Intelligent Real-time Water Level Forecast Models for Pumping Stations

3rd ANNOUNCEMENT

PAWEES 2013

The 12th Conference ofInternational Society of

Paddy and Water Environment Engineering

Intelligent Real-time Water Level Forecast Models for Pumping Stations

Department of Bioenvironmental Systems Engineering, National Taiwan University

Fi-John Chang, Ying-Ray LuDepartment of Bioenvironmental System Engineering, National Taiwan University, Taipei, Taiwan, ROC

Advisor: Distinguished Professor Fi-John Chang ([email protected])


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The 12thConference of

International Society of Paddy and Water Environm

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Outline

Study Motivation

Methodology

Applications

Results and Discussions

Conclusions


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Motivation• Urbanization leads to a reduction in the time of rainfall

concentration.• Climate Change causes fast rising peak flows. → Urban flood control is a crucial task, particularly in developed cities.

達第一次警戒

達第一次警戒

達第一次警戒

達第一次警戒

達第一次警戒

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達第一次警戒

達第一次警戒


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Keelung River

Layout of Pumping Station

Yu-Chung Pumping station Structure ChartRacking MachineFront Pool Pumps

Sewer

Center console


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Materials• Study Area

• Yu-Cheng Pumping Station

• Select Events• 13 events of typhoons &

heavy rainfall in 2004-2013

• Data Collection• Water level at the pumping

station• Water levels of sewer outlets

(YC2-YC12)• Rainfall (R1-R6, Average

Rainfall)Year 2013 2012 2012 2010 2009 2008 2008 2006 2005 2005 2004 2004 2004

Event 511 Saola 612 Megi Parma Jangmi Sinlaku 910 Talim Haitang Nanmadol Nockten Haima

Number of data 85 221 113 145 320 307 197 148 140 143 65 150 148

Mean water level (m) 1.79 2.07 2.57 2.13 2.07 2.05 2.25 2.08 2.25 2.17 2.5 2.23 3.12

Standard deviation (m) 0.37 0.31 0.55 0.09 0.14 0.39 0.28 0.26 0.19 0.18 0.24 0.48 1.04


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Model Construction

Data Collection

Data Analysis

Input Selection

Forecast Models

Pearson's Correlation Coefficient

Rainfall(6 Stations)

Water Level at Pumping Station(1 Station)

Sewer Water Level(11 Stations)

Gamma Test(Key Factors Assessment)

BPNN

Elman NN

NARX

Static Neural Network

Dynamic Neural Network


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Data Analysis

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Rainfall vs. Water level at the pumping station

• Rainfall vs. water level• Rainfall vs. RECOVERED water level• Accumulated rainfall vs. RECOVERED water

level

Water level vs. Water level• Water levels of sewer outlets and the water level

at the pumping station

• Pearson's Correlation Coefficient


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0 10 20 30 40 50 60 700.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

Average RainfallR1R2R3R4R5R6

Time Step Difference (min)

Cor

rela

tion

Coe

ffici

ent

• Rainfall vs. water level at the front poolCorrelation Coefficient Analysis

TimeLag

Average Rainfall R1 R2 R3 R4 R5 R6

0 min 0.38 0.27 0.46 0.29 0.34 0.40 0.3410 min 0.45 0.30 0.52 0.36 0.41 0.46 0.4020 min 0.50 0.33 0.56 0.41 0.46 0.52 0.4430 min 0.52 0.34 0.59 0.42 0.47 0.55 0.4540 min 0.51 0.35 0.59 0.41 0.46 0.55 0.4450 min 0.50 0.34 0.59 0.40 0.44 0.53 0.4260 min 0.48 0.34 0.57 0.39 0.43 0.51 0.4070 min 0.47 0.34 0.56 0.39 0.41 0.50 0.39


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• RECOVER the water level of the pumping station- Estimate the increased water levels based on the number of running

pumps and the actual water storage area of the pumping station.

- Next, recover the front pool water level hydrograph.

Correlation Coefficient Analysis

① Estimate the actual water storage area

② Calculate the effect of the starting water level for pumps

③ Calculate the corresponding number of running pumps each time

Sewer Area (m2)

Fore Bay Area (m2)

Flood Storage Area (m2)

163,008 1,650 164,658

Quantity Capacity (cms) Increased water level (m/10min)

7 26.3 0.096 4 12.5 0.046

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 1001031061091120

2

4

6

8

10

12

14

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Rai

nfal

l (m

m)

Num

bers

of r

unni

ng p

umps

Wat

er le

vel (

m)


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• Rainfall and RECOVERED water level at the pumping station - Correlation Coefficient Analysis

Correlation Coefficient Analysis

TimeLag


0 min 0.43 0.31 0.49 0.36 0.40 0.43 0.3910 min 0.50 0.35 0.54 0.42 0.46 0.49 0.4520 min 0.55 0.38 0.58 0.47 0.51 0.54 0.5030 min 0.58 0.39 0.62 0.50 0.54 0.57 0.5340 min 0.59 0.40 0.63 0.50 0.54 0.58 0.5350 min 0.59 0.40 0.63 0.50 0.53 0.58 0.5260 min 0.58 0.41 0.62 0.50 0.52 0.57 0.5170 min 0.58 0.41 0.61 0.50 0.52 0.57 0.51

