Hidraulica en tuberias y canales.ppsx

8/14/2019 Hidraulica en tuberias y canales.ppsx

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The University of Adelaide, AustraliaSchool of Civil, Environmental & Mining Engineering

Water Systems and Infrastructure Modelling &Management Group(WaterSIMM)

Using Genetic Algorithms to OptimiseNetwork Design and System OperationIncluding Consideration of Sustainability

Professor Angus Simpson

Victorian Modelling Group

24 March 2010


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Outline

1. Simulation of water distribution systems2. Various formulations of equations

3. Todini and Pilati solution method4. Genetic algorithm optimisation of water

distribution system networks

5. Genetic algorithms for optimisingoperations of pumping systems

6. Optimising for sustainability


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My research interests

1. Optimisation of the design and operation ofwater distribution systems using geneticalgorithms [including sustainabilityconsiderations (GHGs)]

2. Monitoring health and assessing conditionof pipes non-invasively in water distributionsystems using small controlled waterhammer events


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My research interests

3. Steady state computer simulation analysis

of water distribution systems - improvingsolvers and modelling of PRVs and FCVs

4. Water hammer modelling in pipelines


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The research team

Total of 14

9 academics (local and overseas) 1 Research Post Doc. 4 PhDs


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The research team - academics

Prof. Angus Simpson Prof. Martin Lambert (condition assessment and

genetic algorithms) Prof. Holger Maier (genetic algorithms and

sustainability) Dr. Sylvan Elhay School of Computer Science,

The University of Adelaide (steady state solution ofpipe networks)

Prof. Lang White School of Electrical andElectronic Engineering, The University of Adelaide

(condition assessment)


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International collaboration

Professor Caren Tischendorf Head of Dept. of Mathematicsand Computer Science, University of Cologne, Germany(steady state solution of pipe networks)

Dr. Jochen Deuerlein 3S Consult, Germany (steady statesolution of pipe networks, correct modelling of PRVs, FCVs inwater networks) ex-University of Karlsruhe

Dr. Arris Tijsseling University of Eindhoven, TheNetherlands (condition assessment)

Prof. Wil Schilders University of Eindhoven, TheNetherlands (speeding up solution of nonlinear steady statepipe network equations)


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Components in a Water Distribution

System


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Simulation of water distributionsystems

Solution of a set on non-linear equations for

flow (Q) and pressure (head or hydraulic grade line H)

EPANET uses Todini and Pilati (1987)method very fast

There are many sophisticated commerciallyavailable software packages


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Assumptions

Fixed demands assumed to be notpressure dependent, for example - 100houses aggregated to a node

Various water demand loadings cases Peak hour (hottest day in summer) Peak day (extended period simulation usually

over 24 hours to check tanks do not run empty) Fire demand loading cases Pipe breakage cases


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Decisions to be made

Diameters and locations of pipes Location of pumps

Locations and setting of valves (PRVs, FCVs) Locations and elevations of tanks Operation of pumps off-peak electricity rates Minimising carbon footprint Reliability considerations


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Design objectives

For theeconomic cost component minimisesumof Capital cost of the water distribution system

(say for a 100 year life) Present value of pump replacement/refurbishment

(every 20 years) Present value of pump operating costs (100 years)

)()()(),(11

pumping NPV pc Ld c P DC k NPUMP

k k k k

NPIPE

k k


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Accounting for Time Present value analysis (PVA)

Usually the discount ratei is selected tobe cost of capital 6 to 8%

For social projects, such as WDSs, asocial discount rate should be used, forexample,i = 1.4% (intergenerational

equity)

t t iC

PV 1

C: Payment/cost on a given future date

t = Number of time periods

i = Discount rate


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Design objectives

Satisfy design criteria for example Minimum/maximum allowable pressures Maximum allowable velocities Tanks must not empty

NDEMANDS j NJ it H t H H ji ji ji ,...,1;,...,1,,)(max,,

min,

NDEMANDS j NP it V t V ji ji ,...,1;,...,1,,)(max,,


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Trial and error approach

User has to choose - diameters of pipes,locations of tanks, pumps, and PRVs

Engineering judgment and experience Run simulation model for demand load cases Check design criteria and compute cost Adjust sizes of elements in response topressures Rerun simulation model


