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Detection of multiple faults with intelligent condition indices
Esko Juuso
Control Engineering Laboratory, Department of Process and Environmental
Engineering, P.O.Box 4300, FI-90014 University of Oulu, Finland
Phone: +358-294-482463
E-mail: esko.juuso@oulu.fi
Sulo Lahdelma
Mechatronics and Machine Diagnostics Laboratory, Department of Mechanical
Engineering, P.O.Box 4200, FI-90014 University of Oulu, Finland
E-mail: sulo.lahdelma@oulu.fi
Abstract
Automatic fault detection with condition indices enables reliable condition monitoring
to be combined with process control. Useful information on different faults can be
obtained by selecting suitable features from generalised norms, which are defined by the
order of derivation, the order of the norm and sample time. The nonlinear scaling based
on generalised norms and skewness extends the idea of dimensionless indices to
nonlinear systems and provides good results for the automatic generation of condition
indices. Condition indices, which are used in the same way as the process measurements
in process control, detect differences between normal and faulty conditions and provide
an indication of the severity of the faults. Feature specific health indices, which are
calculated as ratios of feature values in the reference condition and the faulty case, are
used in selecting efficient features. In the multisensor vibration analysis, the number of
sensors and features were drastically reduced. The number of features is further reduced
by optimal orders for the derivatives and norms. The complexity of the models is
simultaneously reduced. For the supporting rolls of a lime kiln, an efficient indication of
faulty situations is achieved with two features. All the rolls can be analysed with the
same approach throughout the data set. The results of both the applications are
consistent with the vibration severity criteria: good, usable, still acceptable, and not
acceptable. Three standard deviations obtained for the signal
)4(
x
on three frequency
ranges were needed to detect unbalance and bearing faults. The norms based on the
signal
)4(
x
provide the best results in all the frequency ranges.
Keywords: Nonlinear scaling, intelligent stress indices, vibration analysis, condition
monitoring, higher, real and fractional order derivatives
1. Introduction
Industrial processes are subject to many known or unknown malfunctions during their
operational lifetime leading to a reduction in their efficiency and as a result, eventually,
to system breakdowns. Process control aims at improving operational quality by finding
assignable causes to these malfunctions and thus reducing their occurrences through
preventive actions. Fault diagnosis, which basically tries to define causes and effects
relationships in order to answer why a system is failing, can be a difficult task (1,2).
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Symptoms that are used to describe fault modes, whether they are provided by experts
or extracted from data, are frequently vague or incomplete (3,4). Fuzzy logic (5) provides
a representation for complex input-output relationships via qualitative fuzzy rules.
Linguistic equations (LE) also originate from the fuzzy sets theory (6). Tuning of a LE
system is more straightforward than for traditional fuzzy systems, which makes it a
good choice for diagnosis purpose (7). However, both methods are facing similar issues,
and approaches used to improve fuzzy systems can also apply to LE systems.
Feature extraction in vibration analysis can be based on velocity
)1(
x
, acceleration
)2(
x
and higher derivatives,
)3(
x
and
)4(
x
. Statistical features are selected by taking into
account the faults under consideration (8). Frequency range of the measurements is
important and several features are combined with dimensionless indices and the analysis
can be further improved by taking into account nonlinear effects (9).
Multisensor vibration analysis originates from the fact that most modern processes have
multiple inputs and outputs. Model-based fault diagnosis is based on many features and
parameters, which define the models. A test rig with several sensors and a large number
of features were used in (10) to detect and identify faults simulated by a test rig. A model
based on linguistic equations was developed for each fault case. Later the number of
features was reduced by genetic algorithms in (11). The results were in line with previous
studies on the same data set although the number was considerably smaller in (10). A
special artificial immune system (AIS) algorithm, AbNET, used in (12) was an adequate
device to characterize the particular nature of the normal conditions as well as to react
to new and unexpected anomaly situations. The results were not better but comparable
to previous studies with the same data set. However, a large number of equations and
features are not necessarily needed. The number of variables and sensors required to
diagnose each fault can be reduced considerably by selecting the most sensitive features
(13): three sensors are needed from seven, and totally seven features are used to calculate
eight health indices. Good conditions and all six fault types can be identified by seven
rules and the strength of misalignment and unbalance can be calculated. All the labels
can be defined with fuzzy numbers. The LE system reduces to seven equations for
diagnosing the faults and two equations for calculating the strengths of misalignment
and unbalance. The classification results are in line with the previous studies with the
same data set.
