Role of Delivery Systems in Control of Role of Delivery Systems in Control of Water Quantity and Quality

M S Mohan KumarM S Mohan KumarG. R. Munavalli

M Prasanna KumarCelia D D’SouzaCelia D D Souza

Pawan Kumar

Objectives of the Study j y

Water Quantity SimulationWater Quantity SimulationWater Quality Simulation Parameter EstimationSource Strength Identification Bacteriological Growth

In a Water Distribution System

Water Quality SimulationWater Quality Deterioration Water Quality Deterioration

• Blending• Age,type and maintenance of the distribution system• Chemical and biological transformationsChemical and biological transformations

Water Quality Expressed in terms of• Constituent concentration (generally chlorine) • Water age• Water age• Source trace

Water Quality ModelingH d li l i i i i• Hydraulic analysis is prerequisite

• Steady state (ultimate values of water quality)• Dynamic state (spatial and temporal distribution of

water quality)water quality)

3

Chlorine Reaction Kinetics

Bulk Flow Reactions Bulk Flow Reactions

• Due to organic content in water

Fi d fi d ki i• First order or non first order kinetics

Wall Reaction Kinetics

• Due to materials at pipe wall and corrosion products

• First or zero order kinetics

Total Chlorine Decay

• Combination of bulk and wall reactions

• Mass transfer from bulk flow to pipe wall

Steady State Water Quality Model

Objective• Simulate the ultimate spatial distribution of constituent

concentration age and source traceconcentration, age and source traceModel Formulation

• Based on 1D flow, complete mixing at nodes, advection dominated and single constit ent (conser ati e or reacti e)dominated and single constituent (conservative or reactive)

• Hydraulic Analysis Model (Niranjan Reddy 1994)• Water Quality Model

1 Constituent1. Constituent

5

Expressions for Reaction CoefficientC ti Ch i l R 1Conservative Chemical: Reci=1Reactive Chemical

• First order bulk and first order wall reactions

• Second order b lk and first order all reactions• Second order bulk and first order wall reactions

6

Steady State Water Quality Model

2. Water age

3. Source trace

All the above formulations for constituent water All the above formulations for constituent, water age and source trace are solved by Gauss-Siedel Iterative solution technique

7

Dynamic Water Quality Model

Comparative Study of Existing Models TDM and EDM with new Hybrid Method (EDMNET)

• For analytical solutionsFor analytical solutions• For application on network examples

Model Formulation• Static hydraulic model (Niranjan Reddy 1994)• Static hydraulic model (Niranjan Reddy 1994)

modified to handle extended period simulation • Water quality model

1. Transport in pipes1. Transport in pipes

8

Expressions for Reaction Rate and ConcentrationConcentration

Conservative Chemical: R[ci(x,t)]=0Reactive ChemicalReactive Chemical

• First order bulk and first order wall reactions

• First order bulk and zero order wall reactions

9

2. Modeling water age• Modeled as reactive constituent of zero order

growth and R[ci(x,t)]=13. Modeling source trace• Modeled as simulating conservative constituent ode ed as s u at g co se vat ve co st tue t

of 100 units concentration at desired source4. Dilution Equation

5. Mass balance equation at storage tank

10

Model ApplicationModel ApplicationTest Problem 3 Used for Conservative and Reactive

ConstituentTank detailsDiameter 15.24 mInitial height 17 29 mInitial height 17.29 mMinimum height 15.24 mMaximum height 21.34 mFirst order chlorine reactionFirst order chlorine reaction constants usedBulk reaction constant 0.55 /dWall reaction constant 0 15 m/dWall reaction constant 0.15 m/d

11

Test Problem 3 (Conservative Constituent)

12

Test Problem 3 (Reactive Constituent)

13

Water Quality Parameter Estimation

Water Quality (Chlorine) Reaction ParametersWater Quality (Chlorine) Reaction Parameters• Bulk reaction parameters (determined by bottle tests) • Wall reaction parameters (product of calibration)

I M d li g T h i U f l t Inverse Modeling Techniques are Useful to Estimate the Unknown Wall Reaction Parameters and Hence to Calibrate the Water Quality ModelUnknown Reaction Parameters are Expressed as

• Overall first order reaction parameterOverall first order reaction parameter• First order wall reaction parameter• Zero order wall reaction parameter• First order wall reaction-pipe roughness parameterp p g p• Zero order wall reaction-pipe roughness parameter

14

Scope of Present WorkDevelopment of Inverse Models for Autocalibration Development of Inverse Models for Autocalibration of Steady State Water Quality Model

D l t f I M d l f A t lib tiDevelopment of Inverse Models for Autocalibrationof a Typical Dynamic Water Quality Model (TDM)

• To incorporate all types of unknown reaction parameters involved infirst or non first order reaction kinetics

• Free from numerical diffusion• Simulation-Optimization Inverse Modeling

Technique is Used with • Gauss-Newton Sensitivity Analysis Technique (GNSAT)• Genetic Algorithm Technique (GAT) g q ( )

in the optimization module

15

Water Quality Parameter Estimation(Dynamic State)

Model Formulation

Solution by GNSAT• Corrections to parameters are obtained by solving Nup

(number of unknown parameters) linear equations given by

• Sensitivity coefficients are determined by parameter perturbation techniqueperturbation technique

16

• Calibration error statisticso Stastical parameters are computedo Parameter uncertainty is obtained using posterior parameter

covariance matrix given by

where, Jf = final Jacobian of sensitivity coefficients; s2=estimated i Merror variance

Parameter confidence limits are given by

∑ −=j

NupjNE )(

• Choice of weightso Weight based on measured values

Solution by GATSolution by GAT• Exactly similar to steady state case except dynamic water quality model

TDM is used in the forward simulation

17

Model Application

Real Life Network 2

Tank detailsDiameter 15.24 mInitial height 17.29 mMinimum height 15.24 mMaximum height 21.34 mFirst order chlorine reaction constants usedBulk reaction constant 0.55 d-1

