assessing the impact of alternative pipe groupings on multi-objective water distribution network...

Assessing the Impact of Alternative Pipe Groupings on

Multi-Objective Water Distribution Network

Masoud Asadzadeh

Bryan Tolson

OutlineOutline

ObjectivesProblem DescriptionCalibration Problem SetupOptimization AlgorithmsNumerical ExperimentResults and DiscussionMain Findings

WDSA2012, Adelaide, South Australia, Sept. 24-27 2

ObjectivesObjectives

• Assessing the impact of reducing the number of decision variables on the quality of model calibration results

• Comparing PA-DDS and ε-NSGAII across a range of computational budgets


Problem DescriptionProblem Description


DMA1

DMA2

DMA3

DMA4

DMA5

The problem is simplified from the Battle 2010 and needs the Calibration of:Roughness Coefficients of 429 pipes (there could be some partially closed pipes in DMA2)Demand Pattern Multipliers of 5 DMAs

Source

Pumping Station S1

Tank T1

T7

T2

T3

T5 T4

T6

S2

S4

S5

S3

The perfect EPANET2 input file and perfect observed data are taken from Ostfeld et al. (in press).

Pipes and DPMs are grouped:

1. Full Calibration Model with 3232 decision variables:a) Pipes in each DMA are grouped based on their size + 3 groups of pipes to

make the partially closed pipes identifiable 2727 Decision Variables

b) Each DMA has its own DPM 55 Decision Variables

2. Reduced Calibration Model with 77 decision variables:a) Pipes are grouped based on their age 3 groups of pipes to make the partially

closed pipes identifiable 66 Decision Variable

b) All DMAs has the same DPM 11 Decision Variable


Calibration Problem SetupCalibration Problem Setup

Calibration Problem Setup Calibration Problem Setup (cont’d)

EPANET2 toolkit and a MATLAB code are linked to:a) Modify the EPANET2 input file by changing pipe roughness coefficients

and demand pattern multipliers based on decision variable values of each solution

b) Simulate the modified input file

c) Return the desired simulated data points for:1. Tank levels and Pumping Station flows at the end of Hour1

2. Static Pressure

3. Fire Flow Test (FFT) Pressure

4. FFT flow

d) Objective functions are :1. SSRE Hour1

2. SSRE FFT


Optimization Algorithm: Pareto Archive Optimization Algorithm: Pareto Archive Dynamically Dimensioned Search Dynamically Dimensioned Search

(Asadzadeh and Tolson 2009)

Perturb current ND solution

Update ND solutions

Continue?STOP

New solution is ND?

Pick the New solution

Pick a ND solution

Initialize starting solutions

YYNN

Create ND-solution set

YYNN

7

Optimization Algorithm: Optimization Algorithm: εε-NSGAII-NSGAII(Kollat and Reed 2005)

8

• A variant of NSGAII with a modified solution archiving scheme:– Discretize the objective space into grid cells with the size of

epsilon (ε)– Archives at most a single solution in each grid cell– Archives a new solution only if it:

• Dominates a previously archived solutions or • Corresponds to a vacant grid cell

Numerical Experiment & Numerical Experiment & Results ComparisonResults Comparison

• Apply PA-DDS and ε-NSGAII to both full and reduced calibration problems:– With limited (1,0001,000) and large (10,00010,000) computational Budgets– In multiple independent trials (1010)

• Compare the aggregated results of reduced and full models

• Compare PA-DDS and ε-NSGAII in both limited and large computational budgets


0

0.001

0.002

0.003

0.004

0.005

0 0.005 0.01 0.015 0.02 0.025 0.03

SS

RE

Hou

r 1

SSRE Fire Flow Test

Full C-Town

Reduced C-Town

Comparing Final Calibration Results of Comparing Final Calibration Results of Full and Reduced Models Full and Reduced Models (aggregated tradeoffs after 220,000 solution evaluaitons)


Hour 1Hour 1 Tank Levels (m) Pumping Flow (lps)Data Point T1 T2 T3 T4 T5 T6 T7 S1 S2 S3 S4 S5Measured 2.82 0.72 3.51 2.76 1.56 5.46 2.99 192 33 48 35 30

Sim. (Full Model) 2.82 0.72 3.51 2.76 1.571.57 5.45 2.99 192 33 48 35 30

Sim. (Reduced Model) 2.802.80 0.730.73 3.503.50 2.842.84 1.571.57 5.405.40 2.932.93 188188 33 48 3636 30


Static Pressure (m)Static Pressure (m) DMA1 DMA2 DMA3 DMA4 DMA5

Measured 65 66 64 62 24 77 95 85 70 75 87 80 27Sim. (Full Model) 65 66 64 62 2323 77 95 85 70 75 87 80 27Sim. (Reduced Model) 65 66 64 6161 2323 77 95 85 70 75 8686 7777 27

Comparing Final Calibration Results of Comparing Final Calibration Results of Full and Reduced ModelsFull and Reduced Models

(Detailed Evaluation of Selected Solutions)

FFT Flow (lps)FFT Flow (lps) DMA1 DMA2 DMA3 DMA4 DMA5

Measured 247 228 58 50 54 28 48 12 34 38 37 45Sim. (Full Model) 249 228 58 50 54 28 48 12 34 38 37 45Sim. (Reduced Model) 241241 222222 5959 4949 5353 28 4949 12 3636 38 3838 45


FFT Pressure (m)FFT Pressure (m) DMA1 DMA2 DMA3 DMA4 DMA5

Measured 50 51 48 49 12 53 65 55 39 63 58 58 22Sim. (Full Model) 50 51 48 49 12 53 65 55 39 63 58 58 22Sim. (Reduced Model) 4949 51 48 49 12 5252 6464 5454 39 6161 58 58 22

Comparing Final Calibration Results of Comparing Final Calibration Results of Full and Reduced ModelsFull and Reduced Models

(Detailed Evaluation of Selected Solutions cont’d)

Comparing Calibration Problem DifficultyComparing Calibration Problem Difficulty


0

0.0025

0.005

0.0075

0.01

0 0.01 0.02 0.03 0.04 0.05

SS

RE

Hou

r1

SSRE Fire Flow Test

A) Full C-Town Calibration ProblemPA-DDS_10000eNSGAII_10000PA-DDS_1000eNSGAII_1000

0

0.0025

0.005

0.0075

0.01

0 0.01 0.02 0.03 0.04 0.05

SS

RE

Hou

r1

SSRE Fire Flow Test

B) Reduced C-Town Calibration ProblemPA-DDS_10000

eNSGAII_10000

PA-DDS_1000

eNSGAII_1000

Comparing MO Algorithm PerformanceComparing MO Algorithm Performance


0

0.0025

0.005

0.0075

0.01

0 0.01 0.02 0.03 0.04 0.05

SS

RE

Hou

r1

SSRE Fire Flow Test

A) PA-DDSFull 10000Reduced 10000Full 1000Reduced 1000

0

0.0025

0.005

0.0075

0.01

0 0.01 0.02 0.03 0.04 0.05

SS

RE

Hou

r1

SSRE Fire Flow Test

B) eNSGAIIFull 10000Reduced 10000Full 1000Reduced 1000

Main Findings

• Reducing the number of decision variables would:– Make the calibration problem easier to solve– Reduce the quality of calibrated model significantly

• Both optimization algorithms found high quality results of the full model even with limited budget, but PA-DDS performed slightly better

It is recommended to not reduce the number of decision variables only due to the limited computational budget.

Also, if a stochastic optimization algorithm is used, it is recommended to have multiple optimization trials and aggregate the results.


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