t ∈ [0, +∞). After analog-todigital conversion, the digital current signal for the kth phase is
denoted as ik [n] for n = 0, 1, 2, .... Let fS denote the sampling
frequency. For stationary loading conditions, the spectrum of
ik [n] should ideally have a predominant peak at the rated
frequency, denoted as f0 , and its harmonics. On the other end,
in presence of severe BRBs, the absorbed current posses strong
side peaks. While, a full theoretical analysis of induction
motors operating with BRBs is available in [12], suffices
here to say that, in presence of BRBs, the current induced
in the stator winding has pronounced peaks at frequencies
f0 (1 ± 2sq) for q = 1, 2, ... where s is the motor slip, defined
N −ωr
as s := ωSY
where ωSY N is the synchronous rotor speed
ωSY N
0
in revolution per minute (rpm), defined as ωSY N := 60 2f
P ,
with P is the number of poles, and ωr is the rotor speed in
rpm. The slip (as well as the current amplitude) increases with
the load and, typically, the full-load slip, i.e., the slip when
the induced current is equal to the rated current, is known. For
low-slip motors, the side peak displacement 2sf0 can be very
low (below 1 Hz) even at full-load, and a long analysis time
is required.
Hereinafter, spectral analysis is performed by FFT.
Assuming an analysis interval of duration ts (N − 1), the
N -points discrete
Fourier transform (DFT) of ik [n] is defined
P −1
n
−j2πm N
as Ik [m] := N
, for m = 0, 1, . . . , N − 1,
n=0 ik [n]e
which can be evaluated with complexity O(N log N ) via
FFT [9].
Example 1. The typical current spectrum in presence of
BRBs is sketched in Fig. 1 (refer to Sec. IV for a detailed
presentation of the measurement setting and for the motor
type). The current signal is sampled at 1 KHz. The motor
load is stationary and the absorbed current is (approximately)
100% of the nominal current, and 2 BRBs are present. The
rated frequency is f0 = 50 Hz. The slip is s = 0.0567,
therefore 2sf0 = 5.67 Hz. The analysis time is 25 s, therefore
N = 25000. The portion of the spectrum (evaluated via FFT)
between 0 Hz and 60 Hz is depicted in Fig. 1.
Observe that the current spectrum presents significant
peaks at frequencies f0 (1 ± 2sq) for q = 1, 2, . . .. Since
the amplitude of the peaks are expected to decrease with q,
let us focus of the side peaks in the proximity of the rated
frequency, i.e., f0 (1 ± 2s). Let us denote I0,dB the amplitude
(in dB) of the main peak, and ISB,dB the maximum among
the two sideband peaks. Denoting ∆dB := I0,dB − ISB,dB
classical diagnostic of BRBs hinges upon inspection of ∆dB .
To be more specific ∆dB larger than 45-50 dB occurs in
healthy motors. On the other hand, ∆dB smaller than 35-40
dB is a manifestation of BRBs [6]. In Fig. 1, ∆dB = 31.4
dB which is a clear indication that the motor is faulty.
The presented analysis requires an FFT of N = 25000
points, which is not feasible for embedded applications. In
the ensuing section, two methods are presented to lower the
number of FFT points for BRB detection.
III. L OW- COMPLEXITY DETECTION
In this section, the novel MCSA for BRB detection based
on zoom-FFT is presented along with the ZCT method derived
in [3], [4].
A. Zoom FFT
Zoom-FFT is a signal processing technique to reduce the
number of FFT points while retaining high spectral resolution
when only a small portion of the spectrum of a signal is
of interest [7]. The basic scheme of a zoom-FFT analysis is
sketched in Fig. 2.
Assuming that the original signal ik [n] is sampled at fS ,
the maximum (single side) bandwidth that can be analyzed is
B < f2S , and, if a frequency resolution of fres
the
is required,
fS
number of FFT-points required scales as O fres .
If only a small portion of the signal centered around f0
of size 2∆f ≪ 2B is of interest, a substantial reduction of
the number of FFT-points required to guarantee a frequency
resolution of fres can be achieved.
