URBAN WATER DEMAND URBAN WATER DEMAND FORECASTING FORECASTING USING ARTIFICIAL NEURAL USING ARTIFICIAL NEURAL NETWORKS: NETWORKS: A CASE STUDY OF BANGKOK.A CASE STUDY OF BANGKOK.BY

VICTOR SHINDEVICTOR SHINDE

CONTENTSCONTENTS

Need for water demand forecasting Description of ANN Study area description Results of the study Conclusions

INTRODUCTIONINTRODUCTION

Need for water demand forecastingNeed for water demand forecasting

• Water is a finite resource.

• Expanding the capacity of a water distribution system.

• Improving the reliability of supply.

• Effecting demand management instruments.

• Procurement of investment.

DESCRIPTION OF ANNDESCRIPTION OF ANN

Why use ANN?

• Accounts for non linearity between inputs and outputs

• Uses a universal function to convert inputs to output,

for all types of problems.

• More realistic forecasts.

DESCRIPTION OF ANNDESCRIPTION OF ANN A network which mimics the human brain.

Input layer Hidden Layer Output layer

INPUT

OUTPUT

Connection links each having some weight ‘w’

w1j

w2j

w3j

x1

x2

x3

j

yj = f(x1w1j+x2w2j+x3w3j)

f = Transfer function = (1/(1+e-t)

DESCRIPTION OF ANNDESCRIPTION OF ANN Network Training

Input layer Hidden Layer Output layer

INPUT

Output Desired Output

Compares

Cost function E = 2)( do YY

STUDY AREA DESCRIPTIONSTUDY AREA DESCRIPTION

Main study area

Metropolitan Waterworks Authority (MWA) responsibility area – Bangkok Metropolis, Nontaburi & Samut Prakarn

Secondary study areas

Hanoi (Vietnam) and Chiang Mai (Thailand)

STUDY AREA DESCRIPTIONSTUDY AREA DESCRIPTION

MWA responsibility area (2007 statistics)• Population : 7.86 Million

• Population served: 7.36 Million (93.6%)

• Average Daily production : 5.52 MCM

• Non Revenue Water : 30.32 % Secondary study areasSecondary study areas

Hanoi Chiang Mai

Temperature (0C)Maximum 32 31Minimum 14 19Rainfall (mm) 1682 1081Population (Million) 3.4 1.66GDP (USD) 40 Billion 3.3 Billion

Overall objectiveOverall objectiveTo develop ANN models to forecast the water demand for MWA – Bangkok.

Specific objectivesSpecific objectives● To forecastforecast the short term and long term water demand for MWA.

● To identifyidentify the factors most crucial in determining the short term and long term water demands for MWA.

● To comparecompare the factors influencing long term demand for Bangkok, Hanoi and Chiang Mai

OBJECTIVES OF THE STUDYOBJECTIVES OF THE STUDY

Demand Short term (ST) demand – Daily demand, 1,2 & 3 days lead

Long term (LT) demand – Monthly demand, 1,2 & 6 months lead

Data usedST Demand – Historical demand (sales), Rainfall, RH, Mean Temp

LT Demand – Historical demand (sales), Population, GPP, Household

connections, Education status, Rainfall, RH, Max TempFor comparing the cities (Bangkok, Hanoi and Chiang Mai) – Same as LT Demand, only production in lieu of sales & Mean Temp instead of Max Temp

Software used – ANN NeuroSolutions

SCOPE OF THE STUDYSCOPE OF THE STUDY

Methodology for both ST and LT demand Methodology for both ST and LT demand modelsmodels

SCOPE OF THE STUDYSCOPE OF THE STUDY

Data Collection and Analysis

Input Selection

Model Training & Testing for 1st set

Sensitivity analysis

Omission of least sensitive variables

Training & Testing for 2nd set

• Correlation Matrix• Pruning & Construction

Architectures• MLP• GFF• RBFTransfer functions• Hyperbolic tan• SigmoidLearning Rules• Backward Descend• Conjugate Gradient

150 ST Models – 15 sets88 LT Models – 6 sets60 Comparison models

RESULTSRESULTS

Short term demand, 1 day lead

Input Selection : Zhang et al. (2006), Msiza et al. (2007)