Wall reaction constant ?Measurements Known at Nodes3, 6, 10, 11, 19, 25, 28 and 34

18

Global Parameter Estimation

GNSAT Results

GA Parameters Used

GAT Results

19

Global Parameter EstimationCalibration Error Statistics

Zoning as per diameters

20

Chlorine Concentrations for Global and Zoned Cases

21

Source Strength IdentificationImportance of Chlorination

• Required to maintain microbial quality of water• Appropriate chlorine residuals should be maintained to achieve a balance

between benefits (such as cheap, easy to handle, effective in killing b i d l id l ) d ill ff ( i i b d dbacteria and longer residuals) and illeffects (carcinogenic byproducts andtaste-odor problems)

Source Strength• Chlorine concentration or mass rate injected at the supply (treatment

plant) and secondary (booster) water quality sources• Estimation of appropriate value of source strengtho to maintain a specified value or a value between specified range of

chlorine residuals at given monitoring node(s) is importantTypes of Water Quality SourcesC i• Concentration source

• Mass booster source• Flow paced booster sourcep• Set point booster source

22

Scope of Present WorkExtending the Simulation-Optimization Inverse Modeling Procedures to Solve Source Strength Identification Problem which

• Incorporates both first or non first order reaction kineticsIncorporates both first or non first order reaction kinetics• Is free from numerical diffusion• Accounts for the temporally varying source strength(s) at various

types of water quality sourcesyp q yDevelopment of Steady State Strength Identification Model Development of Dynamic State Strength Development of Dynamic State Strength Identification Model for a single monitoring node by GNSAT D l t f D i St t St th Development of Dynamic State Strength Identification Model for a residual value within a range at given monitoring node(s) by GATg g g ( ) y

23

Steady State Strength Identification

Problem is posed as unconstrained evendetermined and hence the model formulation of steady state and hence the model formulation of steady state parameter estimation problem is applicable

The only difference being observed values are the specified chlorine concentration and unknown parameters are source strengths

Number of sources is made equal to number of Number of sources is made equal to number of monitoring nodes

24

Strength Identification Model by GNSAT

Model Formulation

On Conversion to Unconstrained Optimization Problemp

25

Model ApplicationFirst order chlorine

ti t tLake

Source

RiverSource

reaction constants usedBulk reaction constant 0 31 /d (Lake)

Sou ce

0.31 /d (Lake)0.03 /d (River)Wall reaction constant Case (i) I- orderCase (i) I orderZone 1 0.3048 m/dZone 2 1.5244 m/dZone 3 3.0488 m/dZone 4 6.0976 m/dCase (ii) Zero Order215 mg/m2/dMonitoring Node

Chlorine Conc. AtLake: ?River: ?

26

Source and Monitoring Node Concentrations

27

Strength Identification Model by GAT

Model Formulation

On Conversion to Unconstrained Optimization Problem

Fitness Value=1/E

28

Model Application (Example Network 1)For Linear Kinetics

Tank detailsDiameter 15.24 mInitial height 17 29 mInitial height 17.29 mMinimum height 15.24 mMaximum height 21.34 mFirst order chlorine reactionFirst order chlorine reaction constants usedBulk reaction constant 0.55 /dWall reaction constant 0 36 m/dWall reaction constant 0.36 m/dWater Quality Sources atA, B, C, D, E and FMonitoring Nodes: 2 to 36 and Source g

Nodes

29

Model Application (Example Network 1)

GAT Convergence

30

Model Application (Example Network 1)

31

Model Application (Example Network 1)

32

Model Application (Example Network 1)

33

Bacteriological Modeling in Distribution SystemBacterial Growth

• Increase in the cell number by utilizing organic carbon is as a energy source

• Organic matter in drinking water is natural in origin resulting from d i i ( h i d f l i id )decaying vegetation (e.g. humic and fulvic acids)

• Given the presence of nutrients regrowth is theoretically possible• May result in biofilm formation

F t Aff ti B t i l G thFactors Affecting Bacterial Growth• Attachment to and shearing from the surfaces• Age of biofilm• Disinfectant levels

Multicomponent Reaction Transport Model• Used as tool to study the bacterial growthsy g• Components incorporatedo Organic carbon (Substrate)o Bacterial content (Biomass)o Bacterial content (Biomass)o Disinfectant (Chlorine)

34

Scope of Present WorkDevelopment of Multicomponent Reaction Transport Model as Applicable to a Network

• Through simplified expressions for the processes such as bacterial growth, substrate consumption, attachment, detachment and g pdisinfectant action

• Which can predict the spatial and temporal spread of contaminant intruded into the system

• Development of numerical Eulerian and Lagrangian solution methods

to solve multicomponent modelD l t f M lti t R ti Development of Multicomponent Reaction Transport Model as Applicable to Pilot Loop Experiments p

35

Multicomponent Reaction Transport Model Conceptual Basis

36

Multicomponent Reaction Transport Model Governing Equations for Plug Flow

• Bulk flow

37

Multicomponent Reaction Transport Model • Wall Zone

• Mixing at Node

38

Numerical Solution Methods Eulerian Finite Difference Method

• Multistep computing schemeo Decoupling of governing equations into transport and kinetico Solving transport equations by MacCormack schemeo Solving kinetic equations by Runge-Kutta procedure

For each time step

Solve kinetic equationsfor first half time step

Solve transport equationsfor full time step

Solve kinetic equationsfor second half time step

39

Numerical Solution Methods Lagrangian Time Driven Method

• TDM used earlier for single constituent is modifiedo Redistribution of masso Creation of new segments

40

Model Application to a Network Problem

First order chlorine ireaction constants

usedTOC3 55 mg/L (Lake)3.55 mg/L (Lake)0.56 mg/L (River)Wall reaction constant Zone 1 0 3048 m/dZone 1 0.3048 m/dZone 2 1.5244 m/dZone 3 3.0488 m/dZone 4 6.0976 m/d203

Chlorine Conc. AtLake: 0.49 mg/LRiver: Varies between

1.00 and 1.50 mg/L41

Case (i) Chlorine concentrations

42

Case (i) Substrate concentrations

43

Case (ii) Chlorine and Biomass concentrations

44

Case (ii) Substrate concentrations

45

Studies on Application of ControlStudies on Application of Control Systems for Urban Water Networks

Why controls in water supply systems?Why controls in water supply systems?

