Rate of Change (Trend) - IEEEgrouper.ieee.org/.../fluids/C57.104/...Beauchemin.pdf · Rate of...
Transcript of Rate of Change (Trend) - IEEEgrouper.ieee.org/.../fluids/C57.104/...Beauchemin.pdf · Rate of...
Rate of Change (Trend)
∆ PPM, PPM/day or PPM/Year
What make sense?
C. Beauchemin
TJH2b Analytical Services Inc.
IEEE Transformer Committee
Fall 2013 Meeting
C57.104
St-Louis, October 20 – 24, 2013
Fall 2012
• Luiz Cheim presentation (On the Web)
• Review of work done to date
• Review of factors influencing limits
• Presentation also covered various aspect
of rate computation
Rate of Gas Increase (ppm/year) vs Sampling
Interval???
Rate of Gas Increase (ppm/year) vs Sampling
Interval???
Food for Thought…
Rate of Gas Increase (ppm/year) vs Sampling
Interval???
Further work to clarify this question
• Study of a new set of data
• Single source (one lab)
• North America
• Mix of industrial and utilities
Data set
• One source
• 123 469 DGA
• 44 266 Transformers
• Delta computed between actual and
previous DGA
• 78 660 pairs of DGA
• All Gas + TDCG
Sampling Interval
Time between sampling
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0 200 400 600 800 1000 1200 1400
Sampling Interval Days
De
ns
ity
26 D
ays
91 D
ays
186 D
ays365 Days
735 D
ays
942 D
ays
1107 D
ays
551 D
ays
Sampling Interval
Time between sampling
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0 200 400 600 800 1000 1200 1400
Sampling Interval Days
De
ns
ity
1 M
on
th
3 M
on
ths
6 M
on
ths
1 Year
2 Y
ears
2.5
Ye
ars
3 Y
ears
1.5
Ye
ars
Data set
• Table 3 use TDCG rates of 10 - 30 ppm/day
• ppm/year or ml/day is also used to evaluate
gassing rate
• Preliminary study (last meeting) has been
done in ppm/year
• 1 ppm/day = 365 ppm/year
• 10 ppm/day = 3650 ppm/year
• 30 ppm/day = 10950 ppm/year
DGA “Noise”
• Oil sampling, transport and analysis do
introduce DGA variations from one sample
to the next
• The same difference between two samples
could give different ppm/day (or ppm/year)
depending of the period between samples
• It is of particular importance for on-line data
• How that affect interpretation?
An Example: CH4
• The data set was splits in 8 Groups
corresponding to 8 different average
sampling periods
• Week, Month, Quarter, Half-Year, Year,
2 Years, 3 Years and > 4 years
• For each DGA, ppm/year was computed
• For each groups, a standard statistic study
was performed
Time between sampling
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0 200 400 600 800 1000 1200 1400
Sampling Interval Days
De
ns
ity
Month
Quart
er
Half Y
ea
r1 Year
2 Y
ears
3 Y
ears
Long
Week
Sampling Interval
Data SetSampling Intervals
2% 5%7%
11%
57%
10%
4%
4%
Week
Month
Quarter
Half Year
1 Year
2 Years
3 Years
Long
Some Definitions
95 Percentile: 95% of the samples are below that value
Absolute Change (Delta) Delta PPM = PPMnow – PPMlast sample
Normalised Change (Trend)Trend = Delta PPM / (Datenow – Datelast sample)
in PPM/Day
in PPM/Year (PPM/Day * 365)
BoxPlot Graph
BoxPlot Graph
First Quartile (25%)
Third Quartile (75%)
Median50% of
Population
Q1 - 1.5 IQR
Q3 + 1.5 IQR
Outliers
Outliers
Inter Quartile
Range
BoxPlot Graph
• Usefully to visually evaluate a group of
data
– Spread of data
– Middle Value
– Symmetry of distribution
– Outliers
• Easy to compare several groups of data
• So, what do we have with trend data ?