Water Sales Max Temp Min Temp Rainfall RH Evaporation Mean TempWater Sales 1 0.38 0.55 0.39 0.31 0.36 0.52Max Temp 0.38 1 0.78 -0.06 0.19 0.94 0.91Min Temp 0.55 0.78 1 0.42 0.7 0.79 0.96Rainfall 0.39 -0.06 0.42 1 0.85 -0.16 0.27RH 0.31 0.19 0.7 0.85 1 0.17 0.54Evaporation 0.36 0.94 0.79 -0.16 0.17 1 0.88Mean Temp 0.52 0.91 0.96 0.27 0.54 0.88 1

Selected Variables: Mean Temperature, Rainfall and RH

RESULTSRESULTSObserved vs. Predicted Demand for Training Set

2.9

3.1

3.3

3.5

3.7

3.9

1 11 21 31 41 51 61

Exemplars

Dem

and

(MC

M)

Observed

Predicted

Observed vs. Predicted Demand for Testing Set

3.1

3.3

3.5

3.7

3.9

4.1

1 11 21 31 41 51 61

Exemplars

Dem

and

(MC

M)

Observed

Predicted

RESULTSRESULTS

AARE =

1001

1

xO

DO

N

N

i i

ii

RMSE =

2

12

1

))(1

( i

N

ii DO

N

(Threshold static)x = (n/N) x 100

Model Architecture Hidden PE's Transfer Learning AARE RMSELayers function Rule % MCM 0.50% 1% 2% 3% 4% 5%

ST-1A(1) MLP 1 13 tanh BD 1.19 0.054 30.30 56.06 78.79 92.42 96.97 100ST-1A(2) MLP 1 11 Sigmoid BD 1.19 0.054 36.36 54.55 78.79 92.42 96.97 100ST-1A(3) MLP 1 17 tanh CG 1.18 0.052 25.76 54.55 81.82 92.42 96.97 100ST-1A(4) MLP 1 17 Sigmoid CG 1.15 0.05 28.79 54.55 81.82 95.45 100 100ST-1A(5) MLP 2 20 &15 tanh BD 1.15 0.051 30.30 59.09 80.30 93.94 98.48 100ST-1A(6) MLP 2 21 &15 Sigmoid BD 1.19 0.055 28.79 56.06 78.79 92.42 96.97 100ST-1A(7) MLP 2 12&15 tanh CG 1.19 0.054 30.30 57.58 80.30 92.42 96.97 100ST-1A(8) MLP 2 12&15 Sigmoid CG 1.2 0.055 33.33 54.55 78.79 90.91 96.97 100ST-1A(9) MLP 3 20,10&5 tanh BD 1.12 0.05 30.30 59.09 81.82 92.42 100 100ST-1A(10) MLP 3 17,12 &8 tanh CG 1.13 0.049 27.27 53.03 80.30 93.94 100 100ST-1A(11) MLP 3 17,12 &9 Sigmoid CG 1.15 0.052 34.85 57.58 78.79 90.91 96.97 100

Threshold static

Zhang et al. (2008)Adamowski (2008)Ghiassi et al. (2007)Jain et al. (2000)

Observed vs. Predicted Demand for ST-1B(16)

3.15

3.25

3.35

3.45

3.55

3.65

1 11 21 31 41 51 61

Testing Exemplars

Dem

and

(MCM

)

Observed

Predicted

Model Architecture Hidden PE's Transfer Learning AARE RMSELayers function Rule % MCM 0.50% 1% 2% 3% 4% 5%

ST-1B(12) MLP 1 18 tanh BD 1.23 0.056 31.82 54.55 78.79 90.91 96.97 98.48ST-1B(13) MLP 1 16 Sigmoid BD 1.17 0.055 34.85 60.61 80.30 92.42 96.97 98.48ST-1B(14) MLP 1 14 tanh CG 1.26 0.057 27.27 53.03 80.30 90.91 96.97 100ST-1B(15) MLP 1 13 Sigmoid CG 1.2 0.054 28.79 54.55 77.27 90.91 96.97 100ST-1B(16) MLP 2 12&8 tanh BD 1.17 0.053 33.33 59.09 78.79 90.91 96.97 100ST-1B(17) MLP 2 12&8 Sigmoid BD 1.22 0.056 31.82 57.58 78.79 90.91 96.97 98.48ST-1B(18) MLP 2 12&8 tanh CG 1.23 0.056 30.30 54.55 80.30 92.42 96.97 98.48ST-1B(19) MLP 2 12&8 Sigmoid CG 1.21 0.056 33.33 56.06 78.79 93.94 96.97 100