Lime kilns are large machines, approximately 4 meters in diameter and even more than
100 meters long, with very slow rotation speeds. Depending on production conditions,
the kiln must run at different production capacities and rotation speeds. The
distributions of the signals
)1(
x
,
)3(
x
and
)4(
x
have been used in monitoring the
condition of the supporting rolls of a lime kiln (14,15). Detecting bearing faults and
unbalance in very fast rotating rolling bearings (16) was based on standard deviations
calculated for the signal on three frequency ranges.
This paper deals with combining several features in detecting faults on the basis of long-
term research of the authors. The features are selected by comparing sensitivities in
multisensor vibration analysis or developed with the combined signal processing and
feature extraction approach.
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2. Condition indices
2.1 Signal processing and feature extraction
The generalised norm defined by
,)
1
()( /1
1
)(/1 p
N
i
p
pp
p
p
i
x
N
MM ∑
=
==
α
α
τ
α
τ
.......................................... (1)
where
ℜ∈
α
is the order of derivation, the order of the norm
ℜ∈p
is non-zero and
τ
is the sample time. The norm (1) includes the norms from the minimum to the
maximum, which correspond the orders
−∞=p
and
∞=p
, respectively. The norm
values increase with increasing order. (17,18,19) The normalised moments were in (20)
generalised by replacing
)(XE
with the norm (1) as the central value
c
:
()
,
)(
k
X
k
p
p
k
MXE
σ
γ
α
τα
−
=
......................................................... (2)
where
X
σ
is calculated about the origin, and
k
is a positive integer. The 3rd moment,
skewness, is used in the analysis of the corner points, which define the scaling
functions.
2.2 Scaling functions
Both expertise and data can be used in developing the mapping functions (membership
definitions). The basic idea is to extract the meanings of variables from measurement
signals. The scaling function scales the real values of variables to the range of [-2, +2]
which combines normal operation [-1, +1] with the handling of warnings and alarms.
The scaling function contains two monotonously increasing functions: one for the
values between -2 and 0, and one for the values between 0 and 2. (6) The membership
definition
f
consists of two second-order polynomials, i.e. the scaled values, which are
called linguistic levels
j
X
, are obtained by means of the inverse function
1−
f
:
≤−
≤≤−
−−+−
≤≤−
−−+−
≥
=
−−−
+
+++
)min(2
)min(2
2
)(4
)max(2
2
)(4
)max(2
2
2
jj
jjj
j
jjjjj
jjj
j
jjjjj
jj
j
xxwith
cxxwith
a
xcabb
xxcwith
a
xcabb
xxwith
X
......................... (3)
where
−
j
a
,
−
j
b
,
+
j
a
and
+
j
b
are coefficients of the corresponding polynomials,
j
c
is a
real value corresponding to the linguistic value 0 and
j
x
is the actual measured value.
Parameters
)min( j
x
and
)max(
j
x
corresponding to the linguistic values –2 and 2
define the support. The coefficients of the polynomials are defined by points
{ }
)2),(max(),1,)((),0,(),1,)((),2),(min(
jjhjjlj
xcccx −−
, ............. (4)
where [
jhjl cc )(,)(
] is the core.
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The scaling functions are monotonously increasing if the coefficients,
,
)()max(
)(
)()max(
)min()(
)(
)min()(
+
+
−
−
∆
−
=
−
−
=
∆
−
=
−
−
=
j
jhj
jjh
jhj
j
j
jjl
jlj
jjl
j
c
cx
cc
cx
c
xc
cc
xc
α
α
........................................... (5)
are both in the range
3,
3
1
. Corrections are done by changing the borders of the core
area, the borders of the support area or the centre point. The membership definitions of
each variable are configured with five parameters, including the centre point cj and three
consistent sets:
• corner points {
)max(,)(,)(),min(
jjhjlj
xccx
} are good for visualisation,
• parameters {
++−−
∆∆
jjjj
cc ,,,
αα
} are suitable for tuning, and
• coefficients {
++−− jjjj
baba ,,,
} are used in the calculations.
