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Using Condition Indices and Generalised Norms for Complex Fault 255
Institut für Maschinentechnik der Rohstoffindustrie, RWTH Aachen, 2010
Using Condition Indices and Generalised Norms
for Complex Fault Detection
Prof. D.Sc.Tech. Sulo Lahdelma
Universität Oulu, Finnland, Abteilung für Maschinenbau, Lab. für Me-
chatronik und Maschinendiagnostik, Lehrstuhl für Maschinendiagnos-
tik
M.Sc. Tech. Esko Juuso
Universität Oulu, Finnland, Abteilung für Verfahrens- und Umwelttech-
nik, Laboratorium für Regelungstechnik
Prof. Dr.-Ing. habil. Jens Strackeljan
Otto-von-Guericke-Universität Magdeburg, Institut für Mechanik, Lehr-
stuhl für Technische Dynamik
Abstract
Advanced signal processing methods combined with automatic fault detection
enable reliable condition monitoring for long periods of continuous operation.
Any attempt to detect different types of machine faults reliably at an early stage
requires the development of improved signal processing methods. Vibration
measurements provide a good basis for condition monitoring. In some cases
the simple calculation of root-mean-square and peak values obtained from vi-
bration signals are useful features for detecting various faults. Unbalance, mis-
alignment, bent shaft, mechanical looseness and some electrical faults, for ex-
ample, can be detected using features of displacement and velocity. Higher or-
der derivatives provide additional possibilities for detecting faults that introduce
high-frequency vibrations or impacts. New generalised moments and norms
related to l
p
space have been used for diagnosing faults in a roller contact on a
rough surface. This paper extends the field of possible applications from roller
bearing fault detection to more complex faults situations where different kinds of
fault occur simultaneously. In consequence, feature calculation and signal proc-
essing have to be adopted and optimized for each fault type on the basis of one
256 Using Condition Indices and Generalised Norms for Complex Fault
Institut für Maschinentechnik der Rohstoffindustrie, RWTH Aachen, 2010
measured signal. The features of x
(4)
indicate well the intact case and the outer
race fault. Velocity x
(1)
is needed for detecting unbalance. This approach also
works for the combined case, outer race fault and unbalance. Derivation re-
duced the effect of noise by amplifying higher frequency components from bear-
ing faults more than the added noise components.
1 Introduction
Vibration measurements provide a good basis for condition monitoring. Early
vibration measurements by means of mechanical or optical instruments used
displacement x = x(t). The next step was the adoption of velocity, i.e. x
(1)
sig-
nals, which were obtained either by differentiating displacement or using sen-
sors whose output was directly x
(1)
. The drawback with the signals x and x
(1)
is
that they do not usually allow the detection of impact-like faults at a sufficiently
early stage. Examples of these faults are defective bearings and gears. How-
ever, e.g. unbalance and misalignment can be detected successfully with x and
x
(1)
.
Standard sensors in condition monitoring are accelerometers because of their
easy usage and robustness. The signals x and x
(1)
can be obtained from the x
(2)
signal through analogue or numerical integration. The first time derivative of
acceleration had been used earlier for assessing the comfort of travelling e.g. in
designing lifts. Higher, real and complex order derivatives bring additional
methods to signal processing [1, 2, 3, 4, 5, 6]. Different approaches have been
reviewed in [7, 8]. Vibration indices based on several higher derivatives in dif-
ferent frequency ranges were already introduced in 1992 [2, 8, 9]. Higher and
real order derivatives in processing vibration measurements and feature extrac-
tion by generalised moments and l
p
norms have been discussed in [6, 8, 10].
2 Problem description and signal processing
A couple of relevant faults, such as unbalance, misalignment, bent shaft and
mechanical looseness, can be detected by means of displacement and velocity,
i.e. signals
)0(
xx = and
)1(
xx =
&. On the other hand it is well known that the early
detection of bearing faults, as well as cavitation can be detected more efficiently
with the acceleration signal. Often higher order derivatives provide more sensi-
tive solutions, i.e. the ratios of calculated features between the faulty and non-
faulty cases become higher [7, 9, 11].