Threshold static

SA for ST-1A models

0.00

0.02

0.04

0.06

0.08

0.10

0.12

HWD

Mea

nTe

mp

Rain

fall RH

Stan

dard

Dev

iatio

n(M

CM)

Input Variables: HWD, Mean Temp Input Variables: HWD, Mean Temp & Rainfall& Rainfall

RESULTSRESULTSObserved vs. Predicted Demand for Testing Set

3.15

3.25

3.35

3.45

3.55

3.65

3.75

3.85

1 11 21 31 41 51 61

Exemplars

Dem

and

(MCM

)

Observed

Predicted

Model Architecture Hidden PE's Transfer Learning AARE RMSELayers function Rule % MCM 0.50% 1% 2% 3% 4% 5%

ST-1C(20) MLP 1 42 tanh BD 1.31 0.058 23.96 48.96 78.13 91.67 96.88 98.96ST-1C(21) MLP 1 42 Sigmoid BD 1.27 0.057 29.17 55.21 78.13 91.67 96.88 100ST-1C(22) MLP 1 40 tanh CG 1.32 0.058 21.88 48.96 80.21 91.67 96.88 100ST-1C(23) MLP 1 42 Sigmoid CG 1.34 0.059 26.04 46.88 77.08 91.67 96.88 98.96ST-1C(24) MLP 2 15&12 tanh BD 1.29 0.058 28.13 50.00 77.08 92.71 96.88 100ST-1C(25) MLP 2 15&12 Sigmoid BD 1.26 0.056 25.00 56.25 78.13 91.67 97.92 100ST-1C(26) MLP 2 15&12 tanh CG 1.29 0.058 27.08 50.00 78.13 91.67 96.88 100ST-1C(27) MLP 2 15&12 Sigmoid CG 1.28 0.058 29.17 52.08 77.08 91.67 96.88 100

Threshold static

RESULTSRESULTSInput Variables: Only HWDInput Variables: Only HWD

Model Architecture Hidden PE's Transfer Learning AARE RMSELayers function Rule % MCM 0.50% 1% 2% 3% 4% 5%

ST-1D(29) MLP 1 24 tanh BD 1.33 0.058 23.40 46.81 76.60 91.49 96.81 98.94ST-1D(30) MLP 1 28 Sigmoid BD 1.24 0.056 25.53 52.13 77.66 89.36 97.87 100ST-1D(31) MLP 1 28 tanh CG 1.32 0.057 23.40 47.87 77.66 91.49 96.81 100ST-1D(32) MLP 1 28 Sigmoid CG 1.35 0.059 24.47 46.81 76.60 92.55 96.81 98.94ST-1D(33) MLP 2 15&11 tanh BD 1.32 0.059 27.66 50.00 75.53 93.62 96.81 100ST-1D(34) MLP 2 16 &12 Sigmoid BD 1.26 0.057 30.85 54.26 77.66 89.36 96.81 100ST-1D(35) MLP 2 16 &12 tanh CG 1.35 0.06 23.40 47.87 77.66 91.49 96.81 98.94ST-1D(36) MLP 2 15&12 Sigmoid CG 1.36 0.06 24.47 47.87 76.60 91.49 96.81 98.94

Threshold static

Input Variables: HWD -1, HWD -2.Input Variables: HWD -1, HWD -2.

RESULTSRESULTS

Model Architecture Hidden PE's Transfer Learning AARE RMSELayers function Rule % MCM 0.50% 1% 2% 3% 4% 5%

ST-1E(37) MLP 1 21 tanh BD 1.28 0.056 23.08 48.35 79.12 93.41 97.80 98.90ST-1E(38) MLP 1 21 Sigmoid BD 1.24 0.055 27.47 56.04 75.82 90.11 97.80 98.90ST-1E(39) MLP 1 19 tanh CG 1.29 0.057 28.57 48.35 79.12 92.31 97.80 98.90ST-1E(40) MLP 1 21 Sigmoid CG 1.26 0.055 25.27 48.35 81.32 93.41 97.80 100ST-1E(41) MLP 2 16 &12 tanh BD 1.28 0.057 26.37 47.25 78.02 92.31 97.80 98.90ST-1E(42) MLP 2 16 &12 Sigmoid BD 1.22 0.055 29.67 53.85 79.12 90.11 96.70 100