CH4 Normalised RateCH4
PP
M / Y
ea
r
We
ek
Mo
nth
Qu
art
er
Ha
lf Y
ea
r
Ye
ar
2 Y
ea
rs
3 Y
ea
rs
Lo
ng
CH4
PP
M / Y
ea
r
We
ek
Mo
nth
Qu
art
er
Ha
lf Y
ea
r
Ye
ar
2 Y
ea
rs
3 Y
ea
rs
Lo
ng
CH4 Normalised Rate
CH4
PP
M / Y
ea
r
We
ek
Mo
nth
Qu
art
er
Ha
lf Y
ea
r
Ye
ar
2 Y
ea
rs
3 Y
ea
rs
Lo
ng
CH4 Normalised Rate
95 Percentile Rate VS Sampling Interval
0
500
1000
1500
2000
2500
3000
3500
Week Month Quarter Half Year 1 Year 2 Years 3 Years Long
Sampling Interval
95
Pe
rce
nti
le R
ate
(p
pm
/ye
ar)
CH4 Normalised Rate
From Last Presentation
CH4 Normalised Rate
A ratio of 463 between “weekly” and “long term” sampling !!
Sampling Period PPM/Year PPM/Day
Week 3115 8.5
Month 1028 2.8
Quarter 235 0.64
Half Year 55 0.15
1 Year 19 0.052
2 Years 12 0.033
3 Years 8.3 0.023
Long 6.7 0.018
95 Percentile of Rate
CH4 Normalised Rate
• If we want to use PPM/year (or PPM/Day)
we obviously need a method to handle this
spread
• Should we have a table for each period?
• Which periods ?
• How many ?
• How complex ?
• Added to the “other” complexities ?
Normalised Rate and noise
• Maybe we are looking at it the wrong way ?
• If we have noise in the data, it would
probably be the same for short and long
period
• If we divide a fixed value by an increasing
period, we will obtain a log like curve
• As an example, let take 25 ppm / 1 day,
/7 days, /14 days … to ppm / year…..
• Then:
Simulation of a Constant PPM Delta
Example of Fixed Delta / Increasing Sampling Period
0
1000
2000
3000
4000
5000
6000
7000
< 3 3 - 5 5 - 10 10 -
15
15 -
30
30 -
60
60 -
90
90 -
120
120 -
180
180 -
240
240 -
365
> 365
Sampling Period Days
PP
M / Y
ea
r
Simulation of a Constant PPM Delta
Example of Fixed Delta / Increasing Sampling Period
1
10
100
1000
10000
< 3 3 - 5 5 - 10 10 -
15
15 -
30
30 -
60
60 -
90
90 -
120
120 -
180
180 -
240
240 -
365
> 365
Sampling Period Days
PP
M / Y
ea
r
From Previous Presentation
Change of Perspective
• So, let try to drop the notion of normalised
rate (Trend) (PPM/day or PPM/year)
• Let look at the ABSOLUTE difference (in PPM) between two samples (Delta)
• Let group results by sampling period, as a
few slides before
• What do we have ?
CH4 Absolute ChangeCH4
De
lta
PP
M
We
ek
Mo
nth
Qu
art
er
Ha
lf Y
ea
r
Ye
ar
2 Y
ea
rs
3 Y
ea
rs
Lo
ng
CH4 Absolute Change
95 Percentile Absolute Change VS Sampling Interval
0
20
40
60
80
100
120
Week Month Quarter Half Year 1 Year 2 Years 3 Years Long
Sampling Interval
De
lta
(p
pm
)
All samples
CH4 Absolute Change
• Ratio has been reduced by a factor of 100
• A lot more manageable !!
• The use of absolute variation between
consecutive samples, without day or year
normalisation, give more uniform results and
is simpler to use
• What else could we learn from this data set ?