To reach the targets/set points (reservoir flows / levels)To reach the targets as fast as possibleTo reach the targets as fast as possibleTo ensure the smoothest possible operation of valves/pumps

To control the slow transients

For real time operation monitored by SCADA

Particularly useful for complex pipe networks

47

Control in water networks

48

Practical issues

Normal Questions asked

How much supply is made to different reservoirs ?How much supply is made to different reservoirs ?

How to maintain equitable distribution among q gdifferent reservoirs ?

How to minimize leakage ?How to minimize leakage ?

How much throttling needed to achieve targeted g gflows ?

How to maintain sufficient pressure / reduce How to maintain sufficient pressure / reduce pressure ?

49

Mathematical model of a water supply system

D i l b h i f fl id i h i li• Dynamical behavior of fluid in the pipeline( ) ( )( )thh

lgA

dttdQ

lossp

p −Δ= ( ) ( ) ( )ththth llossfplossloss −− +=

• Friction Loss Valve Loss

ldt p

where

( ) ( )tQgAK

thp

vlossvalve

22

2 ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=

( ) ( )tQDHWC

lth

p

pfploss

852.187.4852.1

7.10⎟⎟⎠

⎞⎜⎜⎝

⎛=−

• Head versus Flow characteristics of Pump

( ) CB

• Continuity equation at Reservoir

( ) 22002

0, pppp QnC

NQnB

NAQNh −+=

• Continuity equation at Reservoir( )( ) ( ) ( )tQtQ

dttVd

oi −= 50

PID/PD/PI controllers

Introduction to different controllers

- Proportional Integral (PI) controller, Proportional Derivative (PD) controller and Proportional Integral Derivative controller (PID)-most commonly used controllers.

-Have been in use in different forms since long time.

W k ll f li t-Works well for linear systems

Dynamic inversion based controllers:

- Nonlinear control design

- Technique of feedback linearisation

- Output tracking problems- Output tracking problems

- May be implemented as PD, PI or PID 51

Controller Equations

PD Controller

PID Cont olle

dtdeKeKu dp +=

PID Controller

dtdeKdteKeKu dip ++= ∫

DI based nonlinear controller

dtdip ∫for

⎥⎦⎤

⎢⎣⎡ −= − )()(

.1 XfXXgu des

uXgXfX )()(.

+=52

Solution Procedure

Known initial conditions

Solve the controller equations for control variables

Integrate the state equations to get state i blvariables

Repeat the process till the end of the Repeat the process till the end of the operation period

53

Schematic diagram of the Gaziantep (Turkey) water supply system- Test Problem 1

54

Data for Gaziantep water supply system

lp1 = 669.27m hs1 = 113.4m D=1.4 m

lp2 = 13805.04m hs2 = 210.4m A0 = 0.0001433l 20094 69 h 283 4 B 0 005015lp3 = 20094.69m hs3 = 283.4m B0 = 0.005015

lp4 = 4689.04m hs4 = 279.7m C0 = 3.98

A i= 1 5394 m2 A = 475 m2 n = 1Api 1.5394 m At 475 m n 1

Pump Rated Discharge 2830 lit/sec

Pump Rated Speed 985 rpm

Initial Reservoir levels 3.20 m,2.15 m,4.20 m

Targeted Reservoir levels 4.0 m,2.50 m,3.91 m55

System dynamics

( ) [ ][ ]Tatbtcto

T

QhQhQhQ

xxxxxxxtX

123

7654321

=

=State Vector

( ) [ ][ ]

321T

cba

T

NNN

uuutU

=

=

where

Control Vector

State Equations( )( )( ) ( ) ( )

octt

oootoo

NQkkNkkfQ

QQkh

QRGhkQ

2

3

23

−=

−+=

&

&

&( ) ( )( ) ( )bbbbttbb

aaaataa

QkQRGhhkxf

QkQRGhkxf

−−+−=

−−+−=

where

23

221

23

21

State Equations

( ) ( ) ( )( )( ) ( ) ( ) bbbbbbb

cbtt

ccccccc

NQkkNkkxfQ

QQkh

NQkkNkkxfQ

22

1

2

22

1

++=

−=

++=

&

&

( ) ( )( ) ( )

pptt

ccccttcc

bbbbttbb

CkBkklgA

kAk

QkQRGhhkxf

QkQGhhkxf

=====

−−+−=

,,A,,/1

030201

23

232

321

( )( ) ( ) ( ) aaaaaaa

batt

NQkkNkkxfQ

QQkh

22

1

1

++=

−=&

&

sjsippp

ppp

pptt

hhGgAD

lfR

l

−=⎟⎟⎠

⎞⎜⎜⎝

⎛= ,

2

2

030201

56

[ ]eeeE T321 =

Error vector

PD controllers:

[ ]Ttttttt hhhhhh *11

*22

*33 −−−

Error vector

dtdeKeKN dpc

11 +=

d

PD controllers:

dtde

KeKN dpb2

2 +=

deKKN 3

dtKeKN dpa

33 +=

dtKde

KKN ∫1

PID controller equations:

dteKdt

KeKN idpc ∫++= 11

1

dteKde

KeKN idpb ∫++= 22

2 dtN idpb ∫ 22

dteKdtde

KeKN idpa ∫++= 33

3

57

DI Controller equations

N N N P d( ) ( )( ) ( )( ) ( ) 0

0

0

122

1

222

1

322

1

=++

=++

=++

γ

γ

γ

ccctcct

bbbtbbt

aaataat

NQkkkNkkk

NQkkkNkkk

NQkkkNkkkNa,Nb,Nc are Pump speeds

( ) ( ){ } ( )Δ

where

( ) ( ){ } ( )( ) ( ) ( ) ( ){ }

( ){ } ( )*22

322

12

*331

bd

cbcccbt

ttpoctdct

hhKQQkK

NxkkNkkxfxfk

hhKQQkKxfk

−+−+

−−−=

−+−+=Δ

γ

γ

( ){ } ( )( ) ( ) ( ) ( ){ }

( ){ } ( )*11

522

13

22

ttpbatd

bbbbbat

ttpcbtd

hhKQQkK

NxkkNkkxfxfk

hhKQQkK

−+−+

−−−=

++Δ

γ

58

Target outflow rate (Qo*): 2 4 m3s-1

Case 1: Constant set point over the time period

Target outflow rate (Qo ): 2.4 m s

Target reservoir levels (ht1*, ht2

*, ht3

*): 4.0 m, 2.5 m and 3.91 m

1st Initial condition:X(0) =

= (2.83, 3.20, 2.83, 2.15, 2.83, 4.20, 2.83)T

[ ] 123T

atbtcto QhQhQhQ

2nd Initial condition:X(0) =

(2 20 3 50 2 20 2 70 2 20 3 80 2 20) T[ ] 123

Tatbtcto QhQhQhQ

= (2.20, 3.50, 2.20, 2.70, 2.20, 3.80, 2.20) T

59

Error plots and Variation in pump speeds

60

Case 2: Three changes of set point

Targets:Targets:

Outflow: 2.3 to 2.7 m3s-1

2 7 t 2 8 3 12.7 to 2.8 m3s-1

2.8 to 2.6 m3s-1

For every 2 hrs

1st reservoir level: 4.0m

2nd reservoir level: 2.5m

61

Outflow, reservoir levels and pump speeds for the , p p pcase of step changes in target outflow (Qo

*) using DI

62

Case 3: Reservoir levels and pump speeds for the case of constant target outflow (Q *) with different case of constant target outflow (Qo ) with different

initial conditions using DI

63

Reservoir levels and speed change of the variable speed pump, Na for ±5% outflow disturbance (Q o) - Test problem 1. 64

Bangalore city water supply system – Test problem 4

Salient featuresInflow 673 Mld

Cauvery Stages I (132), II(131), III(294) and ARK(116)

48 reservoirs spread over 2190 sq.km

Several reservoirs on one complex

26 pumps26 pumps

Diameter 1750 mm to 150 mm

Type of pipe and age – MS, CI, DI etc, new to 50 year old

65

Schematic diagram of the Bangalore water supply system- Test problem 4

66

Targeted Inflows to the Ground Level Reservoirs

S.No Reservoir Targeted Inflow Mld

1 KGR 401 KGR 40

2 KUM 10

3 BSK 353 BSK 35

4 BTM 10

5 BTR 755 BTR 75

6 MNK 7

7 BYR 50

8 MR 6

9 AER 60

10 HGR 5067

11 LLR 30

S.No Reservoir Targeted Inflow Mld

30

12 WCR 28

13 BCR 28

14 KMH 40

15 CJF 77

16 KGT I 3716 KGT I 37

17 MBR 50

18 CLR 20

Total 673 68

Error (1-9) plots for flows - Test problem 4. 69

Error (10-18) plots for flows - Test problem 4. 70

Variation in valve loss coefficients (1-9) - Test problem 4.71

Variation in valve loss coefficients (10-18) - Test problem 4.72

Different Tuning approaches for the controllers

- Offline tuning method

* Ziegler Nichols rules

* Genetic algorithm based approach

- Online tuning method

Fuzzy gain scheduler

Design of different controllers using above tuning methodses g o d e e t co t o e s us g abo e tu g et ods

* PID controllers – ZNPID,GAPID,FZPID

* DI controllers - ZNDI,GADI,FZDI, ,

73

1) Ziegler-Nichols rules – for tuning a PID controller

PI controller gains

Kp = 0.45* KuKp 0.45 Ku

Ki = 0.54* Ku/ PuKu: Ultimate Gain

Pu: Period of oscillation

PID controller gains:

Kp = 3* Ku /5

Ki = 6* Ku/(5* Pu)

Kd 3* K * P /40Kd = 3* Ku * Pu /40

74

2) Genetic algorithmic based offline tuning method

Flow chart for GA optimization procedure75

Different performance indices

76

3) Fuzzy based online tuning approach

ii )( KKKkK +−= minminmax )( ppppp KKKkK +

minminmax )( ddddd KKKkK +−=

( )PKK 2/2= ( )upi PKK 2/=

Membership functions for e, Δe, kp and kd.

77

Fuzzy rule base for kp

Fuzzy rule base for kd

78

Comparison of three gain tuning approaches – PID controllers

Errors and variation in pump speeds - Test problem 1 79

Gains found using Fuzzy supervisor - Test problem 180

Test problem 3 – Case 1

Selected error plots and corresponding variation in valve loss coefficients for 70% of initial flows as targets

81

Gains found using Fuzzy supervisor for 70% of initial flows as targets - Test problem 3 82

Test problem 3 – Case 2

Selected error plots and corresponding variation in valve loss coefficients for 30% of initial flows as targets

83

Gains found using Fuzzy supervisor for 30% of initial flows as targets - Test problem 3 84

Gains found using GA – PID controller

ProblemProblem 1 3

Case 1 Case 2

Kp1 0.992*10-3 407.1 308.2

Kp2 0.972*10-3 982.4 848.2p 0.97 0 98 . 8 8.