The upper and the lower parts of the scaling functions can be convex or concave,
independent of each other. Simplified functions can also be used, e.g. a linear
membership definition requires two and an asymmetrical linear definition three
parameters. Additional constraints can be taken into account for derivatives, e.g. locally
linear function results if a continuous derivative is chosen at the centre point. (21)
The value range of
j
x
is divided into two parts by the central tendency value
j
c
and the
core area, [
jhjl
cc )(,)(
], is limited by the central tendency values of the lower and upper
part. The central tendency value is chosen by the point where the skewness changes
from negative to positive, i.e.
0
3
=
γ
. Then the data set is divided into two parts: a lower
part and an upper part. The same analysis is done for these two data sets. The estimates
of the corner points,
( )
j
l
c
and
( )
j
h
c
, are the points where the direction of the skewness
changes. The iteration is performed with generalised norms. Then the ratios
−
j
α
and
+
j
α
are restricted to the range
3,
3
1
moving the corner points
( )
j
l
c
and
( )
j
h
c
or the upper
and lower limits
)min( j
x
and/or
)max(
j
x
. (20)
2.3 Condition and health indices
Cavitation indices obtained from the scaled values (20) provide an indication of the
severity of the cavitation. The indices are calculated with problem-specific sample
times, and variation with time is handled as uncertainty by presenting the indices as
time-varying fuzzy numbers. The classification limits can also be considered fuzzy.
Practical long-term tests have been performed e.g. for diagnosing faults in bearings, in
supporting rolls of lime kilns and for the cavitation of water turbines (20). The indices
obtained from short samples are aimed for use in the same way as the process
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measurements in process control. The new indices are consistent with the measurement
and health indices developed for condition monitoring. (22)
Vibration signals can be utilised in process or machine operation by combining features
obtained from derivatives. Dimensionless vibration indices can be combined in a
measurement index
( )
( )
,
)(
1
10
,...,, ,...,,
21
21
∑
=
=
n
ii
p
p
ppp
i
i
i
i
n
n
x
x
b
n
MIT
α
α
αααα
τ
....................................................... (6)
where the norms
( )
i
i
p
x
α
are obtained from the signals
nix
i
,...,1,
)(
=
α
. Each norm is
divided by its reference value, denoted by index zero, and multiplied by a weight factor
i
b
α
. The sum
nb
n
i
i
=
∑
=1
α
. The reference values correspond to the good conditions. The
inverse of the index
MIT
, denoted as
SOL
, provides a direct indication of the condition
of the machines: small values indicate poor condition and high values good condition.
(9,18)
2.4 LE Models
The LE models are linear equations
,0
1
=+
∑
=ij
m
jji
BXA
.............................................................................. (7)
where
j
X
is a linguistic level for the variable
mjj ...1, =
. Each equation i has its own
set of interaction coefficients
....1, mjA
ji
=
The bias term
i
B
was introduced for fault
diagnosis systems. Various fuzzy models can be represented by means of LE models,
and neural networks and evolutionary computing can be used in tuning. In effect, these
linear equations advantageously replace fuzzy rules as they can potentially compact a
large rule-base into a few linear equations (7,23). Membership definitions transform a
nonlinear problem into a multiple linear regression problem. The first LE application in
condition monitoring was presented in (10). The condition monitoring applications are
similar to the applications intended for detecting operating conditions in the process
industry (24).
3. Combining process and condition monitoring data
Process and condition monitoring data is combined in detecting operating conditions
(Figure 1): normal process measurements are directly used in feature extraction, signal
processing is needed for the condition monitoring data, and some infrequent
measurements need to be interpolated. The first level in the detection of operating
conditions is to find out if the process is in normal operation. Deviation from the good
operation can be detected by condition and stress indices. In complex systems with
several faults, specialised case models are needed to identify the fault cases. Degrees of
membership for the activated cases can be used for estimating some process or product
quality features. (25)
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Figure 1. Detecting operating conditions and faults (25)
4. Applications
The combined signal processing and feature extraction form a unified analysis
methodology, which has been used in various applications (18,19).