CH4 Gas Level in PPM
90 Percentile PPM
0
50
100
150
200
250
300
350
400
Week Month Quarter Half Year 1 Year 2 Years 3 Years Long
Sampling Interval
90
Pe
rce
nti
le P
PM
0
1
2
3
4
5
6
7
8
9
10
% S
am
ple
s >
Co
nd
itio
n 4
All samples
CH4 Gas Level in PPM
Percentage of Samples above condition 4
0
20
40
60
80
100
120
Week Month Quarter Half Year 1 Year 2 Years 3 Years Long
Sampling Interval
De
lta
(p
pm
)
0
1
2
3
4
5
6
7
8
9
10
% S
am
ple
s >
Co
nd
itio
n 4
95 Percentile Absolute Change and % of Samples above
Condition 4
0
20
40
60
80
100
120
Week Month Quarter Half Year 1 Year 2 Years 3 Years Long
Sampling Interval
De
lta
(p
pm
)
0
1
2
3
4
5
6
7
8
9
10
% S
am
ple
s >
Co
nd
itio
n 4
CH4 Absolute Change
Percentage of points
With CH4 in Condition 4
PPM Change between samples
CH4 Absolute Change
95 Percentile Absolute Change VS Sampling Interval
0
20
40
60
80
100
120
Week Month Quarter Half Year 1 Year 2 Years 3 Years Long
Sampling Interval
De
lta
(p
pm
)
All Points
Points Condition 4
Removed
95 Percentile Absolute Change VS Sampling Interval
0
20
40
60
80
100
120
Week Month Quarter Half Year 1 Year 2 Years 3 Years Long
Sampling Interval
De
lta
(p
pm
) CH4 Absolute Change
All Points
Points Condition 4
Removed
Points Condition 3 & 4
Removed
95 Percentile Absolute Change VS Sampling Interval
0
20
40
60
80
100
120
Week Month Quarter Half Year 1 Year 2 Years 3 Years Long
Sampling Interval
De
lta
(p
pm
) CH4 Absolute Change
All Points
Points Condition 4
Removed
Points Condition 3 & 4
Removed
Points Condition 2 & 3 & 4 Removed
Other Gas
• H2, C2H4 and C2H2 have the same type of
distribution
• CO and CO2 form a different group
• C2H6 and TDCG are between the two groups
Other Gas
• “Type I”
• Short Term Rate Higher than long term
• Short Term Level Higher than long term
– Hydrogen
– Methane
– Eyhylene
– Acethylene
H2 Absolute ChangeH2
De
lta
PP
M
We
ek
Mo
nth
Qu
art
er
Ha
lf Y
ea
r
Ye
ar
2 Y
ea
rs
3 Y
ea
rs
Lo
ng
H2 Absolute Change
95 Percentile Absolute Change VS Sampling Interval
0
50
100
150
200
250
300
350
400
450
Week Month Quarter Half Year 1 Year 2 Years 3 Years Long
Sampling Interval
De
lta
(p
pm
)
0
1
2
3
4
5
6
7
8
9
10
% S
am
ple
s >
Co
nd
itio
n 4
C2H4 Absolute ChangeC2H4
De
lta
PP
M
We
ek
Mo
nth
Qu
art
er
Ha
lf Y
ea
r
Ye
ar
2 Y
ea
rs
3 Y
ea
rs
Lo
ng
C2H4 Absolute Change
95 Percentile Absolute Change VS Sampling Interval
0
20
40
60
80
100
120
Week Month Quarter Half Year 1 Year 2 Years 3 Years Long
Sampling Interval
De
lta
(p
pm
)
0
2
4
6
8
10
12
14
% S
am
ple
s >
Co
nd
itio
n 4
C2H2 Absolute ChangeC2H2
De
lta
PP
M
We