Threshold static

Model Architecture Hidden PE's Transfer Learning AARE RMSELayers function Rule % MCM 0.50% 1% 2% 3% 4% 5%

ST-1F(43) MLP 1 10 tanh BD 1.27 0.056 23.26 50.00 79.07 93.02 97.67 100ST-1F(44) MLP 1 9 Sigmoid BD 1.26 0.055 24.42 55.81 77.91 93.02 98.84 100ST-1F(45) MLP 2 16&11 tanh BD 1.31 0.057 19.77 47.67 76.74 91.86 97.67 100ST-1F(46) MLP 2 18&12 Sigmoid BD 1.22 0.055 30.23 53.49 81.40 91.86 97.67 100

Threshold static

Input Variables: HWD -1, HWD -2 & HWD -3.Input Variables: HWD -1, HWD -2 & HWD -3.

Input Variables: HWD -1 through HWD -7Input Variables: HWD -1 through HWD -7

Master model for seven consecutive day Master model for seven consecutive day forecastforecastInput variables: HWD, Rainfall, Mean Temperature & Input variables: HWD, Rainfall, Mean Temperature & RHRHModel Architecture Hidden PE's Transfer Learning

Layers function Rule D+1 D+2 D+3 D+4 D+5 D+6 D+7 AverageAARE 1.32 1.66 1.87 2.00 1.97 2.02 1.96 1.83RMSE 0.058 0.076 0.083 0.084 0.086 0.086 0.081 0.08AARE 1.29 1.64 1.87 2.03 1.98 2.05 2.01 1.84RMSE 0.059 0.076 0.084 0.086 0.087 0.087 0.083 0.080AARE 1.31 1.65 1.88 2.04 2.02 2.08 2.04 1.86RMSE 0.058 0.076 0.084 0.085 0.088 0.088 0.085 0.080AARE 1.32 1.65 1.89 2.03 2.00 2.07 2.04 1.86RMSE 0.059 0.076 0.085 0.085 0.088 0.087 0.085 0.081AARE 1.17 1.52 1.80 1.83 1.82 1.83 1.85 1.69RMSE 0.053 0.068 0.078 0.076 0.076 0.077 0.076 0.072AARE 1.30 1.61 1.84 1.97 1.95 2.03 1.99 1.81RMSE 0.059 0.075 0.082 0.083 0.085 0.086 0.082 0.079AARE 1.33 1.63 1.87 2.06 2.01 2.03 1.96 1.84RMSE 0.058 0.075 0.083 0.086 0.088 0.086 0.081 0.080AARE 1.32 1.64 1.87 2.01 1.99 2.04 2.03 1.84RMSE 0.060 0.076 0.084 0.084 0.087 0.086 0.084 0.080

BDSigmoid

BDtanh

CGSigmoid

CGtanh

BDSigmoid

BDtanh

CGSigmoid

CGtanh

MM-4

MM-3

81MLPMM-2

MLP

MLP

1

1

MM-8

MM-7

MM-6

MM-5

MLP

MLP

MLP

MLP

8

14

2

2

2

2

8 & 7

10 & 7

8 & 7

9 & 7

Error for seven consecutively forecasted seven days

MM-1 1MLP 10

Date Observed Forecasted ARE Avg ARE RMSE Avg RMSEDemand Demand

MCM MCM % % MCM MCM

28-Jun-08 3.502 3.508 0.17 0.00629-Jun-08 3.481 3.489 0.22 0.00830-Jun-08 3.433 3.475 1.22 0.0421-Jul-08 3.410 3.434 0.72 0.0252-Jul-08 3.391 3.431 1.16 0.0393-Jul-08 3.413 3.426 0.37 0.0134-Jul-08 3.471 3.431 1.17 0.041

13-Aug-08 3.406 3.333 2.15 0.07314-Aug-08 3.416 3.334 2.39 0.08215-Aug-08 3.425 3.332 2.72 0.09316-Aug-08 3.410 3.358 1.51 0.05117-Aug-08 3.388 3.358 0.90 0.03018-Aug-08 3.371 3.349 0.64 0.02219-Aug-08 3.391 3.352 1.16 0.039

20-Jul-08 3.450 3.320 3.79 0.13121-Jul-08 3.432 3.323 3.20 0.11022-Jul-08 3.450 3.321 3.74 0.12923-Jul-08 3.425 3.359 1.92 0.06624-Jul-08 3.460 3.357 2.99 0.10425-Jul-08 3.510 3.345 4.70 0.16526-Jul-08 3.452 3.347 3.04 0.105