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New York Tunnels problem

New York City Water Supply Tunnels

Brooklyn

Hillview Reservoir

EL 340 ft

16

9 21

8

20

19

11

7

6

5

4

17 18

13

14

3

2City Tunnel No. 1

City Tunnel No. 2

Bronx

Queens

Richmond

Manhattan

10

12

15


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A very very large search space size

Any one of the 21 existing pipes could beduplicated

Choose from 16 allowable pipe sizes tomeet demands

Search space size = 1.43 x 1021 Eliminate 99.99% of possible solutions by

engineering experience (leaves 1.43 x 1017)


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A very very large search space size

At 10,000 evaluations per second cancompute 3.15 x 1011 per year

It will take 454,630 years to fully enumerate0.01% of the total search space (only for 21

decision variables)


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A typical simple water distribution system


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Simulation Solving for The Unknowns

q Q1 Q2 Q NP T=

Only consider systems with pipes and reservoirs The unknown flow vector (10 pipes in examples)

The unknown head vector (7 nodes in example)(gives pressures)

h H1 H2 H NJ T=


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A total of 17 unknowns Qs and Hs


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Continuity Equation of Flow at a Junction

Flow In = Flow Out + Demand (or Withdrawal Discharge) where

Q j = flow in pipe j (m3/s or ft3/s)

NPJi = number of pipes attached to node i

DMi = demand at the node i (m3/s or ft3/s)NJ = total number of nodes in the water distribution system(excluding fixed grade nodes such as reservoirs)

Q j1=

NPJi

DM i+ =


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Pipe Head Loss Equations in Terms of NodalHeads

H i Hk r Q Q n 1 =

where = nodal head at node i in the water distribution system (m or ft) r j = resistance coefficient for the pipe j depending on the head loss

relationship (for example, Darcy Weisbach or Hazen Williams) Q j = flow in pipe j (m3/s or ft3/s) n = exponent of the flow in the head loss equation (Darcy Weisbach n = 2 or

Hazen Williams n = 1.852)

H


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Four different non-linear formulations

#1 Q-Equations #2 H-Equations #3 LF- Equations (Loop Flow Equations) #4 Todini and Pilati H-Q Equations


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#1 - The Q-equations formulation(10 unknowns)


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The Q-equations (10 unknowns)

q Q1 Q2 Q NP T=


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The Q-equations (Newton iterativesolution technique)


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#4 -Todini and Pilati Q-H formulation

Define topology matrices Develop block form of equations Use an analytic inverse of block matrices to

reduce matrix size from 17 unknowns to 7unknowns (same as unknown heads H)

Fast algorithm


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Todini and Pilati Q-H formulation

Unknownsh H1 H2 H NJ

T=

q Q1 Q2 Q NP T=


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Todini and Pilati Q-Hformulation - Define

topology matrices


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Todini and Pilati Q-Hformulation - Define

topology matrices


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Todini and Pilati Q-Hformulation- continuity at nodes


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Todini and Pilati Q-Hformulation head lossequations for pipes

Note that later on theinverse of this matrixwill give problems forzero flows


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Todini and Pilati Q-H formulation head lossequations for pipes


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Todini and Pilati Q-H formulation two sets of equations


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The Todini and Pilati equations


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Research Issues

Improving solution speed Making solution algorithms more robust zero

flows cause Todini and Pilati method to fail aregularization method has been developed tocontrol the condition number

An improved convergence criterion for stoppinghas been developed


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Research Issues

Decomposing networks into trees, blocks andbridges to speed up analysis

Growing typical networks that have correct mixof loops, links and junctions


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GENETIC ALGORITHMS FOR OPTIMISATIONOF WATER DISTRIBUTION SYSTEMS


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Types of Evolutionary Algorithms

Genetic algorithms(Holland 1976; Goldberg 1989)

Ant Colony Optimisation (ACO) Tabu search Simulated annealing Particle swarm optimisation (PSO) Evolutionary strategy (Germany)


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History of genetic algorithms applied towater distribution systems

Pioneered at the University of Adelaide by LaurieMurphy under my supervision in an honours project in1990 and a PhD starting in 1991