To achieve high spectral resolution while retaining short
FFT-size, the signal is first demodulated around the band of
interest (i.e., f0 ). Clearly, the band of interest for MCSA is
centered around f0 and it is 2∆f wide, with ∆f typically less
100% Nominal current, 2 BRB, s = 5.7%, 2sf
0
= 5.7 Hz
100% Nominal current, 2 BRB, s = 5.7%, 2sf
0
80
= 5.7 Hz
−20
0 Hz,
69.9 dB
70
5.65 Hz,
−32 dB
−30
60
−40
−5.65 Hz,
37.6 dB
40
Amplitude [dB]
Amplitude [dB]
50
30
20
10
−50
−60
−70
0
−80
−10
−20
−50
−40
−30
−20
Frequency [Hz]
−10
0
10
−90
0
5
10
15
20
25
30
Frequency [Hz]
35
40
45
50
Fig. 3. Signal spectrum obtained via zoom-FFT in presence of BRBs. The
FFT has been normalized by the number of samples. Data from motor S1
described in Sec. IV-A are used.
Fig. 4. Signal spectrum of ZCT obtained via FFT in presence of BRBs.
The FFT has been normalized by the number of samples. Data from motor
S1 described in Sec. IV-A are used.
than 10 Hz. Therefore, ik [n] is first demodulated at f0 , i.e.,
f
−j2πn f 0
S . Successively, a low-pass filter by
dk [n] := ik [n] · e
h[n] is employed to discard portions of the spectrum that are
not important, i.e., zk [n] := dk [n] ∗ h[n]. The low-pass filter
should have (single-side) cut-off bandwidth equal (or slightly
larger) to ∆f .
The (complex) signal zk [n] is low-pass with (single-side)
bandwidth of ∆f ≪ B < f2S , and it is sampled at fS ,
therefore,
it can be decimated by a factor D of the order of
fS
, thus allowing to shorten the number of FFT-points
O ∆f
while keeping high resolution. The signal zk [n] is, therefore,
decimated by a factor D, and fed to the FFT analyzer.
Example 2. Considering the signal in Example 1. Assuming
that the signal in the frequency band of [0, 100] Hz is required
for MCSA, the signal is demodulated at 50 Hz, and filtered by
a 64-taps FIR filter of cut-off frequency equal to 50 Hz. The
resulting signal, which is sampled at 1 KHz, has double-sided
bandwidth of 100 Hz. The signal can be, therefore, decimated
by a factor 10 and fed to a 2500-points FFT. The resulting
spectrum is depicted in Fig. 3. Observe that ∆dB = 32.3 dB,
therefore, it is very close to that evaluated via a full-blown
FFT of 25000 points. This shows that the memory as well as
speed requirements of MCSA can be lowered by zoom-FFT
with no significant impact on the performances.
Finally, t0,k [n′ ] is scaled around its mean value, i.e.,
B. Zero-crossing Time
The ZCT signal is defined as the time difference between
two successive zero-crossing points of the stator phase current
ik (t). It is a discrete signal, and its n′ th sample is equal to
tzc,k [n′ ] := t0,k [n′ + 1] − t0,k [n′ ] where t0,k [n′ ] is the instant
of the n′ th zero crossing, for n′ = 0, 1, . . .. Clearly, one
has ik [n] available instead of ik (t), therefore tzc,k [n′ ] can be
obtained analyzing the changing polarity of ik [n], and applying
linear interpolation [5]. More precisely, assuming that ik [n]
and ik [n + 1] have opposite signum, the ZCT signal (in term
ik [n]
1
of discrete samples) is given by t0,k [n′ ] = n + ik [n]−i
.
k [n+1]
1 If i [n] is corrupted by large noise, a short smoothing filter might be
k
required before proceeding to ZCT computation, otherwise a large number of
false zero-crossing are expected to appear.
τ0,k [n′ ] := t0,k [n′ ] − 2
fS
.
f0
(1)
MCSA hinges upon inspection of the peaks of the spectrum
of τ0,k [n′ ]. Observe that the whole samples of ik [n] in one
period have been compressed in two samples of τ0,k [n′ ], thus
achieving a significant reduction of the FFT-points.
