ie-or seminar april 18, 2006 evolutionary algorithms in addressing contamination threat management...
DESCRIPTION
Contamination threat problem in water distribution networksTRANSCRIPT
![Page 1: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/1.jpg)
IE-OR SeminarApril 18, 2006
Evolutionary Algorithms in Addressing Contamination Threat
Management in Civil Infrastructures
Ranji S. RanjithanDepartment of Civil Engineering, NCSU
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Many security threat problems in civil infrastructure systems
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Contamination threat problemin water distribution networks
![Page 4: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/4.jpg)
Water distribution networks… Solve for network hydraulics (i.e., pressure, flow)
Depends on Water demand/usage Properties of network components
Uncertainty/variability Dynamic system
Solve for contamination transport Depends on existing hydraulic conditions Spatial/temporal variation
time series of contamination concentration
![Page 5: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/5.jpg)
Water distribution networks…Contaminant source profile
0
500
1000
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2000
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3000
3500
1 26 51 76 101 126 151 176 201 226 251 276Time step
Sour
ce m
ass
(mg/
min
)
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Water distribution networks…Contaminant source profile
0
500
1000
1500
2000
2500
3000
3500
1 26 51 76 101 126 151 176 201 226 251 276Time step
Sour
ce m
ass
(mg/
min
)
![Page 7: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/7.jpg)
Water distribution networks… Explain the
contamination issues Show animation
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Water distribution networks…
Concentration for node 115
0
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0.7
0 24 48 72 96 120 144 168 192 216 240 264 288Time step
Con
cent
ratio
n(m
g/L)
Concentration for node 265
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0 24 48 72 96 120 144 168 192 216 240 264 288Time step
Con
cent
ratio
n(m
g/L)
Contaminant source profile
0
500
1000
1500
2000
2500
3000
3500
1 26 51 76 101 126 151 176 201 226 251 276Time step
Sour
ce m
ass
(mg/
min
)
![Page 9: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/9.jpg)
Why is this an important problem? Potentially lethal and public health hazard Cause short term chaos and long term issues Diversionary action to cause service outage
Reduction in fire fighting capacity Distract public & system managers
![Page 10: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/10.jpg)
What needs to be done? Determine
Location of the contaminant source(s) Contamination release history
Identify threat management options Sections of the network to be shut down Flow controls to
Limit spread of contamination Flush contamination
![Page 11: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/11.jpg)
What needs to be done? Determine
Location of the contaminant source(s) Contamination release history
Identify threat management options Sections of the network to be shut down Flow controls to
Limit spread of contamination Flush contamination
![Page 12: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/12.jpg)
Example math formulation Find: L(x,y), {Mt}, T0
Minimize Prediction Error ∑i,t || Ci
t(obs) – Cit(L(x,y), {Mt}, T0) ||
where L(x,y) – contamination source location (x,y) Mt – contaminant mass loading at time t T0 – contamination start time Ci
t(obs) – observed concentration Ci
t(L(x,y), {Mt}, T0) – concentration from system simulation model i – observation (sensor) location t – time of observation
![Page 13: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/13.jpg)
Example math formulation Find: L(x,y), {Mt}, T0
Minimize Prediction Error ∑i,t || Ci
t(obs) – Cit(L(x,y), {Mt}, T0) ||
where L(x,y) – contamination source location (x,y) Mt – contaminant mass loading at time t T0 – contamination start time Ci
t(obs) – observed concentration Ci
t(L(x,y), {Mt}, T0) – concentration from system simulation model i – observation (sensor) location t – time of observation