KP Kp3 0.912*10-3 664.7 407.1

Kp4 --- 152.9 156.5

Kp5 --- 301.2 908.2

Proportional gains

Ki1 0.369*10-6 996.5 174.1

Ki2 0.124*10-6 987.7 101.2

KI Ki3 0.115*10-6 1120.6 251.8

Ki4 --- 869.4 107.3

Integral gains

Ki5 --- 992.9 403.5

Kd1 0.0973 114.1 251.8

Kd2 0.0484 177.6 474.1

KD Kd3 0 0344 795 3 565 9D i ti i KD Kd3 0.0344 795.3 565.9

Kd4 --- 611.8 576.5

Kd5 --- 202.4 491.8

Derivative gains

85

Maintain physical barrier between distribution system

i t i d t l

Strategies in the Efficient Management of WDSs

Develop methods to

interior and external environment

Management of WDSs

pdetermine and analyze the quantitative and qualitative status of WDSsstatus of WDSs

To take quick decisions to

Physical

To take quick decisions to maintain the three -physical, hydraulic and

QualityHydraulic

water quality integrity of WDSs Maintain disinfectant residual,

bio-stability, prevent external Maintain desirable

water flows, t contaminationpressures, water age

86

Efficient Management of WDSsEfficient Management of WDSs

Modeling Techniques – to simulate the quantitative and qualitative behaviour ofquantitative and qualitative behaviour of water distribution systems

Decision / Control Systems – to control important parameters of water distribution systems

87

Limitations of Deterministic Water Quality Modeling of WDSs

• Water quality modeling of WDSs has advanced and has become complexadvanced and has become complex

• Number of calibrating parameters with the introduction of other components (like Substrates & Biomass) has increased

• Calibration is tedious 88

Objectives of the StudyObjectives of the Study

• Use of soft computing modeling techniques in• Use of soft computing modeling techniques in the temporal prediction of important water quality indicators of water distribution systemsquality indicators of water distribution systems

• Develop control algorithms in an integrated approach for the quantitative and qualitative control of water distribution systems

89

Objectives in the Data-driven Modeling of WDSs

• Develop models in the temporal prediction of p p p– Chlorine & Biomass

U f diff t l ith f l t k• Use of different algorithms of neural networks– Resilient Back Propagation– Levenberg-MarquardtLevenberg Marquardt – General Regression

f iff i f• Use of different architectures of neural networks– One-output – Two-outputTwo output– Three-output

90

Water Quality Indicators of WDSsWater Quality Indicators of WDSs

• Chlorine and Biomass are the two key parameters of water quality

• Chlorine – a minimum of 0.2 mg/l and a safeguard against further microbial contamination

• Biomass – indicator of the presence of microbial re-growth in water distribution systems

91

Back Propagation AlgorithmBack Propagation Algorithm

Error Equation21 ( )

ON

E d y= −∑Error Equation1

( )pj pjjp

E d yN =

= ∑

( 1) ( ) ( )kj kj p kjw t w t w t+ = + ΔWeight Change

)1()()( −Δ⋅+∂

∂⋅−=Δ twt

wE

tw ijpp

ijp αε∂wij

92

Resilient Back Propagation Algorithm (RP)

⎪⎪⎧ >−

∂∂⋅

∂∂

−Δ⋅+ twEt

wEift

ijijij 0)1()(),1(η

⎪⎪

⎪⎪

⎨ <−∂∂⋅

∂∂

−Δ⋅=Δ − twEt

wEiftt

ijijij

ijij

ij 0)1()(),1()( η+− <<< ηη 10

⎪⎪

⎩−Δ elsetij ),1(

⎪⎧ >

∂Δ− tEiftij 0)()(

⎪⎪

⎪⎪⎪

⎨ <∂∂

Δ

>∂

Δ

=Δ twEift

tw

ift

twij

ij

ijij

ij 0)(),(

0)(),(

)(

⎪⎪⎪

⎩else,0

)()()1( twtwtw ijijij Δ+=+ )()()1( twtwtw ijijij Δ++

93

Levenberg Marquardt AlgorithmLevenberg-Marquardt Algorithm (LM)Error Equation 21 ( )

ON

pj pjE d yN

= −∑

w w wδ= +Weight Change

1pj pj

jpN =∑

1k k kw w wδ+ = +

1

Weight Change

( )( ) 1T Tk k k k kw J e J J Iδ λ

−= − +

94

General Regression Ne ral Net orkGeneral Regression Neural Network2

1( )

exp

m

i ijni

x xY =

⎛ ⎞−⎜ ⎟

⎜ ⎟∑

∑ 12

1^

2

exp2

( )

ij

j

m

Y

Y

σ=

⎜ ⎟−⎜ ⎟⎜ ⎟⎝ ⎠=⎛ ⎞

∑

∑ 2

12

1

( )exp

2

i ijni

j

x x

σ=

=

⎛ ⎞−⎜ ⎟

⎜ ⎟−⎜ ⎟⎜ ⎟⎝ ⎠

∑∑

⎝ ⎠m – number of inputs

n – number of training cases

xi – ith variable of testing case

xij – ith variable of the jth training case

95

Development of the Artificial Neural Network (ANN) Models

• Selection of Input data

• Principal Component Analysis

• Performance of the modelPerformance of the model

I E A l i• Input Error Analysis96

Selection of Input Data for theSelection of Input Data for the Models

• Source chlorine, substrate and biomass• Water age• Inflows • Consumption, if any• Time lagged source chlorine based on• Time-lagged source chlorine based on

average residence time

97

Case Study I – Bangalore WDS y g(1994)

an inflow system

three sources supplying to the main ground level

d h d t kand overhead tanks

98

Hydraulic and Water Quality P i f C S d IProperties of Case Study I

• Cauvery Stage I (node 1), Cauvery Stage II (node y g ( ), y g (2) and Arkavathi scheme (node 3) which supplies 1.577 m3/s, 1.682 m3/s and 1.577 m3/s

• Chlorine concentration at the three source nodes is C o e co ce t at o at t e t ee sou ce odes s0.5 mg/l

• Representative data was generated using Multi-component Reaction transport model (Munavallicomponent Reaction transport model (Munavalli and Mohan Kumar, 2004) 99

Input Data to the Model – Case Study I• The total number of Inputs – 23 (3 inputs each for source

chlorine residual, biomass, substrate and inflow concentrations; 1 input each for consumption and water age; 3concentrations; 1 input each for consumption and water age; 3 time lags of source chlorine for each of the source nodes )