Initial focus was on the optimisation of the design ofwater distribution systems

A spinoff company of Optimatics Pty Ltd formed byUniversity of Adelaide in 1996 operates in Australia,NZ, USA and UK (employs 20 people)

Research focus is now on optimising operations andaccounting for multiple objectives (sustainability,reliability)


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Genetic algorithm optimisation

Population orientated technique (select apopulation size of say 500)

Based on mechanisms of natural selection

and genetics Selection, crossover and mutation operators

produce new generations of designs

Fitness of strings drives process Uses EPANET type simulation model to

assess performance of all trial waterdistribution networks in each generation


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Creating a string from sub-strings -an example

BINARY CODING


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Chromosome of decision variables

Choice tables are required for eachdecision variable

Chromosome

Existing pipe [3] (binary)00 = no change, e = 2.5 mm01 = clean/line, e = 0.3 mm10 = duplicate 306 mm11 = close the pipe


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Model Operation

Optimisation-Simulation Model Link

GA OPTIMISATION MODEL

HYDRAULIC SIMULATION MODEL

Configuration of water distribution andperformance passes back and forth


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Simulate hydraulics of waterdistribution system

Decode each string using the choice tables Run a computer simulation model Simulate demand loading cases

consecutively peak hour, fire, extended period simulation

Record any violation of constraints(e.g. pressures too low, velocities too high)


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Choices for the decision variables

A decoding lookup table NominalDiameter

(mm)

Actual orInternal

Diameter(mm)

BinaryCoding

IntegerCoding

Roughness height(mm) for Darcy-Weisbach friction

factor

Unit Cost($/m)

150 151 000 1 0.25 49200 199 001 2 0.25 63250 252 010 3 0.25 95300 305 011 4 0.25 133

375 384 100 5 0.25 171450 464 101 6 0.25 220500 516 110 7 0.25 270600 615 111 8 0.25 330

l d d f


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Total cost and corresponding fitnessof the string

Total cost is the: example1. Real cost of the water distribution system

design

PLUS 2. A penalty pseudo-cost (or costs) if the

constraint(s) are not met For example

=K*Maximum pressure deficitwhere K=$50,000 per metre

Fitness is often taken as the inverse of the totalcost


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Steps in a genetic algorithm

optimisation

Select a population size (e.g. N=100 or N=500) Select a reproduction or selection operator Select a probability of crossover (Pc) Select a probability of mutation (P

m)


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A Simple Genetic Algorithm

ThisGeneration

N=500

Selection Crossover&

Mutation

The NextGeneration

MatingPool

N=500

l


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Tournament selection

Randomly selectpairs of

chromosomes

versus

Evaluationof the fittest

Forming theMating Pool

1 1 1 1 1

1 11 11 11

1 11 1

1 1

1

1111

1 1 1

11 1

1 11

1

1

11 1 1

1 11 11

1 1

11 1 1 1 1 1

11 1 1

1

1

11

1

00 0 0

0

0

0 0

00

00 0 0 0

00

0 00

0000 0

00000

00000

00000

0

00

0

0 0

0

0 0

0

1 11 1 11 1 000

65

112

94

8398

143

87

130

Fittest strings win

Two sets of tournament selection are required

versus

versus

versus

FITNESS


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Crossover (one-point)

Chromosome A

Chromosome B Parents

Chromosome A`

Chromosome BOffspring

1 1 1 1 1 1

1 1 1 1 1 1 1

1 1 1

1 1 11 1 1

1 1 1 1

0 0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0 0

Randomly select acrossover point

Interchange the tails


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The mutation operator

Mutation occurs with a very small probability One bit switches to a new value


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Produce many generations

Continue to create a series of newgenerations (say 100,000 differentnetworks)

Repeat selection, crossover andmutation

Increasingly fit solutions are

generated The 10 or so lowest cost solutions

must be remembered along the way


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Optimisation of pumping plant operations


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Murray Bridge operations

optimisation United Utilities Riverland water treatment

plant project at Murray Bridge, South Australia

GA optimisation minimises operationselectricity costs by

maximizing off-peak pumping and minimizing static pump head


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Background

Pumps

ElevatedStorage

Water TreatmentPlant

Clear WaterStorage

Case study Murray Bridge system


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Case study Murray Bridge systemlayout