• unsteady• nonlinear• uncertainty/error
![Page 14: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/14.jpg)
Example math formulation Find: L(x,y), {Mt}, T0
Minimize Prediction Error ∑i,t || Ci
t(obs) – Cit(L(x,y), {Mt}, T0) ||
where L(x,y) – contamination source location (x,y) Mt – contaminant mass loading at time t T0 – contamination start time Ci
t(obs) – observed concentration Ci
t(L(x,y), {Mt}, T0) – concentration from system simulation model i – observation (sensor) location t – time of observation
• estimate solution state with currently available data• identify possible solutions that fit the data• assess confidence in current estimate of solution(s)
![Page 15: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/15.jpg)
Interesting challenges Non-unique solutions
Due to limited observations (in space & time)
Resolve non-uniqueness Incrementally adaptive search
Due to dynamically updated information stream
Optimization under dynamic environments Search under noisy conditions
Due to data errors & model uncertaintyOptimization under uncertain environments
![Page 16: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/16.jpg)
Interesting challenges Non-unique solutions
Due to limited observations (in space & time)
Resolve non-uniqueness Incrementally adaptive search
Due to dynamically updated information stream
Optimization under dynamic environments Search under noisy conditions
Due to data errors & model uncertaintyOptimization under uncertain environments
![Page 17: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/17.jpg)
Evolutionary algorithm-based solution approach Evolutionary algorithms (EAs) for numeric
search Genetic algorithms, evolution strategies
Key characteristics Population-based probabilistic search Directed “random” search Conditional sampling of decision space
Updated statistics/likelihood values Based on quality of prior solutions (samples)
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Resolving non-uniqueness Underlying premise
In addition to the “optimal” solution, identify other “good” solutions that fit the observations
Are there different solutions with similar performance in objective space?
Search for alternative solutions
[work conducted by Dr. Emily Zechman]
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Resolving non-uniqueness… Search for alternative solutions
x
f(x)
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Resolving non-uniqueness… Search for different solutions that are far apart in
decision space
x
f(x)
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Resolving non-uniqueness…
x
f(x)
Effects of uncertainty
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Resolving non-uniqueness…
x
f(x)
Search for solutions that are far apart in decision space and are within an objective threshold of best solution
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Resolving non-uniqueness…EAs for Generating Alternatives (EAGA)
Create n subpopulations
Sub Pop 1
Evaluate objfunction values
Best solution (X*, Z*)
Evaluate pop centroid(C1) in decision space
Selection(obj fn values)& EA operators
STOP?
Best Solutions
Sub Pop 2
Evaluate objfunction values
Feasible/Infeasible?
Evaluate distance in decisionspace to other populations
Selection(feasibility, dist)& EA operators
STOP?N Y NY
...
...
![Page 24: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/24.jpg)
EAGA…Illustration using a test function y = [(1 - 10x)*sin(11*x)]2 / [2.83*(10x)1.46]
0
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x
y
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y = [(1 - 10x)*sin(11*x)]2 / [2.83*(10x)1.46]
Generate 3 different solutions Optimal and two alternatives Within a 75% threshold of the optimal solution Search using Evolution Strategies
EAGA…Illustration using a test function
![Page 26: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/26.jpg)
EAGA…Illustration using a test function y = [(1 - 10x)*sin(11*x)]2 / [2.83*(10x)1.46]
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
y
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EAGA…Illustration using a test function
![Page 28: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/28.jpg)
Contaminant source identification
0
5