• 24 and 6 nodes were chosen for training and testing of the model respectively

• the total training and testing dataset used in the development of the models are 1728 (24×3×24) and 432 (6×3×24) ( ) ( )respectively

fi t i i i l t ti f 99 0% f th• first six principal components accounting for 99.0% of the variance of the dataset 100

Bangalore WDS – Temporal Prediction of Chlorine (T ti D t t)(Testing Dataset)

Algorithm ArchitectureChlorine Residual

R2 MAE

Resilient Back Propagation (RP)

6 -10 - 5 -1 0.87 0.054(RP)Levenberg-Marquardt 6 - 8 - 5 -1 0.92 0.048(LM) General Regression NA 0.86 0.046Regression (GR)

NA 0.86 0.046NA – Not Applicable

101

Bangalore WDS – Temporal Prediction of Chlorine at Node 25

Variation of Chlorine concentration (a) without noisy data and (b) with noisy data (LM – 5%, GR and RP – 2%)noisy data (LM 5%, GR and RP 2%)

102

Bangalore WDS – Temporal Prediction ofBangalore WDS Temporal Prediction of Biomass (Testing Dataset)

Algorithm ArchitectureBiomass

R2 MAE

Resilient BackPropagation(RP)

6 -10 - 6 -1 0.74 0.008(RP)Levenberg-Marquardt 6 - 8 - 9 -1 0.80 0.0062(LM)GeneralRegression NA 0.67 0.009Regression(GR)

NA 0.67 0.009

103

Bangalore WDS TemporalBangalore WDS – Temporal Prediction of Biomass at Node 25

Variation of Biomass concentration (a) without noisy data and (b) with noisy data (LM – 5%, GR and RP – 2%)noisy data (LM 5%, GR and RP 2%)

104

Use of Different Architecture Models of ANNs

• Number of Outputs for each of the models is different

• Use of three type of models– One-outputOne output– Two-output

Three output– Three-output105

Water Quality Indicators and Model Outputs

• Chlorine and Biomass are standard water quality indicators

• Substrates (Nutrients) influence the presenceSubstrates (Nutrients) influence the presence and absence of the above two indicators

• Different combinations of water quality indicators (Chlorine – C; Biomass – X; andindicators (Chlorine – C; Biomass – X; and Substrates – S) to produce three types of ANN models

106

Different Models in the Temporal Prediction ofDifferent Models in the Temporal Prediction of Water Quality Indicators

• Three outputs for each case study Chlorine (C)• Three outputs for each case study – Chlorine (C), Biomass (X) and Substrate (S)

• The different combinations of ANN models– One output – chlorine biomass or substrateOne output chlorine, biomass or substrate

– Two output – chlorine + biomass, chlorine + substrate, pbiomass + substrate

– Three output – chlorine + biomass + substrate107

Development of Different Architecture ANN Models

• Selection of Input data

• Principal Component Analysis

• Performance of the models based on LM algorithm

• Input Error Analysis

108

Case Study II – North Marins WDSCase Study II North Marins WDSTwo sources of water:

Stafford Lake and the North Marin Aqueduct

Stafford Lake source t l d i thoperates only during the

peak demand period -16 hours per day p y

Stafford Lake water has high humic content

North Marin Aqueduct water is derived from a Raney Well Fi ldField

109

Hydraulic and Water QualityHydraulic and Water Quality Properties of Case Study II

• At each source the chlorine concentration is 0.5 mg/lg/

• The lake water has a slightly high humic contentThe lake water has a slightly high humic content thus increasing the TOC content (5-12 mg/l) entering into the system

• There are flow reversals in many of the pipes of y p pthe system due to the draining and filling cycles of tanks 110

Input Data to the Models – Case Study II

• The total number of Inputs – 30 (2 each for source chlorine, biomass and substrate concentration, 2 for inflows 1 each for consumption water age and 10 timeinflows, 1 each for consumption, water age and 10 time lags of source chlorine residual for both sources)

• 26 and 6 nodes were randomly chosen for training and testing of the model respectively

• The total training and testing dataset used in the development of the model is 1872 (26×3×24) and 432development of the model is 1872 (26 3 24) and 432 (6×3×24) respectively

• 18 principal components accounting for 98% of the total variance of the input dataset 111

Different ANN Models in the Temporal Prediction of Water Quality Indicators (TestingPrediction of Water Quality Indicators – (Testing

Dataset)

Architecture

Type C X Syp

(C, S, X) 18-8-9-1 18-8-9-1 18-8-9-1

(C+X) 18-15-12-2 18-15-12-2 -(C+X) 18-15-12-2 18-15-12-2 -

(C+S) 18-10-8-2 - 18-10-8-2

(X+S) - 18-15-12-2 18-15-12-2

(C+S+X) 18-15-12-3

112

Performance Index (R2) for each of the ANN M d l (T i D )ANN Models – (Testing Dataset)

Type C X S

(C, S, X) 0.85 0.91 0.93

(C+X) 0.82 0.95 -

(C+S) 0.84 - 0.92

(X+S) - 0.96 0.92(X S) 0.96 0.92

(C+S+X) 0.80 0.96 0.92

113

Performance Index (MAE) for each ofPerformance Index (MAE) for each of the ANN Models – (Testing Dataset)

MAE

Type C X SType C X S

(C, S, X) 0.137 0.006 0.096

(C+X) 0 128 0 006(C+X) 0.128 0.006 -

(C+S) 0.122 - 0.097

(X+S) - 0.006 0.101

(C+S+X) 0.129 0.006 0.101

114

North Marin WDS – Temporal Prediction of Chlorine at Node 153

Variation of Chlorine concentration (a) without noisy data and (b) with noisy data

115

North Marin WDS TemporalNorth Marin WDS – Temporal Prediction of Biomass at Node 153

Variation of Biomass concentration (a) without noisy data and (b) with noisy data

116

North Marin WDS TemporalNorth Marin WDS – Temporal Prediction of Substrate at Node

153

Variation of Substrate concentration (a) without noisy data and (b) with noisy data