White HillStorage Tank (WHS)

OffTakes

MurrayBridge

OnkaparingaPipeline

Murray Bridge WaterTreatment Plant

Clear WaterStorage Tank (CWS)

3 Parallel FixedSpeed Pumps


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Traditional approach to control

Trigger levels in storage tanksOR Pump scheduling


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Controls based on trigger levels

Lower Trigger Level (Minimum Allowable Level)

Upper Trigger Level (Maximum Allowable Level) More Peak

Pumping thanNecessary

Time

T a n

k L e v e

l

Peak Tariff Period

Tank not Fullfor Next

Peak TariffPeriod

Tank not Full atStart of PeakTariff Period

Off-Peak Tariff Period

7am 7am 9pm


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Optimisation-Simulation Model Link

GA OPTIMISATION MODEL

HYDRAULIC SIMULATION MODEL

Operating policies for pumpingsystem - trigger levels, schedules for

pumps turning on and turning off

Model operation


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Decision variables - operationsoptimisation at Murray Bridge

Used a combination of real-value and integer valuerepresentation of the decision variables

Four decision variable for final formulation: Pump start time to fill tank Pump stop time to drain tank to minimum level Reduced upper trigger level for tank Initial level in CWS tank


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A system controlled with original trigger

levels and schedules

Lower Trigger Level(Minimum Allowable Level)

Upper Trigger Level (Maximum Allowable Level)

Time

Peak Tariff Period

Tank Full atStart of Peak

Tariff Period


7am 7am9pm

Start PrimaryPump

Stop PrimaryPump

Tank at Minimum Level atEnd of Peak Tariff Period

T a n

k L e v e

l


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A system controlled with both schedulesand a reduced upper trigger level (1)

Time



Peak Tariff Period

Tank Full at Start of PeakTariff Period


7am 7am9pm

Start PumpReduced Upper Trigger Level

Tank at Minimum Level at

End of Peak Tariff Period

T a n

k L e v e

l


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T a n

k L e v e

l



Time

Peak Tariff Period

Tank Full at Start ofPeak Tariff Period


7am 7am9pm

Start Pump

Reduced Upper Trigger LevelExtended into Off-Peak Tariff Period

Tank at Minimum Levelat End of Peak Tariff Period

Switch Time

A system controlled with both schedulesand a reduced upper trigger level (2)

Modelled System - Original Trigger


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Modelled System Original TriggerLevels

L e v e

l ( m )

4

5

6

7

Daily electricity cost (averaged over 28 days) = $313.65

Time (hrs)

Daily peak pumping(averaged over 28 days): $286.05

Initial Level in CWS = 3.4m

Lower trigger level = 5.49m

Upper trigger level = 6.98m

0

1

2

3

8

11 am 9 am 7 am 7 am 5 am 3 am 1 am 11 pm 9 pm 7 pm 5 pm 3 pm 1 pm

Daily off-peak pumping(averaged over 28 days): $27.60

WHS (m)

CWS (m)

WHS and CWS tank levels for first 24hours of a 28-day simulation under fixedtrigger level control for a 7.17 ML/D flow

Optimised system new approach


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Optimised system - new approach

Initial Level in CWS = 3.675 m

Lower trigger level = 5.49 m

Reduced trigger level = 5.76 m

Upper trigger level = 6.98m

WHS and CWS tank levels after optimisationfor a 7.17 ML/D flow

0

1

2

3

4

5

6

7

8

Time (hrs)

L e v e

l ( m )

WHS

CWS

Pump on at 1:54:13 am

Peak Pumping: $189.51 Off-peak Pumping: $67.63

Total electricity cost = $257.14. Hence a $56.51 or 18.0%

11 am 9 am 7 am 7 am 5 am 3 am 1 am 11 pm 9 pm 7 pm 5 pm 3 pm 1 pm

Switch time 2:15 am


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Results - savings from new approach

18.284.34378.76463.110

13.646.3293.02339.328

18.056.48257.16313.647.17

22.459.72207.13266.866

22.936.17121.57157.744

54.950.6141.6592.262

(%)($)ImprovedControlsCurrent

Controls

SavingsPumping Cost($/Day)DailyDemand(ML/Day)