0.72 0.025

TEST SAMPLE - 1

TEST SAMPLE - 2

TEST SAMPLE - 2

0.1163.34

0.0561.64

Best fit models for Short term Demand

RESULTSRESULTS

Lead Period Input variables Architecture Accuracy• MLP - 3 layers

HWD, Rainfall, • tanh transfer functionMean Temp, RH • 20, 10 & 5 PE's

• Back Descend Rule• MLP - 2 layers• Sigmoid transfer function

HWD-1, HWD-2 • 16 & 10 PE's• Back Descend Rule• MLP - 2 layers• tanh transfer function

HWD-1 • 13 & 6 PE's• Back Descend Rule• MLP - 3 layers

HWD, Rainfall, • tanh transfer functionMean Temp, RH • 8, 7 & 7 PE's

• Backward Descend Rule

7 day consecutive

98.88%

98.53%

98.35%

98.51%

1 day

2 day

3 day

Lead Period Input variables Architecture AccuracyPopulation, GPP, Education • MLP - 3 layersstatus, Household connections • Sigmoid transfer functionHWD, Rainfall, Max Temp • 20, 10 & 8 PE's

• Conjugate Gradient RulePopulation, GPP, Education • GFF - 1 layerstatus, Household connections • tanh transfer functionHWD, Rainfall, RH • 11 PE's

• Conjugate Gradient RulePopulation, GPP, Education • MLP - 1 layerstatus, Household connections • tanh transfer functionHWD, Rainfall, Max Temp • 10 PE's

• Backward Descend Rule

1 month

2 month

6 month

98.88%

98.53%

98.35%

RESULTSRESULTS

Best fit models for Long term Demand

Factors influencing ST & LT Demand

Sensitivity Analysis

• Standardize all data

xx

Y = x & σ are the mean and standard deviation

• Increases and decreases the input variables between the standardized -1 and +1

• Thus a standardized value of ‘zero’ represents the mean of the sample

• Presents the trend of change in the demand.

RESULTSRESULTS

Sensitivity indices for ST-Demand

0.00

0.02

0.04

0.06

0.08

0.10

0.12

HWD

Mea

nTe

mp

Rainf

all RH

Stan

dard

Dev

iatio

n(M

CM)

Sensitivity indices for LT Demand

0.0

0.5

1.0

1.5

2.0

2.5

HWD

GPP

Popu

latio

n

Educ

ation

Stat

us

Hous

ehol

dCo

nnec

tions

Max

Tem

p

Rain

fall RHSt

anda

rd D

evia

tion

(MCM

)

Factors influencing ST & LT Demand

RESULTSRESULTS

20 models prepared for each city using MLP & GFF Input VariablesInput Variables: Population, GPP, Household : Population, GPP, Household

connections, Education status, HWD, Rainfall, Max connections, Education status, HWD, Rainfall, Max Temperature, RHTemperature, RH

Best fit model results, AARE

• Bangkok – 1.06%

• Hanoi – 2.18 %

• Chiang Mai – 1.26%

Sensitivity analysis to determine influencing variables

Demand models for Bangkok, Hanoi & Chiang Mai

RESULTSRESULTS

Demand models for Bangkok, Hanoi & Chiang Mai

Sensitivity indices of Input parameters for best models of the three study areas

01234567

HW

D

GP

P

Pop

ulat

ion

Edu

catio

n

Hou

seho

lds

Mea

n T

emp

Rai

nfal

l

RH

Per

cen

tag

e ch

ang

e in

Dem

and

Bangkok

Hanoi

Chiang Mai

RESULTSRESULTS

CONCLUSIONS

ANN can provide the MWA with a powerful instrument to forecast the demands. Forecasting accuracy will be over 98% for both ST & LT. Advantages for MWA• Schedule pumping operations• Reduce detention time to improve water quality• Monthly revenues can be estimated upto 6 months in advance• Diversions, Basin transfers can be planned in dry years

Factors Influencing MWA sales demandST Demand : Historical water demandLT Demand : Education status & Household connections

Comparison of factors influencing production demands of Bangkok, Hanoi and Chiang MaiBangkok : HH connections, GPP and EducationHanoi : Education status, Mean Temperature and PopulationChiang Mai : HH connections, Mean Temperature & Rainfall(This information could prove vital for goverments, international agencies and funding organizations)