If the three-phase signals are available, the ZCT signal of the
three phases, i.e., t0,k [n′ ] for k = 1, 2, 3, can be merged into
the signal t0 [n′ ] by superimposing the zero-crossing instant
and jointly processed. In this case, the correction in (1)
becomes
fS
τ0 [n′ ] := t0 [n′ ] − 6 .
(2)
f0
Example 3. Considering the same portion of signal in
Examples 1 and 2, the ZCT signal is extracted, and corrected
via (1). Assuming a sampling frequency of 2f0 for τ0,k [n′ ]
(since 2 samples per period are expected), the ZCT signal is
fed to a 2500-points FFT, since N ′ = 2500 zero-crossings
are expected in the analysis time. The spectrum of τ0,k [n′ ] is
depicted in Fig. 4
As stated in [3], [4], sharp and high peaks (larger than 40dB) of the ZCT spectrum at frequencies 2qf0 s for q =
1, 2 . . . are expected when the motor has severe BRBs. Let
us focus on the peak at frequency 2f0 s which is expected to
be the largest, and denote its amplitude as ΣdB . In Fig. 4, a
strong peak of amplitude -32dB around 5.65 Hz (very close
to 2f0 s) is an indication of BRBs.
IV. T EST RESULTS
Systematic tests have been carried out to assess the performance of the zoom-FFT and ZCT methods for BRB detection
in IMs. In the ensuing section, the test setup is first described,
and the methods are tested in two settings:
s1)
In Sec. IV-B, long datasets are analyzed entailing
large computational burden and memory requirements. A single decision is taken over the whole
observation interval;
TABLE I
M OTOR S1 SPECIFICATION .
Parameter
Active power [kW]
Nominal voltage [V]
Nominal current [A]
Nominal power factor
Nominal Rotor speed [rpm]
No load speed [rpm]
Winding connection
Number of poles per phase winding p
Nominal frequency [Hz]
Number of rotor bars
Number of stator slots
Rotor inertia [kg m2 ]
s2)
TABLE II
M OTOR S2 SPECIFICATION .
Value
0.8
380
2.2
0.74
1400
1497
Y
2
50
22
24
0.0025
In Sec. IV-C, the long datasets are segmented in
short subdatasets, entailing low complexity processing, and multiple independent decisions are taken in
different segments.
A. Description of the test setup
Real data from two motors have been recorded for testing.
More specifically, Tables I and II show the specifications of
the two motors, denoted S1 and S2, respectively.
The analysis time is 25 s, and the three-phase stator current
waveforms are acquired at sampling frequency fS =1 KHz,
for a total of N = 25000 samples. For each motor, measures
with no BRB, 1 BRB, 2 BRBs and 3 BRBs, have been
performed. For setting, 5 current loads have been tested: 60%,
80%, 90%, 100%, and 110% of nominal current.
Next, complexity-agnostic MCSA via full-blown FFT of the
current waveform and of the three-phase ZCT is performed.
Successively, low-complexity methods are presented and their
performance assessed.
B. High-complexity methods
Observe that the nominal slip for S1 and S2 is 0.067 and
0.037, respectively, therefore, 2sf0 corresponds to 6.7 and 3.7
Hz, respectively.
For each motor setting and current load, a 25000-points
FFT analysis of the current (in one phase) is performed, and
∆dB is evaluated as the difference of the overall maximum
of the spectrum and the maximum in the frequency intervals
[f0 + 2, f0 + 10] Hz and [f0 − 10, f0 − 2] Hz2 .
As far as the ZCT is concerned, the ZCT signal from the
three-phase current signal is collected, and a 7500-points FFT
analysis of the ZCT is performed. Finally, ΣdB is evaluated
by finding the maximum of the spectrum in the frequency
intervals [0, 10] Hz (as shown in Fig. 4, ZCT spectrum does not
have main peak width problem which might be an advantage
for low slip).