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Accounting for Sustainability in theDesign and Operation of WaterDistribution Pumping Systems


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Research Objectives

To construct a sustainability integratedmulti-objective genetic algorithmoptimisation model for the planning,design and evaluation of WDSs

To explore the impacts different

sustainability criteria (Greenhouse Gasemissions) will have on the results ofWDS optimisation


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Aspects of Sustainability-

Social

Environmental

Economic Technical

1: Total cost ofthe system

2: GHGemissions

3:Systemreliability 4: Robustness ofPareto-optimal Front


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Two of the Main Conflicting Objectives

Minimisation of thetotal life cyclesystem costs

Minimisation of thetotal life cycle systemGHG emissions


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Higher CostLower GHG

Lower Cost

Higher GHG

Big pumpSmall pipe

Small pumpBig pipe


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Evaluating multi-objective optimisation

results using a Pareto tradeoff curve

Cost

GHG

TradeoffCurve


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Determining life cycle economic costs

Total Cost

Capital CostsPump

Refurbishment

Costs (PVA)

Operating Costs

(PVA)

Pipes andPump Stations

Pumps Pumping


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Determining life cycle GHG emissions(no discounting i = 0% IPCC)

Total Emissions

Capital Emissions Operating Emissions

Embodied Energyof Pipes

Electricity Consumptionof Pumping

Emission Factor Analysis


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Optimisation Framework

Generate Options

M O GA

Simulation

Evaluation

Comparison& Selection

WDS Optimisation

O b j e c t i v e s

Minimisationof total cost

Minimisation ofGHG emissions

Maximisation ofsystem reliability

Maximisationof robustness

of Pareto-optimal

solutions


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Multi-objective optimisation using genetic

algorithms MOGA: NSGA-II Generate initial population Objectiveevaluation

Simulationmodels

Ranking

Generate globalpopulation

Non-dominatedsorting

Crowding

distance

Comparison &selection

Constrainthandling

Generate child population

Crossover

Mutation

Stoppingcriteria met?

Stop

Yes

No


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Case Study The network consistsof a lower reservoir

(water source), onepump, one rising main

and an upper reservoir

1,500,000

951,500120100

Average peakday flow (L/s)Design life (years)

Design conditions of case 1 Annual demand (m 3)

Static headPipe length


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Pareto optimal tradeoff curve


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Pareto optimal tradeoff curve multi-objective optimisation i = 6%

6% discount rate for costs

A

B

G H

C D E F

87.0

91.0

95.0

99.0

103.0

4.3 4.7 5.1 5.5

System cost (M$)

G H G

( k - t

o n n e )

$21.8/tonneCO 2-e

$134/tonneCO 2-e

$371/tonne CO 2-e

(300)

(450)(375)

6% discount rate for costs

A

B

G H

C D E F

87.0

91.0

95.0

99.0

103.0

4.3 4.7 5.1 5.5

System cost (M$)

G H G

( k - t

o n n e )

$21.8/tonneCO 2-e

$134/tonneCO 2-e

$371/tonne CO 2-e

(300)

(450)(375)

Diameter for lowest cost solution

Tradeoff for i = 1.4%


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1.4% discount rate for costs

B

C DE

H

FG

88.5

89.5

90.5

91.5

92.5

10.1 10.3 10.5 10.7 10.9 11.1

System cost (M$)

G H G

( k - t o n n e

) $72.1/tonneCO2-e

$376/tonne

CO2-e $1,468/tonne CO2-e

(375)

(450)

1.4% discount rate for costs

B

C DE

H

FG

88.5

89.5

90.5

91.5

92.5

10.1 10.3 10.5 10.7 10.9 11.1

System cost (M$)

G H G

( k - t o n n e

) $72.1/tonneCO2-e

$376/tonne

CO2-e $1,468/tonne CO2-e

(375)

(450)

Lowest cost

Lowest GHGs

Conclusions


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Conclusions

Evolutionary algorithm optimisation hasapplication in design and operation of waterdistribution systems

It is relatively easy to tack on an evolutionaryalgorithm optimisation onto existing simulationmodels

Capital costs and operating costs can bereduced significantly Sustainability can be optimised

Hidraulica en tuberias y canales.ppsx

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