117

Need for Quantity ControlNeed for Quantity Control • Increased and uneven consumer demands

• Operation of WDSs is complex• Operation of WDSs is complex

S dd t / f d d• Sudden event / emergency of demands

• Human intervention in control – erroneous results for large networks

118

Need for Quality ControlNeed for Quality Control• Water quality deteriorates throughout the system

• High dose of chlorine injection at source not g jsuitable

• Maintain minimum residual as well as avoid Disinfection-By-Products (DBP) productss ect o y oducts ( ) p oducts

• To address a sudden event of contamination• To address a sudden event of contamination119

Objectives in the Control of WDSsObjectives in the Control of WDSs

• Quantity and Quality (Chemical) Control1. SEQ-PID controller2. SIM-PID controller3. NOM-PID controller

• Quantity and Quality (Chemical & Biological) ControlBiological) Control1. SIM-PID controller2 NOM-PID controller2. NOM-PID controller

120

Different Propositions of PIDDifferent Propositions of PID controller

Integrated Approach – Solutions for both hydraulic and water quality control y q y

Three propositions of PID controllerThree propositions of PID controller1. SEQ-PID2 SIM PID2. SIM-PID3. NOM-PID

121

SEQ PID controllerSEQ-PID controller (Sequential)( q )

Different set of tuning gains for each of the targetsg

The water quality controller action beginsThe water quality controller action begins only when the flow control has been achievedachieved

122

SIM PID ControllerSIM-PID Controller (Simultaneous)

Different set of tuning gains for each of the targetsg

The water quality and hydraulic controllerThe water quality and hydraulic controller work simultaneously and independently

123

NOM PID controllerNOM-PID controller (Normalized)( )

Single set of tuning gains for any set of targets

Error for each of the targets is normalized

The control action for each of the targets work at the same timeat the same time

124

Procedure for Control of QuantityProcedure for Control of Quantity and Quality in WDSs

Known initial conditions

Determine the initial error for each of the targets

Solve the controller equations for control variables

Integrate the state equations to get new state variables

Repeat the process till the end of the operation period125

Case Study I Faridabad WDSCase Study I – Faridabad WDSFlow Control – To

maintain flow - 70% of initial flows

Quality Control –/ f0.4 mg/l of chlorine

residual

126

Details of the NetworkDetails of the Network• Water is pumped from the source node (Node p p (

1) and is distributed to seven major tanks • The pipe sizes of the distribution system varyThe pipe sizes of the distribution system vary

from 150 to 900 mm • Total design discharge of the pump is 0 6 m3/s• Total design discharge of the pump is 0.6 m3/s• Lift for the seven tanks varies from a minimum

f 2 0 t i f 10 5of 2.0 m to a maximum of 10.5 m

127

State / Control / Error EquationsState / Control / Error Equations

( ) [ ]TX& 1 2 3

1 2 3 7 1 2 30 1 2 3 30

( ) [ , , ,..... ]

[ , , ,... , , ,... , , , ,.... ]

Tn

T

X t x x x x

h h h h Q Q Q c c c c

=

=

&

13 17 27 28 29 12 15 19 26 30( ) [ , , , , , , , , , ]v v v v vU t K K K K K c c c c c=

* * * * *13 13 17 17 27 27 28 28 29 29( ) [ , , , , ,E t Q Q Q Q Q Q Q Q Q Q= − − − − −

* * * * *2 2 3 3 5 5 7 7 8 8, , , , ] c c c c c c c c c c− − − − −

128

Formulation of the ProblemMM

( )2 2

. .41 4

1 1 4

0 ( )( ) ( )tt N

t t

Qdh Q tX t h A Q tdt A A

−= = = = =

( )2 2

. .12 1

2 2 1

0 ( )( ) ( ) ( )tt N

t t

Qdh Q tX t h t A Q tdt A A

−= = = = =

.1.852 213 13 13 13 13

21 13 2 131.852 4.8713 13 13

.1.852 2

13 13 13 2 13 2 13 13

10.71( ) ( ) ( ) ( )2

[( ) ( ) ]

v

t t s s p vj

dQ gA l K QX t h h Qdt l c D g A

Q P h h h h H Q K Q

⎡ ⎤×= = − − −⎢ ⎥

⎣ ⎦

= − + − − −2 2

MM.

1.8521 1 19 12 13 11.852 4.87

1 1

10.71( ) ( ) ( )dQ gA lX t h h Qdt l c D

⎡ ⎤×= = − −⎢ ⎥

⎣ ⎦

MM

13 13 13 2 13 2 13 13[( ) ( ) ]t t s s p vjQ Q Q

d k1 1

.1.852

1 12 13 12 13 1

.1.852

1 12 13 1

( ) ( )

[( ) ]

p t t s s p

p t t ij p

Q P h h h h H Q

Q P h h S H Q

⎣ ⎦

⎡ ⎤= − + − −⎣ ⎦

= − + −

.1 1 1

38 ( )2

dc k cX tdt

= = −

MM.

2 212 420 9 10 12 122

4

.2 24

12 9 10 9 10 12 12

( ) ( ) ( ) ( )

( ) ( )

o oo

t t

B CdQ gAX t h h A N NQ Qdt l n n

gAQ h h h h A N B NQ C Q

⎡ ⎤= = − + + +⎢ ⎥⎣ ⎦

⎡ ⎤= − + − + + +⎣ ⎦

1

n

Nt

AA

= pp

p

gAP

l= 1.852 4.87

10.71 pp

p

lH

c D×

=

S h h=12 9 10 9 10 12 124

.2 2

12 4 9 10 12 12

( ) ( )

[( ) ]

t t s s o o o

t t ij o o o

Q h h h h A N B NQ C Ql

Q P h h S A N B NQ C Q

⎡ ⎤+ + + +⎣ ⎦

= − + + + +

ij si sjS h h= −

129

Errors in Flows and ValveErrors in Flows and Valve Settingsg

130

Errors in Chlorine Residual Targets in TanksErrors in Chlorine Residual Targets in Tanks and Chlorine Injection Rates

