Quantitative and qualitative data analysis,
Condition based maintenance,
Evidential reasoning
Damir BLAŽEVIĆ1
Franjo JOVIĆ1
Igor LUKAČEIVĆ2
COMPLEX DATA ANALYSIS IN CONDITION BASED MAINTENANCE
The article describes numerical techniques used for translating quantitative data collected by power distribution
system's measuring equipment in to a qualitative domain.
Plausible qualitative degrees are essential in process of assessing condition state of power distribution system.
Entire aggregation process is based on evidential reasoning algorithm and it relays upon accuracy of the
qualitative degrees. Special effort must be engaged in the translation process to ensure data integrity.
Techniques for quantitative to qualitative conversion of data are proposed.
Condition based maintenance of power distribution system can be performed after successful translation process
and object decomposition based on Dampster-Shaffer theory.
The major obstacle is one – to – many correspondences of real-time measurement data and object condition
based decomposition.
Results for quantitative to qualitative data conversion and corresponding aggregation processes are presented.
1. INTRODUCTION
Condition based maintenance is one of several types of technical maintenance. This
kind of maintenance is based on the state of an object or system to be maintained. In spite of
condition based maintenance, preventive maintenance is performed by a specific schedule
with intend to avoid functional errors and failures. The basic advantage of this kind of
maintenance is guaranteed high availability of maintained object or system. Basic
disadvantage is partial and not adequate use of an object lifetime. Maintenance after failure
is the next kind of maintenance where in opposite of the preventive maintenance entire
lifetime of an object is used. Major disadvantage of this approach is the fact that failure
needs to happen for the maintenance to begin with. Also it is not possible to predict time or
expenses needed for failure recovery. This approach demands certain supply of the spare
parts and/or adequate substitutes. The type of maintenance to be considered here is the
1
Faculty of Electrical Engineering Osijek
2
HEP – Croatian National Grid Company
condition based maintenance. It is a demanding approach because of the need for frequent
inspection and monitoring of an object, part of the system or entire maintained system, but it
offers an optimal usage of the objects lifetime. Experience with degradation of the object
condition and analytic skills are required for this approach. Relevant information needs to
be gathered frequently or even constantly. If this information can also be easily measured,
then they are suitable for online intelligent monitoring. This means that this kind of
information are gathered, locally processed and transferred to the central part of the
monitoring system where it can be further processed by the use of complex algorithms,
analyzed and stored. In spite of modern and powerful monitoring equipment there will still
be information that cannot be online monitored due to complex measuring procedure or
information nature (oil chromatography, assessment of objects general state, etc.). This kind
of information requires a trained professional to provide measurement or assessment.
Gathered information should be adequately processed and interpreted.
This article describes numerical techniques used for translating gathered information
in to qualitative domain. The nature of gathered information (measured values) determines
translation techniques to be used. There are several different types of information and
adequate techniques for translating them. Procedures used for translation of continue values
in to qualitative degrees are revised in the next section. In section 3, techniques used for
assessing component condition state based upon component or object's age are presented.
Translation of discrete values is covered in section 4, while conclusion is given in section 5.
After the translation process the necessary input values for multiple attribute decision
analysis (MADA) [1,3] and evidential reasoning (ER) [2,8] approach are obtained. MADA
and ER approach used in condition based maintenance of power distribution station (PDS)
and power distribution system (PDSY) are in detail described in [4] and [13].
2. CONTINUES VALUE TRANSLATION
Let us assume that object condition state assessment is based on measurement of
continuous value x (transformers oil humidity level, circuit breaker time off, etc.). Due to
different variables in measuring process one or more measured values will have different
values. Such gathered data are distributed according to certain statistical distribution. In
most cases that distribution can be represented by normal or Gaussian distribution with
following parameters: x and 2 (mean and standard deviation). By the use of mean and
standard deviation measured values are transformed in to qualitative values.