Using Condition Indices and Generalised Norms for Complex Fault 257
Institut für Maschinentechnik der Rohstoffindustrie, RWTH Aachen, 2010
The severity of faults can be assessed by comparing signals and features in
different orders of derivation [2, 12, 13]. For sinusoidal signals
tXtxx
ω
sin)(
=
=
we obtain
),sin()
2
sin(
)(
αα
αα
α
α
ϕω
π
αωω
+=+== tXtXx
dt
xd
.................... (1)
where the order of derivation α is a real number, the amplitude
,XX
α
α
ω
=
and
the change of the phase angle is .
α
ϕ
[6]
Real order derivatives increase the number of signal alternatives. New general-
ised moments and norms related to l
p
space have been used for diagnosing
faults in a roller contact on a rough surface. Kurtosis provides a strong indica-
tion of impacts if the order
α
is 4, for example. The generalised moment and
norm can be defined by the order of derivation, the order of the moment p and
sample time
τ
. Reliable results for bearing faults can be obtained by relative
norms if
α
and p are in the range between 4 and 6. In this investigation, time
signals are from a test rig (Fig. 1), which allows the generation of different fault
and condition states. For each state 50 samples with a fixed rotational fre-
quency of 30 Hz were measured and stored for further digital pre-processing.
The condition states are: Class1 - intact, Class 2 – unbalance, Class 3 - outer
race fault, Class 4 – outer race fault and unbalance, and Class 5 – outer race
fault, unbalance and noise.
Figure 1: Test rig for the simulation of different faults.
258 Using Condition Indices and Generalised Norms for Complex Fault
Institut für Maschinentechnik der Rohstoffindustrie, RWTH Aachen, 2010
Figure 2a shows the raw acceleration signal x
(2)
obtained from an accelerome-
ter with a time length of 0.5 s and a sampling rate of 131072 Hz. All the time
signals used in this paper were acquired with these settings. It could be seen in
the corresponding amplitude spectra that frequency components up to 40 kHz
are present. Figure 2e shows the signal x
(2)
in the case of unbalance, generated
by a disk with an unbalance of 3.6 kgmm. The signal has a clear sine-shape
with an additional noise level, which is comparable to the level in Figure 2a. The
amplitude of the harmonic vibration induced by the unbalance of the rotor could
be accurately determined by the FFT (Fig. 4).
All the other signals in Figure 2 are derived from these acceleration signals. In
Figures 2b and 2f both the time signals x
(4)
are very similar. The reason is ob-
vious, because these signals only differ in the low frequent unbalance compo-
nent at 30 Hz. On the other hand, unbalance could be clearly identified in the
x
(1)
signal, which is generated by the integration of x
(2)
. The velocity increases
considerably in the case of unbalance (Figs. 2c and 2g). According to the ISO
2372 standard, the vibration rms value of approx. 30 mm/s is far away from any
acceptable level. Figure 3 shows time signals from the two other classes: outer
race fault and a combination of this with the unbalance. While the signals x
(4)
and x
(2)
from the outer race fault have a typical structure with relative constant
peaks (Figs. 3a and 3b), the combinations of outer race and unbalance are less
structured (Figs. 3e and 3f). The reason is the time dependent load that occurs
during the contact between the roller and the damaged area caused by unbal-
ance. This effect leads to slightly higher peaks than in the pure outer race fault
situation.
Using Condition Indices and Generalised Norms for Complex Fault 259
Institut für Maschinentechnik der Rohstoffindustrie, RWTH Aachen, 2010
Figure 2: Time signals and frequency spectrum for x
(4)
, x
(2)
, x
(1)
and x
(0)
: intact sys-
tem (left), and unbalance fault (right).
260 Using Condition Indices and Generalised Norms for Complex Fault
Institut für Maschinentechnik der Rohstoffindustrie, RWTH Aachen, 2010
Figure 3: Time signals and frequency spectrum for x
(4)
, x
(2)
, x
(1)
and x
(0)
: outer race
fault (left), and outer race fault and unbalance (right).
Using Condition Indices and Generalised Norms for Complex Fault 261
Institut für Maschinentechnik der Rohstoffindustrie, RWTH Aachen, 2010
Using the derivative x
(4)
the typical fault structure is improved for the outer race
fault (Fig. 3a). When integrating the acceleration, the unbalance is clearly de-
tectable in Figures 2g and 3g. The use of different orders of derivation could
help in separating a complex fault from single fault types.