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0 10 20 30 40 50
Well 1
Well 2Source 1
Observations at Well 2
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0.8
1
1.2
1.4
1.6
0 500 1000 1500 2000 2500
Time (days)
Con
cent
ratio
n (m
g/L)
Source 1 Source 2
1
t
c
Groundwater contamination problem
![Page 29: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/29.jpg)
Resolving non-uniqueness
0
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25
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0 10 20 30 40 50
Well 1
Well 2Source 1
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10
15
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25
30
0 10 20 30 40 50
Source 2Well 1
Well 2
Observations at Well 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 500 1000 1500 2000 2500
Time (days)
Con
cent
ratio
n (m
g/L)
Source 1 Source 2
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Resolving non-uniqueness…
0
5
10
15
20
25
30
0 10 20 30 40 50
Well 1
Well 2Source 1
0
5
10
15
20
25
30
0 10 20 30 40 50
Source 2Well 1
Well 2
Observations at Well 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 500 1000 1500 2000 2500
Time (days)
Con
cent
ratio
n (m
g/L)
Source 1 Source 2
Observations at Well 2
0
0.2
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0.6
0.8
1
1.2
1.4
1.6
0 500 1000 1500 2000 2500
Time (days)
Con
cent
ratio
n (m
g/L)
Source 1 Source 2
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Resolving non-uniqueness…Using EAGA
0
5
10
15
20
25
30
0 10 20 30 40 50
Well 1
Well 2Source 1
Observations at Well 2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 500 1000 1500 2000 2500
Time (days)
Con
cent
ratio
n (m
g/L)
Source 1 Source 2
1
Decision Variables:- center of source (x, y)- size in x direction- size in y direction- concentration
Objective function:- minimize prediction error
EAGA settings:- four different solutions- evolution strategies- = 200, µ = 100- 40 generations- subpopulation size 100- 30 random trials
![Page 32: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/32.jpg)
Resolving non-uniqueness, using EAGA… Observations from Well 1 only
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Resolving non-uniqueness, using EAGA… Observations from Well 1 only…
Alt. 1
0.00
0.20
0.40
0.600.80
1.00
1.20
1.40
1.60
0 500 1000 1500 2000
Con
c. (m
g/L)
PredictedConcentrationObservedConcentration
Alt. 2
0.000.20
0.400.600.80
1.001.20
1.401.60
0 500 1000 1500 2000
Alt. 3
0.000.200.400.600.801.001.201.401.60
0 500 1000 1500 2000
Time (days)
Con
c. (m
g/L)
Alt. 4
0.000.200.400.600.801.001.201.401.60
0 500 1000 1500 2000
Time (days)
PredictionsAt Well 1
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Resolving non-uniqueness, using EAGA… Observations from Well 1 only…
PredictionsAt Well 2
Alt. 1
0.00
0.20
0.40
0.600.80
1.00
1.20
1.40
1.60
0 500 1000 1500 2000
Con
c. (m
g/L)
PredictedConcentrationObservedConcentration
Alt. 2
0.00
0.200.40
0.600.80
1.00
1.201.40
1.60
0 500 1000 1500 2000
Alt. 3
0.000.200.400.600.801.001.201.401.60
0 500 1000 1500 2000
Time (days)
Con
c. (m
g/L)
Alt. 4
0.000.200.400.600.801.001.201.401.60
0 500 1000 1500 2000
Time (days)
![Page 35: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/35.jpg)
Resolving non-uniqueness, using EAGA… Observations from Wells 1 & 2
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Resolving non-uniqueness, using EAGA… Observations from Wells 1 & 2…
Alt. 1
0.00
0.20
0.40
0.600.80
1.00
1.20
1.40
1.60
0 500 1000 1500 2000
Con
c. (m
g/L)
PredictedConcentrationObservedConcentration
Alt. 2
0.000.20
0.400.600.80
1.001.20
1.401.60
0 500 1000 1500 2000
Alt. 3
0.000.200.400.600.801.001.201.401.60
0 500 1000 1500 2000
Time (days)
Con
c. (m
g/L)
Alt. 4
0.000.200.400.600.801.001.201.401.60
0 500 1000 1500 2000
Time (days)
PredictionsAt Well 1
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Resolving non-uniqueness, using EAGA… Observations from Wells 1 & 2…
PredictionsAt Well 2
Alt. 1
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
0 500 1000 1500 2000
Con
c. (m
g/L)
PredictedConcentrationObservedConcentration
Alt. 2
0.000.20
0.400.60
0.801.00
1.201.40
1.60
0 500 1000 1500 2000
Alt. 3
0.000.200.400.600.801.001.201.401.60