According to the manufacturers recommendation and users experience observed objects are
grouped into classes with assigned qualitative degrees. Classes are defined according to
gathered data discrepancy. Boundaries between classes are not strictly defined and degree
overlapping is present. Instead of firm boundaries definition, mean and standard deviation
are calculated for each class of data (shown in Figure 1.).
To each data set class n = 1, … N, qualitative degree Hn, mean x n and standard deviation
 n2 are assigned. Parameters x n and  n2 are assessed on different ways according to type of
measured value, type of an object, manufacturers recommendation, malfunction statistic and
experience of an assessor.
bn
0.6
b 5 (x)
0.5
b 4 (x)
0.4
b 3 (x)
b 2 (x)
b3
0.3
b 1 (x)
0.2
0.1
b4
0
b2
0
2
4
6
8 x 10
m
12
14
16
18
20
x / ppm
Fig. 1. Division of measured value x into five qualitative classes with assigned values for b n
Qualitative degree Hn with degree of belief n is defined by normal distribution with x n and
 n2 parameters as follows:

1
n ~ bn 
( x  xn ) 2
2 n2
(1)
 n 2
It is reasonable to assume that measurement of physical value is exact procedure and that
involved uncertainty does not exist. According to the above, degree of belief n is
normalized as follows:
N

n 1
n 
n
e
1
(2)
bn
N
b
n 1
(3)
n
Normal distribution of data suggests certain probability for each measured value, therefore
each qualitative degree would have certain probability. To simplify the procedure we can
discard degrees with low probability (less then 0.05). Figure 1. and Figure 2. represent
translating process and degree assessment of transformers oil according to the measurement
of humidity level in ppm.
Similar graph can be generated for all assessment attributes where qualitative degree is
proportional to measured value (oil's gas level, joint temperature, load, circuit breaker's time
off, etc.)
n
1
5
2
3
4
1
0.9
3
0.8
0.7
0.6
0.5
0.4
0.3
0.2
4
0.1
2
0
0
2
4
6
8 xm 10
12
14
16
18
20
x / ppm
Fig. 2. Normalized degrees of belief for each qualitative deegre
For assessment of attributes where the observed value is positive or negative deviation from
optimal or ideal value, qualitative degree is proportional to absolute value of difference
between optimal and measured value. For this case typical example is measurement of
synchronous circuit breaking of three-pole circuit breaker (shown in Figure 3.). Ideal
latency of other two poles over first one is t0 = 2 ms. Observed value is absolute value
between measured time t and ideal value t0:
(4)
t  | t  t0 |
bn
0.6
b5 (t)
0.5
b4 (t)
0.4
b3 (t)
b2 (t)
0.3
b1 (t)
0.2
0.1
0
0.5
1
1.5
2
2.5
t / ms
Fig. 3. Assessment of synchronous circuit breaking of three-pole circuit breaker
3. TIME (AGE) TRANSLATION
In case when object's condition is performed on the basis of objects age attribute, the
reliability time function is determined first. To determine this function, knowledge of failure
statistic for observer or similar object is necessary. One of the major parameters is failure
intensity (t), witch represents probability for failure to happen in certain point of time.
Reliability function is given as follows:
t
R(t )  e

  dt
(5)
In most cases failure intensity is constant value for considerable objects exploitation time.
Often it is expressed as Mean Time To Failure (MTTF):
MTTF 
0
1
(6)

If  is a constant then expression (5) can be written as follows:
(7)
R(t )  e  t
Reliability interval R(t) [0,1] is divided into N intervals with corresponding qualitative
degrees Hn, n=1,…,N. Division of reliability interval can be uniform (shown on Fig. 4) or
different according to the assessors decision.