4.1 Multisensor vibration analysis
A multisensor approach has been used for fault diagnosis in a test rig that consists of an
electric motor and a transmission between two axes with SKF single row ball bearings
6002. Two sensors measured axial vibration and five accelerometers radial vibration in
the vertical direction. The rig was used to simulate nine independent fault modes: rotor
unbalance at two levels, three coupling misalignment cases between the motor and input
shaft, bent shaft, and three bearings faults. The faults were simulated one at a time. All
measurements were done by the Mechatronics and Machine Diagnostic Laboratory,
Department of Mechanical Engineering in University of Oulu. (10)
In addition to the rotation speed, five others features were calculated for each of the
seven sensors. Root-mean-square (
)2(
rmsrms xa =
) and kurtosis (
4,2
γ
) were obtained from
acceleration signals. Average of the three highest value of the jerk signal is marked )3(
p
x
. Root-mean-square velocities (
)1(
rmsrms xv =
) were calculated in two frequency ranges, 10-
1000 Hz and 20-85 Hz, and the resulting features were denoted as
1
)(
rms
v
and
2
)(
rms
v
,
respectively. The same data and the same test rig have already been used in earlier
studies (10). Root-mean-square (rms) and peak values are most commonly used for these
faults: low order derivatives can be compensated by using higher order moments (8).
Health indices SOL were used in (13) to select features from the full 35 alternatives:
specialised sensors and features can be found for the faults. Features
)3(
p
x
,
rms
a
and
4,2
γ
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of sensor 7 react only to the bearing faults. However, )3(
p
x of sensor 2 reacts to bearing
faults as well. Four alternative faults need four features:
4,2
γ
,
rms
a
and )3(
p
x of sensor 7,
and )3(
p
x of sensor 2. Health index
)( )3(
p
xSOL
has closely identical behaviour for
sensors 2 and 3. There is a small difference: sensor 2 is slightly more sensitive to
misalignment, and sensor 3 to bearing faults, respectively.
The SOL values were calculated separately for each rotation speed and the selection
was done by using the mean of the feature specific SOL values. The faults must be
analysed in two groups:
(1) misalignment and bearing faults,
(2) unbalance and bent shaft.
The diagnosis system is considerably reduced from the ones presented in (10,11,12). Three
sensors are selected from seven, and totally seven features are needed to calculate eight
health indices (Table 1). SOL indices are calculated for each feature as an inverse of the
MIT index (6), i.e.
1=n
and
1
1=
α
b
. The decision table uses indices
8,.1, =mSOL
m
,
which are weighted averages of feature specific SOL indices. The weights (1/4, 1/3, 1/2
and 1) are shown in Table 1. The good condition and all six fault types can be identified
by seven rules shown in Table 1. ‘One’ means that the health index m
SOL
is very close
to one, and ‘<1’ is ‘less than one’, i.e. the health index provides a symptom. The value
range is divided into three levels: ‘very high (VH)’, ‘high (H)’ and ‘low (L)’. All the
labels can be defined with fuzzy numbers.
Table 1. Decision table of fault detection, see (13)
SOL(Feature)
1
SOL
2
SOL
3
SOL
4
SOL
5
SOL
6
SOL
7
SOL
8
SOL
74,2
)(
γ
SOL
1/3
1
1/3
7
)( rms
aSOL
1/3
1
1/3
1/4
7
)3(
)(
p
xSOL
1/3
1
1/4
2
)3(
)(
p
xSOL
1
1/3
2
)( rms
aSOL
1/2
12 ))(( rms
vSOL
1/4
21 ))(( rms
vSOL
1/4
1/2
Good
One
One
One
Unbalance
One
<1
<1
Bent shaft
<1
One
<1
Misalignment
<1
VH
VH
VH
<1
Rolling element
<1
H
L
L
<1
Inner race
<1
H
H
L
<1
Outer race
<1
L
L
L
<1
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The first stage is to detect with the indices
1
SOL
,
5
SOL
and
7
SOL
if everything is in
good condition, i.e. these indices are ‘One’. If both
1
SOL
and
5
SOL
are less than one,
there is a fault which belongs to the group of misalignment and bearing faults. The fault
type is identified by comparing indices
2
SOL
,
3
SOL
and
4
SOL
(Table 1). The strength
of misalignment can be estimated by
5
SOL
. If
7
SOL
is less than one, the fault is either
unbalance or bent shaft. More information is obtained by
4
SOL
and
8
SOL
. The strength
of unbalance can be estimated by
8
SOL
.(13)
There are small changes in the SOL values when the rotation speed increases (Figure 2).
Differences between the features are clear in most cases. The rules presented in Table 1
can be used in detecting bearing faults and misalignment (group 1) and even the
strength of misalignment can be evaluated in these cases. More uncertainty remains in
the second group (unbalance and bent shaft) since 21 ))(( rms
vSOL depends strongly on
the rotation speed in the unbalance cases 6-10.