0 0.1 0.2 0.3 0.4 0.5
-20
0
20
accel. [m/s²]
time [s]
time signal
0 200 400 600 800 1000
0
5
10
accel. [m/s²]
frequency [Hz]
frequency spectrum
Figure 4: The acceleration signal and the zoomed frequency spectrum of the un-
balance rotor.
To increase the complexity and demonstrate the advantage of higher deriva-
tives, additional noise in the frequency range between 100 Hz and 5 kHz was
added to the signal x
(2)
of the combination fault outer race and unbalance (Fig.
3f). The selected noise level masks the typical fault structure in the x
(2)
signal
completely (Fig. 5). The signal x
(4)
is adequate to indicate the fault while the sig-
nals x
(1)
and
x
(0)
highlight the unbalance.
0 0.1 0.2 0.3 0.4 0.5
-500
0
500
accel. [m/s²]
time [s]
time signal
01234
x 10
4
0
5
10
accel. [m/s²]
frequency [Hz]
frequency spectrum
0 0.1 0.2 0.3 0.4 0.5
-2000
0
2000
x(4) [Gm/s4]
time [s]
time signal
0 1 2 3 4
x 10
4
0
10
x(4) [Gm/s4]
frequency [Hz]
frequency spectrum
0 0.1 0.2 0.3 0.4 0.5
-100
0
100
veloc. [mm/s]
time [s]
time signal
0 200 400 600 800 1000
0
50
veloc. [mm/s]
frequency [Hz]
frequency spectrum
0 0.1 0.2 0.3 0.4 0.5
-0.5
0
0.5
displ. [mm]
time [s]
time signal
0 200 400 600 800 1000
0
0.2
displ. [mm]
frequency [Hz]
frequency spectrum
Figure 5: Time signals x
4)
, x
(2)
, x
(1)
and x
(0)
in a complex fault situation including an
outer race fault, unbalance and a high noise level.
262 Using Condition Indices and Generalised Norms for Complex Fault
Institut für Maschinentechnik der Rohstoffindustrie, RWTH Aachen, 2010
To understand features which are derived from signals x
(α)
with α>2, it is impor-
tant to obtain some information on frequency distribution in the original time sig-
nal. The derivative x
(4)
in Figure 6 of the unbalance signal could have a struc-
ture of a sine-shaped signal (bottom right), if the time signal is filtered with a cut-
off frequency close to the rotation frequency. A standard frequency range in
condition monitoring is 10-1000 Hz. The signal in Figure 6 (bottom left) is domi-
nated by the amplified noise level. In consequence, the kurtosis value will in-
crease from 1.8 (about sine-shaped: right) to 4.7 (random noise + peaks: left).
0 0.1 0.2 0.3 0.4 0.5
-20
0
20
accel. [m/s²]
time [s]
time signal
0 200 400 600 800 1000
0
5
10
accel. [m/s²]
frequency [Hz]
frequency spectrum
0 0.1 0.2 0.3 0.4 0.5
-10
0
10
accel. [m/s²]
time [s]
time signal
0 200 400 600 800 1000
0
5
10
accel. [m/s²]
frequency [Hz]
frequency spectrum
0 0.1 0.2 0.3 0.4 0.5
-100
0
100
x
(4)
[Mm/s
4
]
time [s]
time signal
0 200 400 600 800 1000
0
5
10
x
(4)
[Mm/s
4
]
frequency [Hz]
frequency spectrum
0 0.1 0.2 0.3 0.4 0.5
-1
0
1
x
(4)
[Mm/s
4
]
time [s]
time signal
0 200 400 600 800 1000
0
0.2
0.4
x
(4)
[Mm/s
4
]
frequency [Hz]
frequency spectrum
Figure 6: Filtered time signals x
(2)
and x
(4)
: x
(2)
in 0-1000 Hz with unbalance (top
left), x
(2)
in 0-50 Hz (top right), x
(4)
in 0-1000 Hz (bottom left), and x
(4)
in 0-50 Hz
(bottom right).
3 Feature extraction
3.1 Statistical features, moments and norms
There are a couple of different feature which are well established in condition
monitoring. A systematic approach is given by features which are calculated by
means of a generalised moment about the origin:
,
1
1
)(
∑
=
=
N
i
p
i
p
x
N
M
α
α
τ
(2)
Using Condition Indices and Generalised Norms for Complex Fault 263
Institut für Maschinentechnik der Rohstoffindustrie, RWTH Aachen, 2010
where the real number
α
is the order of derivation, the real number p is the or-
der of the moment,
τ
is the sample time, i.e. the moment is obtained from the
absolute values of signals
)(
α
x. The number of signal values
s
NN
τ
=
where N
s
is the number of samples per second. Alternatively, the signals values
)(
α
i
x
can
be compared to the mean
)(
α
x:
.