bn, R
1
0.9
0.8
H5
b5 (t)
0.7
H4
b4 (t)
0.6
0.5
H3
b3 (t)
0.4
0.3
H2
0.2
b2 (t)
0.1
b1 (t)
H1
R(t)
0
0 t5 t4 t310
t2
20
t1 30
40
50
60
t / months
Fig. 4. Assessment of qualitative degrees based on age of observed object
Each data class is represented by its mean Rn , witch is mirrored to time line as follows:
R n  e  t n
1
t n   ln Rn
(8)
(9)

For known age level t qualitative degrees Hn are assigned to observed attributes. The degree
reliability is increasing with variable t closing to the middle of tn interval. For this reason
each interval n = 1,…,N is assigned normal distribution with mean n = tn:
bn 

1
 n 2
e
( t t n ) 2
2 n2
(10)
Standard deviation is chosen as follows:
bn (t n )  Rn
1
n 
Rn 2
(11)
(12)
Overall reliability of all degrees is normalized according to following expression:
n 
bn
N
b
n 1
 (1   H )
(13)
n
where H is measurement uncertainty. Mentioned measurement uncertainty can occur by the
influence of several different factors like lack of knowledge of exact object age level or
failure intensity of such devices. Figure 6. represents reliability for each five qualitative
degrees normalized to 100 % for disconector with mean time to failure MTTF = 12 months.
n
4
5
1
1
2
3
0.8
0.6
0.4
0.2
0
0
10
20
30
40
50
60
t / months
Fig. 5. Normalized reliability of qualitative degrees for disconector with MTTF=12 months
4. DISCRETE VALUE TRANSLATION
In general discrete value x can obtain an finite number of values K :
x   xk ; k  1, 2, ..., K 
(14)
Therefore xk can be:
- Specific numeric value (surge arrester count number).
- One value from a finite set of values (for example in assessment of Buholtz relay
condition state three states are possible: A – functional state; B – warning; and C –
failure/shutdown state).
- Descriptive value (for example good, bad, average).
In most cases number of values K is relatively small, meaning that K is lower than 10. For
values greater than 10, methods for continuous variables mentioned above are appropriate.
For each value xk set of qualitative degrees of belief is assigned upon following expression:
(15)
xk  ( H n ,  n ) k n  1, 2, ..., N
The simplest way for degree assignment is by the use of a following lookup table.
state\degree
x1
x2
…
xk
…
xK
H1
H2
…
Hn
…
…
11
21
n1
…
…
12
22
n2
…
…
…
…
1k
2k
nk
…
…
…
…
…
1K
2K
nK
Table 1. Lookup table for transformation of discrete data into qualitative degrees
HN
N1
N2
…
Nk
…
NK
In practical assessment each state of xk is assigned with one or two degrees so that most
cells of the table will be zeros. Uncertainty of a single state is analytically determined from
the uncertainty of all states as follows:
N
 Hk  1    nk
(16)
n 1
Expert assessor or a group of experts for specific device type assigns values of parameters
nk. Methods used for uncertainty definition are mostly experience based and defined for
each assessment separately.
Let us have a closer look at the Buholtz relay:
- Buholtz relay is component with strong influence on overall assessment of
transformer. (Especially state C – failure/shutdown possess a strong negative
influence.) Therefore the weight of its attribute 1142 is relatively high.
- When Buholtz relay is in state C – failure/shutdown, transformer and corresponding
elements of power distribution station are shutdown. In such case the qualitative
degree 13 is strictly negative meaning 13=1.
- Desirable state for Buholtz relay s state A – witch indicates normal functional state of
a device. In such case state A is neutral meaning that it does not give us any specific
information about transformers condition, so this degree should not have strong
influence on aggregation process and overall qualitative degree of transformer.
Because the defined weight 1142 cannot lowered because state C, average qualitative
degree for its condition state is assigned. It is possible for relay to be malfunction and
in spite of a failure it signals A state. Therefore certainty of this degree is 70%.