Figure 2. Health indices of the selected features for the measurement cases:
rotor unbalance at two levels (1-5 and 6-10), bent shaft (11-15), three coupling
misalignment cases (16-30) and three bearings faults (31-45), each obtained for five
rotation speeds from 15 to 19 rps
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The results in (26) clearly show that an extended analysis with a wide range of orders α
and p is needed for the detection of simultaneous faults in order to obtain the best
sensitivity for specific faults, also if the measurements are noisy. The power of
generalised norms is in selecting the amplified frequency ranges by the order of
derivation and in fine-tuning the sensitivity with the order of moment. The generalised
norms with orders p from 0.2 to 8 with a step of 0.2 were calculated for all the signals
)(
α
x
,
.10,8.1,2 −−=
α
The whole sample was used, i.e. the sample time
4=
τ
seconds in this study. Sensitivity is defined by dividing the norm of the signal in the
faulty case by the norm in the non-faulty case. High sensitivity for misalignment is
achieved when
6.3≈
α
and
5≥p
. For the order
α
, this area is quite narrow, but the
order
p
can be chosen from a wide range (Figure 3). The unbalance is detected well
when
1<
α
, and low orders
p
are slightly better than high orders for this fault.
Figure 3. Sensitivity of norms obtained from the signals in the faulty case (26)
4.2 Supporting rolls of a lime kiln
The norms
)max(
1
1
4
15
M
and
)max(
25.4
25.4
4
15
M
are highly sensitive to faulty situations
in the supporting rolls of a lime kiln. Surface damage and alignment problems are
clearly detected and in the present system also identified with two norms of different
order obtained from the signals
)4(
x
. An early indication of a friction increase is also
achieved. The data set covers the following cases: (1) surface problems, (2) good
conditions after grinding, (3) misalignment, (4) stronger misalignment, (5) very good
conditions after repair work, and (6) very good conditions one year later. Maintenance
was done for one of the supporting rolls. All the rolls can be analysed using the same
The Tenth International Conference on Condition Monitoring and Machinery Failure Prevention Technologies
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features throughout the data set. All the faults, friction and minor fluctuations were
validated by listening to the recorded acceleration signals and analysing time domain
signals and frequency spectra with an oscilloscope and a real time analyser. (27)
The scaled features provide a clear indication of the condition in each measurement
point (Figure 4). The overall condition can be defined as an average of the scaled
features. All the very good cases are close to the lower corner
[ ]
2,2 −−
. The average
index is below zero for the good cases and also for cases with small fluctuations. These
cases are clearly usable. For still acceptable cases, the index is below one. All the faults
and clear friction cases are in the area where the index
,1>
i.e. the severity level is ‘not
acceptable’. The levels {-1, 0, 1} are analogue to the lower limits of the vibration
severity ranges {usable, still acceptable, not acceptable} defined in the VDI 2056 (28,29).
Figure 4. Scaled norms, p = 1 and 4.25, to different condition of the points 1-16:
surface damage (), misalignment (), friction (), very good (), good (), small
fluctuations (), and special cases () (20)
The upper corner
[ ]
2,2
is related to the case where the temperature was reduced by
cooling. The very high signal levels are caused by noise, but the hidden faults can be
detected by stopping the cooling for a moment. The abnormal feature levels mean that
some additional analysis needs to be carried out. Special cases, such as the effects of the
rotation counter and jingles, can be detected by comparing the indices obtained from the
maximum values to those obtained from the mean values. All the condition levels can
be defined with fuzzy membership functions. (20) A basis for fuzzy rules for detecting
friction, surface damage and misalignment can be seen in Figure 4 and specialised
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condition indices can be developed for different types of fault by using the weighted
sums of the features. The levels {-1, 0, 1} are then used as warning and alarm limits.
4.3 Very fast rotating rolling bearings
For fast rotating bearings, the condition index is a sum of the scaled standard deviations
of the signal
)4(
x
calculated for three frequency ranges:
)()()(
43
1
4342
1
4241
1
41
σσσ
−−−
++= fffInd
............................................... (8)
where
1
4−
i
f
is the scaling function of the standard deviation i4
σ
in three frequency
ranges 10 –1000 Hz, 10 –10000 Hz, and 10 –50000 Hz. The faults are correctly detected
(Figure 5) with the algorithm (16):
• Calculating the condition index.
• The condition is normal if Ind < -5…-4.
• There is an outer race fault in the bearings if Ind < 0.