0 500 1000 1500 2000
Time (days)
Con
c. (m
g/L)
Alt. 4
0.000.200.400.600.801.001.201.401.60
0 500 1000 1500 2000
Time (days)
![Page 38: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/38.jpg)
Interesting challenges Non-unique solutions
Due to limited observations (in space & time)
Resolve non-uniqueness Incrementally adaptive search
Due to dynamically updated information stream
Optimization under dynamic environments Search under noisy conditions
Due to data errors & model uncertainty
Optimization under uncertain environments
![Page 39: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/39.jpg)
Dynamic optimization Minimize Prediction Error
∑i,t || Cit(obs) – Ci
t(L(x,y), {Mt}, T0) ||
Cit(obs) – streaming data
Objective function is dynamically updated Dynamically update estimate of source
characteristics
![Page 40: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/40.jpg)
Dynamic optimization… Underlying premise
Predict solutions using available information at any time step
Search for a diverse set of solutions (EAGA) Current solutions are good starting points for
search in the next time step
[work conducted by Ms. Li Liu]
![Page 41: IE-OR Seminar April 18, 2006 Evolutionary Algorithms in Addressing Contamination Threat Management in Civil Infrastructures Ranji S. Ranjithan Department](https://reader034.vdocuments.site/reader034/viewer/2022051303/5a4d1b587f8b9ab0599aa327/html5/thumbnails/41.jpg)
Dynamic optimization…
x
f(x)
t = 1
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Dynamic optimization…
x
f(x)
t = 2
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Dynamic optimization…
x
f(x)
t = 3
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Dynamic optimization…Adaptive Dynamic OPt Technique (ADOPT)
1. Set time step t=0
2. Initialize sub-populations with random solutions
3. Construct obj function for time step t+1
4. Apply EAGA to all sub-populations
5. Merge solutions to identify unique set of solutions
6. If t < Tmax, go to Step 3
7. Record solution and stop
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ADOPT…Illustration using a test function Test function
where B(x) is a time-invariant “basis” landscape P is the function defining the shape of peak i each of peak has its own time-varying parameters
h (height) w (width) p (shift)
35 time steps
)))(),(),(,(max),(max(),(...1
tptwthxPxBtxF iiimi
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ADOPT…Illustration using a test function
2-D case
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ADOPT…Results for the test function
5-D case; avg error & std over all time steps, & 30 random trials
Dynamic optimization
methods{h=7, w=1}
changes severities
{7,3}
changes severities
{15,1}
changes severities
{15,3}
Time-based objective 12.06 ± 0.64 12.96 ± 0.81 12.06 ± 0.80 15.06 ± 1.00
Random objective 11.29 ± 0.55 12.30 ± 0.96 14.79 ± 0.66 14.20 ± 0.83
Inverse objective 12.37 ± 0.87 13.96 ± 0.87 15.98 ± 0.89 15.28 ± 0.88
DCN 9.52 ± 0.45 10.42 ± 0.71 12.68 ± 0.60 12.56 ± 0.62
ADI 9.74 ± 0.35 9.31 ± 0.51 13.18 ± 0.52 13.00 ± 0.63
DBI 12.24 ± 0.55 11.79 ± 0.71 14.05 ± 0.61 13.96 ± 0.74
ADOPT 6.93 ± 0.19 8.57 ± 0.21 9.20 ± 0.15 9.82± 0. 17
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ADOPT…Illustration using a test function
5-D case; avg error & std dev over all time steps
Dynamic optimization
methods{h=7, w=1} {h=7, w=3} {h=15, w=1} {h=15, w=3}
Time-based objective 12.06 ± 0.64 12.96 ± 0.81 12.06 ± 0.80 15.06 ± 1.00
Random objective 11.29 ± 0.55 12.30 ± 0.96 14.79 ± 0.66 14.20 ± 0.83
Inverse objective 12.37 ± 0.87 13.96 ± 0.87 15.98 ± 0.89 15.28 ± 0.88
DCN 9.52 ± 0.45 10.42 ± 0.71 12.68 ± 0.60 12.56 ± 0.62
ADI 9.74 ± 0.35 9.31 ± 0.51 13.18 ± 0.52 13.00 ± 0.63
DBI 12.24 ± 0.55 11.79 ± 0.71 14.05 ± 0.61 13.96 ± 0.74
ADOPT 6.93 ± 0.19 8.57 ± 0.21 9.20 ± 0.15 9.82± 0. 17
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Contaminant source identification
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ADOPT…Contaminant source identification Minimize Prediction Error
∑i,t || Cit(obs) – Ci
t(L(x,y), {Mt}) ||
Cit(obs) – streaming data
Objective function is dynamically updated
Is available information sufficient to be confident about current solution?
