li liu, e. downey brill, g. mahinthakumar, james uber, emily m. zechman, s. ranjithan

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.