• The condition is unbalance if the index for the low frequency range is very high,
• Otherwise the condition is inner race fault in the bearings.
The minimum of the index Ind is -6 which is achieved when all the features are at the
lowest level.
Figure 5. Classification results for fast rotating bearings, the rotation frequency
was 525 Hz (9)
The applicability of different norms has been studied in (30). The norms based on the
signal
)4(
x
provide the best results in all the frequency ranges. The high range has the
best indication results: all the sensitivity values are high, and the values for different
faults are at specific levels. In the low frequency range, the order
p
has a strong effect
on the indication of the inner and outer race faults, especially when
p
increases from 1
to 3. It is interesting that the signal
)4(
x
provides better sensitivities for the outer race
faults in the range 10-1000 Hz than in the range 10-10000 Hz, if the order
p
is high
enough. This means that the number of required signal points can be reduced to 1/10
when the signal
)4(
x
is used. The absolute mean is sufficient in many cases. Unbalance
The Tenth International Conference on Condition Monitoring and Machinery Failure Prevention Technologies
12
is detected in the frequency range 10-1000 Hz with all the signals
)(
α
x
,
α
=1, 2, 3 and
4. All the faults were detected with the relative
)max(
4p
p
M
τ
in the low frequency
range 10-1000 Hz, which is very important for the development of intelligent sensors.
5. Conclusions
Features can be selected by using feature specific health indices: the number of sensors
and features were drastically reduced in multisensor vibration analysis, where the
decision table contains four feature specific and four combined health indices. The
advanced signal processing and feature extraction approach produces efficient
generalised norms, which further reduce the number of features and simplify the
models.
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C Technica 255, Oulu University Press, 2006.
8. S Lahdelma and E Juuso, ‘Advanced signal processing in mechanical fault
diagnosis’, CM 2008 – MFPT 2008, 5th International Conference on Condition
Monitoring & Machinery Failure Prevention Technologies, Edinburgh, Coxmoor,
Oxford, UK, pp 879-889, July 2008.
9. S Lahdelma and E Juuso, ‘Advanced signal processing and fault diagnosis in
condition monitoring’, Insight, Vol 49, No 12, pp 719–725, 2007.
10. E K Juuso, M Kivistö and S Lahdelma, ‘Intelligent Condition Monitoring Using
Vibration Signals’, Proceedings of EUNITE 2004, Aachen, Germany, Verlag
Mainz, Aachen, pp 381-390, June 2004.
11. O Rami-Yahyaoui, S Gebus, E Juuso and M Ruusunen,’Tuning of linguistic
equations for failure mode identification using genetic algorithms’, Proceedings
CM 2008 – MFPT 2008, pp 1543-1553, July 2008.
12. J Strackeljan and K Leiviskä, ‘Artificial immune system approach for the fault
detection in rotating machinery’, Proceedings CM 2008 – MFPT 2008, pp 1365-
1375, July 2008.
The Tenth International Conference on Condition Monitoring and Machinery Failure Prevention Technologies
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13. E Juuso, M Ruusunen and G Perigot, ‘Linguistic Equation Models for Failure
Mode Identification from Multisensor Vibration Analysis’, Proceedings CM 2010 –
MFPT 2010, 7th International Conference on Condition Monitoring & Machinery
Failure Prevention Technologies, Stratford-upon-Avon, UK, BINDT, UK, Vol 2,
pp 1408-1420, June 2010.
14. S Lahdelma and E Juuso, ‘Intelligent Condition Monitoring for Lime Kilns’,
Tagungsband zum 6. Aachener Kolloquium für Instandhaltung, Diagnose und
Anlagenüberwachung, AKIDA 2006, Aachen, Germany, Aachener Schriften zur
Rohstoff- und Entsorgungstechnik des Instituts für Bergwerks- und
Hüttenmaschinenkunde, ASRE, Band 63, RWTH Aachen, pp 399-408, November
2006.
15. E Juuso and S Lahdelma, ‘Advanced Condition Monitoring for Lime Kilns,
Proceedings WCEAM-CM 2007, 2nd World Congress on Engineering Asset
Management and 4th International Conference on Condition Monitoring, Harrogate,
UK, Coxmoor, Oxford, UK, pp 931-942, June 2007.