2 As one can observe from Figs. 1 and 3, the main peak has a ceratin width,
and one cannot distinguish other peaks within that width. This enforces a
limitation on the minimal slip for BRBs. In this setting, we are guaranteed
that, at nominal current, the frequencies f0 (1 ± 2s) are contained in the
aforementioned intervals.
Parameter
Active power [kW]
Nominal voltage [V]
Nominal current [A]
Nominal power factor
Nominal Rotor speed [rpm]
No load speed [rpm]
Winding connection
Number of poles per phase winding p
Nominal frequency [Hz]
Number of rotor bars
Number of stator slots
Rotor inertia [kg m2 ]
Value
1.33
380
2.867
0.84
1445
1492
Y
2
50
28
24
0.0197
Figures 5 and 6 shows ∆dB versus ΣdB for 0 BRB, 1 BRB,
2 BRBs, and 3 BRBs, and 60%, 80%, 90%, 100%, and 110%
of nominal current.
Observe that both ∆dB and ΣdB are not effective spectrum metrics for motor condition monitoring at 60% nominal
current. Nevertheless, for current larger than 80% one can
correctly detect BRBs. Indeed, for full-blown FFT, ∆dB
smaller than 40÷45 dB are a clear indication of BRBs. On
the other hand, ΣdB larger than -40÷-35 dB signifies that the
motor has BRBs.
The proposed analysis can effectively detect BRBs but
requires computation and memory resources that are generally
not available in embedded systems. In the ensuing section,
low-complexity methods tailored for embedded systems are
proposed.
C. Low-complexity methods
To enable embedded implementation of MCSA, zoom-FFT
is applied to the signal. More precisely, each phase current is
demodulated at 50 Hz, and filtered by a 64-taps FIR filter
of cut-off frequency equal to 50 Hz. The resulting signal
is then decimated by a factor 10, resulting in 2500 points
per phase. The signal is then segmented in batch of 512
consecutive samples, and fed to a 512-points FFT. Finally,
∆dB is evaluated as the difference of the overall maximum
of the spectrum and the maximum in the frequency intervals
[f0 + 2, f0 + 10] Hz and [f0 − 10, f0 − 2] Hz. Therefore, for
25 s, approximately 5 independent detections per phase are
taken, for a total of approximately 15 consecutive detections.
As far as the ZCT is concerned, the three-phase signal consisting in 7500 samples is simply segmented in approximately
15 batches of 512 points, and fed to a 512-points FFT.
Since the very first seconds of the data represents the motor
start, they are not used for assessing BRBs. Therefore, for each
motor, measurement setting and current load, we end up in 12
independent detections for the zoom-FFT and 13 independent
detections for ZCT.
While it is desirable that consecutive detections are fused to
get a more reliable global detection (e.g., declare BRBs only if
a certain number of consecutive detections have declared the
fault), in this paper the detections are treated as independent,
and used to extrapolate the performance of the MCSA method
BRB with MCSA: Full−blown FFT vs ZCT
−25
−25
−30
−30
−35
−35
ΣdB [dB]
−20
−40
Σ
dB
[dB]
BRB with MCSA: Full−blown FFT vs ZCT
−20
−40
−45
−45
−50
−50
−55
−55
−60
30
35
40
∆
dB
45
50
−60
28
55
[dB]
Fig. 5. Motor S1. Black, 60% of nominal current; Blue, 80% of nominal
current; Red, 90% of nominal current; Magenta, 100% of nominal current;
Green, 110% of nominal current. Marker for healthy motor; Marker + for
1 BRB; Marker ∗ for 2 BRBs; Marker for 3 BRBs.
for threshold tuning purpose. The goal of the ensuing analysis
is to estimate the detection threshold for the zoom-FFT and
ZCT method. Let T HZF F T and T HZCT denote the detection
threshold for zoom-FFT and ZCT, respectively. As already
discussed, denoting with Θ = 1 the event MCSA declares the
motor faulty, and with Θ = 0 the event MCSA declares the
motor healthy, given ∆dB and ΣdB , the detection rules are as
follows:
> T HZF F T ,
then Θ = 0
Zoom-FFT: if
∆dB
< T HZF F T ,
then Θ = 1
> T HZCT ,
then Θ = 1
ZCT: if
ΣdB
< T HZCT ,
then Θ = 0.