131

Gains of the Different ControllersGains of the Different Controllers

Type Controller K K KType Controller Kp Ki Kd

SEQ-PIDQuantityQuality

1.80 1.80 0.45SEQ PID Quality 0.6 0.6 0.15

SIM PIDQuantity 1.80 1.80 0.45SIM-PID Quality

1.800.6

1.800.6

0.450.15

QuantityNOM-PID

QuantityQuality 0.3 0.6 0.03

132

Case Study III Bangalore InflowCase Study III – Bangalore Inflow System

133

Details of the NetworkDetails of the NetworkIt has four sources of river supply. CauveryIt has four sources of river supply. Cauvery stage 1 (source 1), Cauvery stage II (source 2), Cauvery stage III (source 4) and Arkavatti Cauve y stage (sou ce ) a d avattriver (source 3) supplying 1.577 m3/s, 1.682 m3/s, 3.15 m3/s and 1.577 m3/s 3/s, 3. 5 3/s d .577 3/s

Th f l t 18 i t kThese four sources supply to 18 main tanks spread over the entire area of Bangalore City

134

State / Control / Error EquationsState / Control / Error Equations

1 3 4 16 17 18 1 105 1 2 3 135( ) [ , , ,... , , , ,.... , , ,.... ]Tt t t t t tX t h h h h h h Q Q c c c c=&1 3 4 16 17 18 1 105 1 2 3 135( ) t t t t t t Q Q

18 23 7 10 12 18 25 64 60 112( ) [ , ,........ , , , , , , , ,v v v v vU t K K K K K c c c c c=

32 51 70 38 134, 86 97 93 107, 5 9 12, , , , , , , , , ] c c c c c c c c c c c c

* * * * * * *14 14 22 22 33 33 61 61 5 5 9 9 11 11( ) [ , , , ,..... , , ,E t Q Q Q Q Q Q Q Q Q Q Q Q Q Q= − − − − − − −

* * * * * * *22 22 27 27 66 66 27 27 7 7 11 11 14 14, , , ,............. , , ] c c c c c c c c c c c c c c− − − − − − −

flow_st =[420.0 378.0 248.0 125.8 541.8 223.4 400.9 120.9 278.10 530.40 626.3 421.5 354.6 340.56 339.85 346.24 302.60 588.61]

cl_st =[0.2 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.4 ]

135

Errors in Flows and ValveErrors in Flows and Valve Settingsg

136

Errors in Chlorine Residual Targets i T k d Chl i I j iin Tanks and Chlorine Injection

Rates

137137

Gains of the Different ControllersGains of the Different Controllers

Type Controller Kp Ki Kdyp p i d

SEQ-PIDQuantityQuality

5001 32

8.01 32

0.80 33Q Q y 1.32 1.32 0.33

SIM PIDQuantityQ li

500 8.0 0.8SIM-PID Quality 1.5 1.5 0.38

QuantityNOM-PID

QuantityQuality 1.26 1.00 0.39

138

Quantity and Quality (Chemical &Quantity and Quality (Chemical & Biological) Control

• Providing safe drinking water remains a top prioritypriority

• A minimum of 0 2 mg/l chlorine residual to• A minimum of 0.2 mg/l chlorine residual to be maintained

• To safe-guard systems from microbial contaminants we need to measure indicatorscontaminants we need to measure indicators of contamination in WDSs 139

Monitoring of Water Quality IndicatorsMonitoring of Water Quality Indicators

• US EPA (2005) conducted a study to determine water quality indicators which influence an event of waterquality indicators which influence an event of water quality change and accidental contamination

• Baseline water quality parameters - pH, conductivity, dissolved oxygen, free and total chlorine and TOC d sso ved o yge , ee d o c o e d OC

• Experimental studies have shown that chlorine andExperimental studies have shown that chlorine and total organic carbon are able to respond and trigger alarms thus giving a warning in the event of

140

contamination140

Water Quality Scenarios inWater Quality Scenarios in WDSs

• Presence of organic carbon after treatment

• Bacterial contamination cannot be totally removedremoved

• Rejuvenation of injured bacterial components in conducive environments

141

Objectives of Quantity andObjectives of Quantity and Quality (Chemical & Biological)

Control• To maintain sufficient chlorine residual to

prevent formation of bacterial re-growth

• To address events of contamination at any point within the systempoint within the system

U f SIM PID d NOM PID t ll142

• Use of SIM-PID and NOM-PID controllers 142

Mutli component ReactionMutli-component Reaction Transport Model

• Model – gives the distribution of chlorine organic carbon (BDOC) and biomass

• Takes into consideration important processes of the three componentsthe three components

• Considers the bulk and wall zone of pipes• Considers the bulk and wall zone of pipes

Can predict the spread of contaminants intrudingCan predict the spread of contaminants intruding into the system

143

Main Work Done• Development of Inhouse Deterministic Models for

Prediction Hydraulics and Water Quality ( both Chemical Biological Reactions)Chemical Biological Reactions)

• Parameter Estimation Based on Traditional as well as Heuristic Approaches

l f l d d l d• Development of Control Based Models Based on PI, PID and DI Controllers to Control Water Quantity Q y

• Development of SIMULINK / MATLAB approaches for Control of Water Networks

144

Main Work Done (Contd)

• ANN based models for prediction of Water Quality – Different inputs, different Q y p ,architectures – Multiple outputs- Simple calibration

• Application of Control algorithms for control of Water Quality – Both Chemicalcontrol of Water Quality Both Chemical and Biological quality

145

Future Work

• Prediction of Reaction Kinetics using Pilot loop experiments

l f i i• Development of CWS – Contaminant Warning System – Accidental, Intentional Contamination

• Sensor application in Water Networks Real time• Sensor application in Water Networks – Real time monitoring as well as control

• Reliability, Resilience and Vulnerability of Water y, yNetworks

• Efficient Operation of Asset Management

146

Thank YouThank You

147