16. S Lahdelma, E Juuso and J Strackeljan, ‘Neue Entwicklungen auf dem Gebiet der
Wälzlagerüberwahung’, Tagungsband zum 6. Aachener Kolloquium fűr
Instandhaltung, Diagnose und Anlagenűberwachung, AKIDA 2006, November 14-
15, 2006, Aachen, Germany, pp 447-460, 2006.
17. S Lahdelma and E Juuso, ’Signal Processing in Vibration Analysis’, Proceedings
CM 2008 – MFPT 2008, 5th International Conference on Condition Monitoring &
Machinery Failure Prevention Technologies, Edinburgh, Coxmoor, Oxford, UK, pp
867-878, July 2008.
18. S Lahdelma and E Juuso, ‘Signal Processing and Feature Extraction in Vibration
Analysis, Part I: Methodology’, The International Journal of Condition Monitoring,
Vol 1, No 2, pp 46-53, 2011.
19. S Lahdelma and E Juuso, ‘Signal Processing and Feature Extraction in Vibration
Analysis, Part II: Applications’, The International Journal of Condition Monitoring,
Vol 1, No 2, pp 54-66, 2011.
20. E Juuso and S Lahdelma, ‘Intelligent scaling of features in fault diagnosis’,
Proceedings CM 2010 – MFPT 2010, 7th International Conference on Condition
Monitoring and Machinery Failure Prevention Technologies, Stratford-upon-Avon,
UK. BINDT, Vol 2, pp 1358-1372, June 2010.
21. E K Juuso, ’Tuning of large-scale linguistic equation (LE) models with genetic
algorithms’, Adaptive and Natural Computing Algorithms, Revised selected papers
- ICANNGA 2009, Kuopio, Finland ICANNGA 2009, Lecture Notes in Computer
Science (LNCS) 5495, pp 161-170, Springer, Heidelberg, 2009.
22. E Juuso and S Lahdelma, ’Intelligent Condition Indices in Fault Diagnosis’,
Proceedings CM 2008 – MFPT 2008, 5th International Conference on Condition
Monitoring & Machinery Failure Prevention Technologies, Edinburgh, Coxmoor,
Oxford, UK, pp 698-708, July 2008.
23. S Gebus and E K Juuso, ‘Industrial utilization of linguistic equations for defect
detection on printed circuit boards’, Proceedings of IECON’02, Sevilla, Spain, pp
1887 – 1892, November 2002.
24. E Juuso and S Lahdelma, ‘Intelligent Trend Indices and Recursive Modelling in
Prognostics’, Proceedings CM 2011 – MFPT 2011, 8th International Conference on
Condition Monitoring and Machinery Failure Prevention Technologies, Cardiff,
UK. BINDT, Vol 1, pp 440-450, June 2011.
The Tenth International Conference on Condition Monitoring and Machinery Failure Prevention Technologies
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25. E Juuso and K Leiviskä, ‘Combining Process and Condition Monitoring Data’,
Maintenance, Condition Monitoring and Diagnostics, Oulu, Finland, POHTO
Publications, POHTO, Oulu, pp. 120-135, September 2010.
26. S Lahdelma, E Juuso and J Laurila, ‘Real Order Derivatives and Generalised
Norms in Condition Monitoring with Noisy Data’, Proceedings CM 2012 – MFPT
2012, 9th International Conference on Condition Monitoring and Machine Failure
Prevention Technologies, BINDT, Vol 2, pp 879-895, June 2012.
27. S Lahdelma and E Juuso, ‘Generalised lp Norms in Vibration Analysis of Process
Equipments’, Proceedings CM 2010 – MFPT 2010, 7th International Conference on
Condition Monitoring & Machinery Failure Prevention Technologies, Stratford-
upon-Avon, UK, BINDT, UK, Vol 1, pp 614-626, June 2010.
28. VDI 2056 Beurteilungsmaβstäbe für mechanische Schwingungen von Maschinen,
VDI-Richtlinien, Oktober 1964.
29. R A Collacott, ‘Mechanical Fault Diagnosis and Condition Monitoring’, Chapman
and Hall, London, 1977.
30. S Lahdelma and E Juuso, ‘Generalised Moments and lp Norms in Vibration
Analysis’, Proceedings CM 2009 – MFPT 2009, 6th International Conference on
Condition Monitoring & Machinery Failure Prevention Technologies, Dublin,
Coxmoor, Oxford, UK, pp 607-619, June 2009.
The Tenth International Conference on Condition Monitoring and Machinery Failure Prevention Technologies