1
)(
1
)( p
N
i
i
p
xx
N
M
αα
α
τ
−=
∑
=
.................................... (3)
The generalised central moment can be normalised by means of the standard
deviation
α
σ
of the signal
)(
α
x:
( )
,
1)(
1
)( p
N
i
i
p
pxx
N
M
αα
α
α
τ
σ
σ
−= ∑
=
........................ (4)
which was presented in [10]. The order of derivation ranges from 1 correspond-
ing to velocity to 4, which corresponds to the signal x
(4)
. The moment
1
2
=
α
τ
σ
M
,
and the moment 4
α
τ
σ
M
corresponds to the kurtosis of the signal. The standard
deviation
α
σ
can be obtained from (3) by taking the square root [6]:
.)
1
()(
2/1
2
)(
1
)(2/1
2
αα
α
τ
α
σ
xx
N
M
N
i
i
−==
∑
=
............. (5)
There are many alternative ways of normalisation, e.g.
)(
1
)(
1
1
αα
α
τ
xx
N
M
N
i
i
−=
∑
=
....................................... (6)
can be used.
A norm can be defined for example by
,)
1
()(
/1
1
)(/1 p
N
i
p
i
ppp
x
N
MM
∑
=
==
α
α
τ
α
τ
................. (7)
which is the l
p
norm
.
)(
p
p
xM
α
α
τ
≡ .................................................... (8)
This norm has same dimensions as the corresponding signals )(
α
x
. The l
p
norms are defined in such a way that
.1
∞
<
≤
p
[6]
The absolute mean,
,
1
1
)()(
1
)(
∑
=
==
N
i
i
av
x
N
xx
ααα
................................... (9)
264 Using Condition Indices and Generalised Norms for Complex Fault
Institut für Maschinentechnik der Rohstoffindustrie, RWTH Aachen, 2010
and the rms value,
,)
1
(
2/1
1
2
)()(
2
)(
∑
=
==
N
i
irms
x
N
xx
ααα
....................... (10)
are special cases of (8). Faults can also be detected with other types of norm,
e.g. maximum norm
,max
)(
,...,1
)(
αα
i
ni
xx
=
∞
=
.......................................... (11)
or norm
,
0
)(
∑
=
=
n
i
C
i
n
xx
α
α
.............................................. (12)
which is the sum of the norms obtained for different orders of derivatives. The
rms values of displacement and velocity can be obtained from (10) by using the
values zero and one for the order of derivation, respectively:
,)
1
(
2/1
1
2
2
∑
=
==
N
i
irms
x
N
xx
................................ (13)
and
.)
1
(
2/1
1
2
2
∑
=
==
N
i
irms
v
N
vv
(14)
These norms can be used for detecting unbalance, misalignment, bent shaft
and mechanical looseness. For bearing faults, displacement and velocity should
be replaced by acceleration or higher derivatives. [6] The generalised moments
and norms have been used for diagnosing faults in a roller contact on a rough
surface [14].
3.2 Order of moments and derivative
The peaks of the signal have a strong effect on the moments (2), (3) and (4).
The norm (7) combines two trends: a strong increase caused by power p and a
decrease with power 1/p. For the order p = 1, there is no amplification. The sig-
nificance of the highest peaks will decrease if p < 1. The moments calculated
for higher order derivatives are more sensitive to impacts than the ones calcu-
lated for the acceleration. In Figure 7, the norm (7) was used in a relative form,
i.e. the norm of the signal in the four faulty cases is divided by the norm calcu-
lated from the signal in the non-faulty case. For this example, steps of 0.2 for
α
and 0.25 for p were used. It has been shown in further papers that sample time
τ
is an essential parameter in the calculation of moments [10] and norms [6].
To reduce the complexity of the present investigation, sample time
s5.0
=
τ
is
Using Condition Indices and Generalised Norms for Complex Fault 265
Institut für Maschinentechnik der Rohstoffindustrie, RWTH Aachen, 2010
equal to complete measurement time and was not considered as a free pa-
rameter.