30
32
34
36
∆
38
40
[dB]
42
44
46
48
dB
Fig. 6. Motor S2. Black, 60% of nominal current; Blue, 80% of nominal
current; Red, 90% of nominal current; Magenta, 100% of nominal current;
Green, 110% of nominal current. Marker for healthy motor; Marker + for
1 BRB; Marker ∗ for 2 BRBs; Marker for 3 BRBs.
•
it faulty;
Detection probability PD : this is the probability that the
motor is faulty and the detection algorithm declares it
faulty.
In detection problems, the performances are typically measured by two metrics:
• False alarm probability PF A : This is the probability that
the motor is healthy and the detection algorithm declares
It would be desirable that PF A ≈ 0 and PD ≈ 1.
Clearly, small T HZF F T entails small probability of false
alarm but also small probability of detection. However, increasing T HZF F T would imply an increase of both PF A and
PD . On the other end, small T HZCT entails large probability
of false alarm but also large probability of detection, and
increasing T HZCT would imply a decrease of both PF A
and PD . Therefore, selection of the optimal threshold is a
fundamental problem to address.
In the following, the algorithms are applied using several
thresholds and, for each threshold, PF A and PD are estimated.
To estimate PF A , we resort to the data with healthy motor,
Fig. 7. PF A and PD versus threshold for different current, motor S1,
utilizing zoom-FFT method.
Fig. 8. PF A and PD versus threshold for different current, motor S2,
utilizing zoom-FFT method.
Fig. 9. PF A and PD versus threshold for different current, motor S1,
utilizing ZCT method.
PN s
Θ
n
and PF A ≈ n=1
where Θn is the detection result during
Ns
the nth segment, and Ns is the number of segments. As far
as PD P
is concerned, data with faulty motors are used, and
Ns
Θn
PD ≈ n=1
.
Ns
Figures 7 and 8 depict PF A and PD versus T HZF F T for
motor S1 and S2, respectively. Observe that for current larger
than 90%, T HZF F T ∈ [40, 45] guarantees good performance.
This threshold level is in accordance with the results in Figs.
5 and 6.
Figures 9 and 10 depict PF A and PD versus T HZCT for
motor S1 and S2, respectively. Observe that, as anticipated,
BRB detection is reliable even at lower currents (i.e., 80%).
On the other hand, an universal threshold, independent on the
current level and analysis time, seams to lack (i.e., it occurs
that the threshold has to increase with the current). In fact, the
threshold levels are not in accordance with the levels in Figs.
5 and 6.
Remark 1. It is worth pointing out here that the performance
of zoom-FFT method can be improved for low current by resorting to peak peaking methods. This, together high frequency
methods operating on the decimated signal, constitute topics
of future research.
Remark 2. As pointed out in [11], pulsating loads constitute
a challenge for BRB detection. Low-complexity MCSA does
not aim at revealing BRBs in these challenging settings. In
embedded devices such as motor controllers, softstarters and
drives, the current amplitude is monitored very often (e.g., for
electronic overload protection). Therefore, BRB detection can
be enabled only if the current is found to be relatively stable
during the analysis time.
V. C ONCLUSIONS
In this paper, low-complexity automatic detection methods
of broken rotor bars are proposed and tested using real motor
data. A novel method based on zoom-FFT is proposed and
compared to the existing ZCT method. The algorithms are
amenable to an embedded implementation. It turns out that
Fig. 10. PF A and PD versus threshold for different current, motor S2,
utilizing ZCT method.
both methods can reliably detect BRBs for current equal or
larger than the nominal. ZCT method can be made effective
for low currents as well, but, unlike the zoom-FFT method,
finding an universal detection threshold is challenging. This
characteristic makes zoom-FFT methods more promising for
embedded devices such as motor controllers, softstarters, and
drives that operate under a variety of IM types.
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