- State B indicates a warning, meaning failure or decreased oil level. Described state
usually demands maintenance to occur so it is necessary that qualitative degrees are
relatively poor, 12 = 0.4 and 22 = 0.3. For the same reasons mentioned above
uncertainty of a given degree is relatively high H = 0.3.Asigned qualitative degrees
and related uncertainty are given in Table 2.
state\degree
Poor
Indifferent
Average
Good
Excellent
A – functional
0
0
0.7
0
0
B – warning
0.4
0.3
0
0
0
C –failure/shutdown
1.0
0
0
0
0
Table 2. Assessment of transformer based on Buholtz relay condition state
Uncertainty
0.3
0.3
0
Assessment of qualitative degrees for surge arrester, based upon the surge count, is
described in following example. Observed variable is surge count that can be rather high:
(17)
x 0, 1, 2, ... .
Rough assessment of average surge count for local power grid company is estimated to 0.1
counts per surge arrester per year. During the average surge arrester's lifecycle
(approximately 15 to 20 years) average count is 2. Surge counter counts only significant
cases where high-energy surges are involved. More sophisticated surge arrestor design tends
to rank current impulse of a surge, since it is crucial information for condition assessment.
Because of very small set of data x is available these attributes cannot be statistically
analyzed attributes analyzed in previous sections. For this attribute degree assessment
following graphic representation is used as shown at Fig. 6.
1
H
0.8
5
1
0.6
4
3
0.4
2
0.2
0
1
2
3
4
5
6 x
Fig. 6. Assessment of qualitative degrees for surge arrestor based upon surge count number
Assessment of attributes degrees is proportional to 1/surge count number. Uncertainty of
qualitative degrees depends upon uncertainty of component it self witch is subject to
manufacturer, type and construction of surge arrestor.
5. CONCLUSION
Once the decomposition of power distribution station (or any other observed object)
is performed and actual measurement has been accomplished, techniques described here are
used to prepare measured variables for aggregation process. Methods for translating
gathered data (quantitative and qualitative) are rather complicated as seen. Different types of
data demand different translation techniques. Lots of experience knowledge is needed for a
plausible translation.
Decomposition of power distribution station and qualitative degrees obtained by the use of
described techniques are given in Table 3.
General attribute
Basic attribute
Gas level 1111
Transformer oil 111
Coil 112
Transformer
11
Power
distribution
station
Load 113
Measuring and
protection equipment
114
Cooling system 115
Primary
equipment
1
Humidity level
1112
Age state 1113
Winding
temperature 1121
Temperature
sensor 1141
Buholtz relay 1142
Tap changer 116
Circuit breaker 12
Disconnector 13
Busbar 14
Vibration 141
Joint temperature
142
Instrument transformers 15
Surge arrester 16
Secondary
equipment
2
Measuring equipment 21
Power supply 22
Protection 23
Communication equipment 24
Surge counter 161
Leakage current
162
Assess
ment of
PDS
A(0.7),
G(0.2)
A(0.5),
G(0.5)
G(1)
G(0.5),
E(0.5)
G(0.4),
E(0.6)
G(1)
G(1)
G(1)
A(0.3),
G(0.6)
A(0.4),
G(0.6)
G(1)
G(1)
A(05),
G(0.4)
G(0.7),
E(0.3)
G(1)
A(0.3),
G(0.7)
A(0.8)
G(0.7)
A(1)
G(1)
Table 3. Decomposition of power distribution station and qualitative degrees
Data shown in Table 2. is just an input for aggregation process described in detail in [4] and
[13]. This paper in addition to [4] and [13] represent set of procedures needed for Condition
based maintenance of power distribution station or a power distribution system consisted of
several distribution stations.
If procedures described here, in [4], and [13] are performed continuously, or at regular time
intervals, then we have appropriate data to describe condition state of a power distribution
station as a time function. Based on analysis of this time function it is possible to make
decisions concerning maintenance. In case when we have condition state of power
distribution station described as a time function and appropriate knowledge base system,
prediction of failures may be achieved.
Example calculations in assessment of the power distribution system are performed by the
use of windows based System assessor software (SAS) with implemented evidential
reasoning algorithms for aggregation process.
This tool gives us ability to possess an on demand insight of the condition state of a power
distribution system and it’s degradation in operation and improvement after maintenance, as
well.
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