The optimal setting of α and p is fault specific. In this application, a low value for
α and p gives the highest sensitivity for the detection of unbalance (Fig. 7). The
absolute average (p=1) of the velocity (α=1) is the best for unbalance (upper
left). For the outer race fault (upper right), sensitivity improves with increasing α,
when p is low. If , sensitivity reaches a maximum on a specific α for each
p, and the pair (α, p) moves from (4.8, 2.25) to (3.2, 6) when p increases. The
sensitivity plot of the combined fault (lower left) can be understood as a combi-
nation of the individual sensitivity plots. When noise is added (lower right), sen-
sitivity becomes higher for all α and p, and the maximum is around α Noise
has the same effect as an additional fault, and the effect is most evident for ac-
celeration, since noise was added to it. Derivation reduced the effect of noise by
amplifying higher frequency components from bearing faults more than the
noise components. This can be seen by comparing the signals in Figures 3 and
5. On the other hand, integration works as a low-pass filter, as it reduces all
high frequency components.
1
2
3
4
5 1
2
3
4
5
6
0
20
40
60
p
unbalance
α
rel. ||
0.5
M
p
α
||
12345
1
2
3
4
5
6
0
5
10
15
20
25
30
35
40
α
outer race
p
rel. ||
0.5
M
p
α
||
12345
1
2
3
4
5
6
0
10
20
30
40
50
60
70
80
α
outer race + unbalance
p
rel. ||
0.5
M
p
α
||
12345
1
2
3
4
5
6
0
20
40
60
80
100
α
outer race + unbalance + noise
p
rel. ||
0.5
M
p
α
||
Figure 7: Relative norm, p
Mrelative
α
5.0 , for the different condition states.
266 Using Condition Indices and Generalised Norms for Complex Fault
Institut für Maschinentechnik der Rohstoffindustrie, RWTH Aachen, 2010
3.3 Kurtosis and crest factor
Kurtosis
4
α
τ
σ
M
(4) is normalized and as a dimensionless number therefore not
affected by attenuation in the signal transmission path, for example, from the
source of vibration to the sensor. For roller bearing fault detection the fourth
moment provides a reasonable compromise between insensitive low order mo-
ments and the very sensitive high orders. Figure 8 demonstrates the influence
of the order of derivatives on two features, crest factor and kurtosis, for all 5
classes.
Figure 8: Feature map for all 5 condition states using kurtosis and crest factor as a
feature for the signals x
(1)
, x
(2)
and x
(4)
. The notations are unb=unbalance, out-
er=outer race fault and Cl=Class.
When using x
(4)
for class 4 (outer race fault + unbalance) and class 5 (outer
race fault+unbalance+noise), the variation of kurtosis is very high with maxi-
mum values about 250 (Fig. 8 bottom left). Class 3 (only outer race) has much
Using Condition Indices and Generalised Norms for Complex Fault 267
Institut für Maschinentechnik der Rohstoffindustrie, RWTH Aachen, 2010
less variation, since the load is more stationary in the absence of unbalance.
The time signals x
(4)
of class 1 (intact) and class 2 (unbalance) lead to kurtosis
values of 3 with very low variation (bottom right), i.e. the signals are very close
to Gaussian signals. The component caused by the unbalance weakens with
derivation.
Velocity x
(1)
eliminates all high frequency components. As a result, all kurtosis
values are between 1.5 and 3. In the unbalance case, velocity is very close the
sine-shaped signals: kurtosis goes to 1.5 and crest factor to Unbalance is
detected in the combined case also when noise is included. In the intact case,
slight unbalance can be seen with these features as well. The outer race fault
can be seen, but sensitivity is rather low.
Features of the acceleration are in a compact area for the outer race fault (mid-
dle left), and unbalance is also detected. For the combined fault with noise, the
feature values are very similar to the values of the intact case. Strong noise
moves the signal towards the Gaussian signal. This example clearly indicates
that an optimum setting of the derivative is only possible for individual fault de-
tection. The use of one fixed value for the order for the combination of faults will
lead to a compromise setting.