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Dynamic optimization, using ADOPT… Observations from Well 1 only
Measurement Time Step: 1
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Dynamic optimization, using ADOPT… Observations from Well 1 only
Measurement Time Step: 2
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Dynamic optimization, using ADOPT… Observations from Well 1 only
Measurement Time Step: 3
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Dynamic optimization, using ADOPT… Observations from Well 1 only
Measurement Time Step: 4
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Dynamic optimization, using ADOPT… Observations from Well 1 only
Measurement Time Step: 5
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Dynamic optimization, using ADOPT… Observations from Well 1 only
Measurement Time Step: 6
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Dynamic optimization, using ADOPT… Observations from Well 1 only
Measurement Time Step: 7
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Dynamic optimization, using ADOPT… Observations from Well 1 only
Measurement Time Step: 8
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Dynamic optimization, using ADOPT… Observations from Well 1 only
Measurement Time Step: 9
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Dynamic optimization, using ADOPT… Observations from Well 1 only
Measurement Time Step: 10
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Dynamic optimization, using ADOPT… Observations from Well 1 only
Measurement Time Step: 15
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Dynamic optimization, using ADOPT… Observations from Well 1 only
Measurement Time Step: 20
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Contaminant source identification…Observations from wells 1 & 2
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Observations at Well 2
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Dynamic optimization, using ADOPT… Observations from Wells 1 & 2
Measurement Time Step: 1
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Dynamic optimization, using ADOPT… Observations from Wells 1 & 2
Measurement Time Step: 2
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Dynamic optimization, using ADOPT… Observations from Wells 1 & 2
Measurement Time Step: 3
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Dynamic optimization, using ADOPT… Observations from Wells 1 & 2
Measurement Time Step: 4
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Dynamic optimization, using ADOPT… Observations from Wells 1 & 2
Measurement Time Step: 5
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Dynamic optimization, using ADOPT… Observations from Wells 1 & 2
Measurement Time Step: 6
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Dynamic optimization, using ADOPT… Observations from Wells 1 & 2
Measurement Time Step: 7
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Dynamic optimization, using ADOPT… Observations from Wells 1 & 2
Measurement Time Step: 8
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Dynamic optimization, using ADOPT… Observations from Wells 1 & 2
Measurement Time Step: 9
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Dynamic optimization, using ADOPT… Observations from Wells 1 & 2
Measurement Time Step: 10
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Dynamic optimization, using ADOPT… Observations from Wells 1 & 2
Measurement Time Step: 11
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Final remarks & ongoing/future work EA-based algorithms to address new
challenges Non-uniqueness Dynamic environments Uncertain environments Multiple sources
Application to water distribution network threat management
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Water distribution networks…
Concentration for node 115
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Concentration for node 265
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0 24 48 72 96 120 144 168 192 216 240 264 288Time step
Con
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n(m
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Contaminant source profile
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1 26 51 76 101 126 151 176 201 226 251 276Time step
Sour
ce m
ass
(mg/
min
)
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Acknowledgements Thank you for listening NSF funding
ITR (Information Tech Research) Program DDDAS (Dyn Data Driven Application Systems) Program
Collaborators Mahinthakumar, Brill
People who made this possible Li Liu, Emily Zechman Others in the research group: Mirghani, Xin, Tryby