ek
Mo
nth
Qu
art
er
Ha
lf Y
ea
r
Ye
ar
2 Y
ea
rs
3 Y
ea
rs
Lo
ng
C2H2 Absolute Change
95 Percentile Absolute Change VS Sampling Interval
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Week Month Quarter Half Year 1 Year 2 Years 3 Years Long
Sampling Interval
De
lta
(p
pm
)
0
1
2
3
4
5
6
7
8
9
10
% S
am
ple
s >
Co
nd
itio
n 4
Other Gas
• “Type II”
• Short Term Rate Lower than long term
• Short Term Level similar to long term
– Carbon Monoxide
– Carbon Dioxide
CO Absolute ChangeCO
De
lta
PP
M
We
ek
Mo
nth
Qu
art
er
Ha
lf Y
ea
r
Ye
ar
2 Y
ea
rs
3 Y
ea
rs
Lo
ng
CO Absolute Change
95 Percentile Absolute Change VS Sampling Interval
0
100
200
300
400
500
600
Week Month Quarter Half Year 1 Year 2 Years 3 Years Long
Sampling Interval
De
lta
(p
pm
)
0
1
2
3
4
5
6
7
8
9
10
% S
am
ple
s >
Co
nd
itio
n 4
CO2 Absolute ChangeCO2
De
lta
PP
M
We
ek
Mo
nth
Qu
art
er
Ha
lf Y
ea
r
Ye
ar
2 Y
ea
rs
3 Y
ea
rs
Lo
ng
CO2 Absolute Change
95 Percentile Absolute Change VS Sampling Interval
0
500
1000
1500
2000
2500
3000
3500
4000
4500
Week Month Quarter Half Year 1 Year 2 Years 3 Years Long
Sampling Interval
De
lta
(p
pm
)
0
1
2
3
4
5
6
7
8
9
10
% S
am
ple
s >
Co
nd
itio
n 4
Other Gas
• “Type III”
• Middle Term Rate Lower than shorth
and long term
• Short Term Level lower than long term
– Ethane
– TDCG
C2H6 Absolute ChangeC2H6
De
lta
PP
M
We
ek
Mo
nth
Qu
art
er
Ha
lf Y
ea
r
Ye
ar
2 Y
ea
rs
3 Y
ea
rs
Lo
ng
C2H6 Absolute Change
95 Percentile Absolute Change VS Sampling Interval
0
5
10
15
20
25
30
35
40
Week Month Quarter Half Year 1 Year 2 Years 3 Years Long
Sampling Interval
De
lta
(p
pm
)
0
2
4
6
8
10
12
14
% S
am
ple
s >
Co
nd
itio
n 4
TDCG Absolute ChangeTDCG
De
lta
PP
M
We
ek
Mo
nth
Qu
art
er
Ha
lf Y
ea
r
Ye
ar
2 Y
ea
rs
3 Y
ea
rs
Lo
ng
TDCG Absolute Change
95 Percentile Absolute Change VS Sampling Interval
0
100
200
300
400
500
600
700
800
900
1000
Week Month Quarter Half Year 1 Year 2 Years 3 Years Long
Sampling Interval
De
lta
(p
pm
)
0
1
2
3
4
5
6
7
8
9
10
% S
am
ple
s >
Co
nd
itio
n 4
Conclusion
• Use Delta PPM directly without
Normalisation (no ppm/day)
• Use 90 or 95 Percentile of the whole population (maybe excluding > cond X ?)
• Determine sampling frequency on actual
level ppm value (Similar to actual Table 3)
• Adjust Value per period for CO, CO2 and
maybe for C2H6 and TDCG
Conclusion
• A possible table could look like:
Period: <= 1.5 Year 1.5 - 2.5 Years >= 2.5 Years
H2
CH4
C2H4
C2H2
C2H6 15 25 30
CO 200 300 400
CO2 2000 2500 3000
TDCG 300 400 500
Maximum PPM variation between sample
40
25
15
1
Questions ?
• To Be continued….