The experiments indicate that the kurtosis value of an intact bearing is close to
3 and that kurtosis in general provides a measure of the occurrence of peaks in
a signal. If only one parameter is not sufficient for the classification or
separation of different faults, the distribution of all digital values x
i
of the signals
have to be taken under consideration. The x
i
were sorted to one of the four
classes with fixed limits: 0 < |x
i
|< 1·σ
α
; 1 ·σ
α
≤ |x
i
|< 2 ·σ
α
; 2·σ
α
≤ |x
i
| < 3·σ
α
; 3·σ
α
≤ |x
i
|. Figure 9 shows the relative frequency distribution for four condition states
and three different signals x
(1)
, x
(2)
and x
(4)
. Fault-related indices could be calcu-
lated from this distribution.
The signal x
(4)
from the non-faulty case (Fig. 9a) is close to normal distribution
(Tab. 1). In the signal x
(1)
, the sine-shaped component (Fig. 2g) caused by
unbalance changes the distribution towards the sine-shaped case (Fig. 9b).
268 Using Condition Indices and Generalised Norms for Complex Fault
Institut für Maschinentechnik der Rohstoffindustrie, RWTH Aachen, 2010
Table 1. Histograms of the signals x
(1)
, x
(2)
, x
(4)
in the intact case compared to a
Gaussian signal and a sine-shaped signal.
Signal Bin 1 Bin 2 Bin 3 Bin 4
Gaussian 0.6827 0.2718 0.0428 0.0026
x
(4)
0.6858 0.2710 0.0435 0.0027
x
(2)
0.6721 0.2722 0.0549 0.0038
x
(1)
0.6484 0.3280 0.0267 0
Sine-shaped 0.5 0.5 0 0
The signal x
(1)
is almost a sine-shape signal when we have unbalance. For a
sinusoidal signal, the relative frequencies are 0.5 for Bin 1 and 0.5 for Bin 2. All
the other are zero. Impacts from outer race fault cause a slight increase of
standard deviation of x
(1)
, which can be seen as an increase of the frequency in
Bin 1 (Fig 9c). Higher signal values are needed in order to obatain considerable
effects in Bin 4. This effect is seen in Bin 4 for x
(2)
and x
(4)
(Figs. 9c and 9d).
The borders of the bins could be defined by the intact case, when the rotation
frequency does not change too much. This could be used in this example, since
rotation frequency was constant.
a) intact x
(1)
, x
(2)
, x
(4)
b) unbalance x
(1)
, x
(2)
, x
(4)
Using Condition Indices and Generalised Norms for Complex Fault 269
Institut für Maschinentechnik der Rohstoffindustrie, RWTH Aachen, 2010
c) outer race + unbalance x
(1)
, x
(2)
, x
(4)
d) outer race x
(1)
, x
(2)
, x
(4)
Figure 9: Relative frequency distribution (4 classes) for four condition states and
three different signals x
(1)
, x
(2)
and x
(4)
. The bins are based on standard deviation σ
α
of the corresponding signal x
(α)
.
In this investigation, random noise was taken as a disturbance. However, in real
applications, a careful analysis is needed: signal components, which could
easily be considered as noise, can provide important information. For example,
friction has been detected by the norms of x
(4)
in the supporting rolls of a lime
kiln [15, 16]. A signal with a similar distribution in all derivatives is an indicator of
an intact state. An adapted signal pre-processing technique [17] is needed in
order to obtain the best sensitivity for specific faults.
4 Conclusion
Advanced signal processing and feature extraction methods for vibration meas-
urements are chosen in a specific way in order to detect different faults. Gener-
alised moments and norms obtained from higher or real order derivatives pro-
vide informative features for diagnosing faults in a roller contact on a rough sur-
face. For this investigation, the features of x
(4)
indicate well the intact case and
the outer race fault. Velocity x
(1)
is needed for detecting unbalance. This ap-
proach also works for the combined case (outer race fault and unbalance).
Added random noise affects as an additional fault, which in this case makes the
detection of bearing fault more difficult with the acceleration. Derivation reduced
the effect of the noise by amplifying higher frequency components from bearing
faults more than the noise components. The results clearly show that the detec-
tion of combination of faults need an adapted signal pre-processing technique in
order to obtain the best sensitivity for specific faults. A general setting of para-
meters will lead to a compromise that will reduce classification accuracy.
270 Using Condition Indices and Generalised Norms for Complex Fault
Institut für Maschinentechnik der Rohstoffindustrie, RWTH Aachen, 2010
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