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Effects of Measurement Uncertainties on Adaptive Source Characterization in Water Distribution Networks. Li Liu, E. Downey Brill, G. Mahinthakumar, James Uber, Emily M. Zechman, S. Ranjithan North Carolina State University. Contaminant Source Determination. Rapid identification of … - PowerPoint PPT Presentation
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Effects of Measurement Uncertainties on Adaptive Source Characterization in Water Distribution Networks
Li Liu, E. Downey Brill, G. Mahinthakumar,James Uber, Emily M. Zechman, S. Ranjithan
North Carolina State University
Contaminant Source Determination Rapid identification of …
Contamination source location Starting time Mass loadings at different time
When to stop the search and make final decision Necessary information for threat management in water distribution systems
Challenges of Source Identification
Inverse Problem Ill-posed/Non-uniqueness
Under dynamic environments Dynamic system Dynamically updated observations
Under noisy environments Measurement error Uncertain demands Model error
Simulation-Optimization Method
Hydraulic Simulation
Water Quality Simulation
EA-based Optimizer
Observed Data
Csim
Source characteristics t
Co
b
s
Adaptive Dynamic Optimization Technique (ADOPT) An EA-based search Solves as information becomes
available over time Multiple solutions to assess non-uniqueness
Objective Investigate the effects of sensor
errors on source characteristics obtained
using ADOPT
Assumptions Deterministic demand values Conservative contaminant Contamination occurs at any one location in the network Only sensor errors are considered
Scenarios with Sensor Error Scenario 1: Sensor with continuous malfunction Scenario 2: Sensor with intermittent malfunction Scenario 3: Sensor activates after a lag time of first detection Scenario 4: Sensor with systematic reading error
Contamination Case A
0
1
2
3
4
5
6
7
5 7 9 11 13 15 17
Time Step (10 min) .
Mass L
oadin
g (g/m
in)
.
Mass Loading Profile
0
0.5
0 20 40
0
0.5
0 20 40
0
0.5
0 20 400
0.5
0 20 40
Contamination Case A…
Node 197 Node 184 Node 211
Node 115
Time Step (10 mins)
Obse
rved C
onc.
(m
g/L
)O
bse
rved C
onc.
(m
g/L
)
Time Step (10 mins) Time Step (10 mins) Time Step (10 mins)
0
0.5
0 10 20 30 40
0
0.5
0 20 40
0
0.5
0 20 40
0
0.5
0 20 40
Results for Case A with Perfect Data
Node 197 Node 184 Node 211
Node 115
True source
Best solution
Best solution
Prediction Error = 0.026 mg/L
Obse
rved C
onc.
(m
g/L
)O
bse
rved C
onc.
(m
g/L
)
Time Step (10 mins)
0
0.5
0 20 40
Case A : scenario 1Node 115
True concentration Observed concentration
Ob
serv
ed C
onc.
(m
g/L
)
0
0.5
0 20 40
Case A : scenario 1Node 115
True concentration
0
0.5
0 20 40
Node 184
Observed concentration
Best solution
Ob
serv
ed C
onc.
(m
g/L
)
Time Step (10 mins)
Ob
serv
ed C
onc.
(m
g/L
)
Case A: scenario 2, 3 & 4
Best solution
0
0.5
5 10 15 20 25 30
0
0.5
5 10 15 20 25 30
0
0.5
5 10 15 20 25 30
True concentration Observed concentration
Scenario 2
Scenario 3 Scenario 4
Ob
serv
ed C
onc.
(m
g/L
)
Time Step (10 mins) Time Step (10 mins)
Time Step (10 mins)
Ob
serv
ed C
onc.
(m
g/L
)
Node 115
Node 115 Node 115
Contamination Case B
True Source Mass Loading Profile
0
1
2
3
4
5
6
7
5 7 9 11 13 15 17
Time Step (10 min) .
Mas
s Load
ing (g/m
in)
.
Case B …
Time Step (10 mins)
Obse
rved C
onc.
(m
g/L
)
Time Step (10 mins)
Time Step (10 mins)
Obse
rved C
onc.
(m
g/L
)
0
0.5
1 9 17 25 33 41
0
0.5
1 9 17 25 33 41
0
0.5
1 9 17 25 33 41
Node 197
Node 184 Node 211
Mass Loading Profile
0
1
2
3
4
5
6
7
8
9
0 5 10 15 20 25 30Time Step
Mass L
oadin
g (g/m
in)
.
True Source
Solution 1
Solution 2
Solution 3
Solution 4
Results for Case B with Perfect Data
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 6 11 16 21 26 31 36 41Time Step
Conce
ntr
atio
n (m
g/L
)
.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 11 21 31 41
Time Step
Conce
ntr
atio
n (m
g/L
)
.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 11 21 31 41Time Step
Conce
ntr
atio
n (m
g/L
) .
True Solution
Solution 1
Solution 2
Solution 3
Solution 4
Node 197Node 211
Node 184
Results for Case B with Perfect Data
Case B: scenario 1
Time Step (10 mins)
Obse
rved C
onc.
(m
g/L
)
Time Step (10 mins)
Time Step (10 mins)
Obse
rved C
onc.
(m
g/L
)
0
0.5
1 9 17 25 33 410
0.5
1 9 17 25 33 41
0
0.5
1 9 17 25 33 41
Node 197
Node 184 Node 211
0
0.5
1 9 17 25 33 41
Case B: scenario 2
Time Step (10 mins)
Obse
rved C
onc.
(m
g/L
)
Time Step (10 mins)
Time Step (10 mins)
Obse
rved C
onc.
(m
g/L
)
0
0.5
1 9 17 25 33 41
0
0.5
1 9 17 25 33 41
Node 197
Node 184Node 211
Case B: scenario 3 & 4Scenario 3 Scenario 4
Summary for results
0
1
2
3
4
5
6
7
1 2 3 4
.
Case ACase B
Nu
mb
er
of
alt
ern
ati
ve
sou
rce locati
on
s
Scenario #
0
0. 5
1
1. 5
2
1 2 3 4
Case ACase B
Summary for results…
Scenario #
Mass L
oad
ing
diff
ere
nce a
t tr
ue s
ou
rce locati
on
(g
/min
)
Final Remarks Source characteristics identified by ADOPT are influenced by the type of sensor errors. Investigate effects of demand uncertainty. Update ADOPT to be robust under combined noisy conditions.
Acknowledgements This work is supported by National Science
Foundation (NSF) under Grant No. CMS-0540316 under the DDDAS program.