Cumulative Time


10 min 0.43 0.31 0.49 0.36 0.40 0.43 0.3920 min 0.49 0.38 0.55 0.42 0.46 0.49 0.4630 min 0.55 0.43 0.60 0.48 0.52 0.53 0.5140 min 0.59 0.46 0.64 0.52 0.56 0.57 0.5550 min 0.62 0.49 0.68 0.55 0.59 0.61 0.5860 min 0.65 0.51 0.70 0.58 0.62 0.63 0.6070 min 0.66 0.53 0.73 0.60 0.63 0.65 0.62

• Accumulated Rainfall and RECOVERED water level at the pumping station - Correlation Coefficient Analysis


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• Water levels of sewer outlets and the water level at the pumping stationCorrelation Coefficient Analysis

Before 2005

Time Lag YC2 YC3 YC4 YC5 YC6 YC7 YC8 YC9 YC10 YC11 YC12

0 min 0.82 0.59 0.95 -0.06 -0.16 0.78 0.87 0.94 0.98 0.89 0.5110 min 0.81 0.58 0.95 -0.06 -0.17 0.82 0.87 0.93 0.97 0.89 0.5220 min 0.8 0.57 0.94 -0.07 -0.17 0.85 0.86 0.92 0.95 0.88 0.5330 min 0.78 0.56 0.92 -0.08 -0.17 0.86 0.85 0.91 0.93 0.86 0.5440 min 0.76 0.54 0.9 -0.08 -0.18 0.85 0.83 0.89 0.9 0.85 0.5550 min 0.74 0.51 0.88 -0.08 -0.18 0.84 0.82 0.87 0.88 0.83 0.5760 min 0.72 0.48 0.86 -0.09 -0.19 0.82 0.8 0.85 0.85 0.81 0.5870 min 0.69 0.45 0.84 -0.08 -0.2 0.8 0.79 0.83 0.82 0.8 0.59

Time Lag YC2 YC3 YC4 YC5 YC6 YC7 YC8 YC9 YC10 YC11 YC12

0 min 0.01 -0.14 0.03 -0.13 0.02 0.09 0.30 0.05 0.28 0.05 -0.0810 min 0.01 -0.14 0.03 -0.12 0.03 0.10 0.30 0.05 0.27 0.05 -0.0820 min 0.02 -0.13 0.03 -0.12 0.03 0.10 0.30 0.06 0.26 0.06 -0.0730 min 0.03 -0.13 0.04 -0.11 0.04 0.11 0.30 0.06 0.25 0.06 -0.0740 min 0.04 -0.12 0.04 -0.10 0.04 0.11 0.29 0.06 0.24 0.06 -0.0650 min 0.04 -0.11 0.05 -0.10 0.05 0.12 0.29 0.07 0.23 0.07 -0.0660 min 0.05 -0.11 0.05 -0.09 0.06 0.12 0.29 0.07 0.23 0.07 -0.0670 min 0.06 -0.10 0.06 -0.08 0.07 0.12 0.29 0.08 0.22 0.08 -0.05

After 2005

- Water levels of sewer outlets can not be used as input factors


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Input Selection• Gamma Test (GT)：

• The GT (Agalbjörn et.al, 1997; Koncar, 1997) estimates the noise level (Γ value) present in a data set.

• The GT can produce the estimation directly from the data without assuming any parametric form of the equations that govern the system. The only requirement is that the system is smooth.


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R2 Average Rainfall R5 R1 R6 R3 R40

2

4

6

8

10

12

14

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%100%

90% 88%

69%63%

44%

25%

F(d<d10) F(d>d90) 1-F(d>d90)/F(d<d10)

Freq

uenc

y

Scor

e

Input Selection• Gamma Test：

• Select 6 rainfall station and average rainfall. (7 factors)• Blue Bar: the occurrence frequency of a factor in the best results.• Red Bar: the occurrence frequency of a factor in the worst results.• Green Line: the score of the factors. (1-worst/best))

→ Select the factors (R2, AR, R5) higher than 80% to be input factors.


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Model

• Water Level Forecast Model Construction:

• Artificial Neural Network:• Back-Propagation Neural Network (BPNN)

Model Construction

Water level (t) ANNModelRainfall (t)

Water level(t+n)

‧‧‧

1

n

1

1

R1 (t)

2

3

4

R2 (t)

R3 (t)

H (t)

H (t+1)

Input layer Hidden layer Output layer

n=10-60min


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Model


• Artificial Neural Network:• Elman Neural Network (Elman NN)

Model Construction


Water level(t+n)


‧‧‧

1

n

1

1

R1 (t)

2

3

4

R2 (t)

R3 (t)

H (t)

H (t+1)

‧‧‧

1

n

w1 (t)

wn (t)


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Model


• Artificial Neural Network:• The nonlinear autoregressive network with exogenous inputs

(NARX)

Model Construction


Water level(t+n)


‧‧‧

1

n

1

1

R1 (t)

2

3

4

R2 (t)

R3 (t)

H (t)

H (t+1)

1

n

H1 (t+n)

H1 (t+1)

←


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Results and Discussion

200 400 600 8000.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

Wat

er le

vel (

m)

Training

100 200 300 400 500 600Time (10min)

Validation

100 200 300 400 500

Testing

ObeservedPredicted

200 400 600 8000.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

Wat

er le

vel (

m)

Training

100 200 300 400 500 600Time (10min)

Validation

100 200 300 400 500

Testing

ObeservedPredicted

200 400 600 8000.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

Wat

er le

vel (

m)

Training

100 200 300 400 500 600Time (10min)

Validation

100 200 300 400 500

Testing

ObeservedPredicted

NARX

10-min-ahead

30-min-ahead

50-min-ahead


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Results and Discussion• Compare BPNN and NARX, t+6 (60-min-ahead)

200 400 600 800

1

2

3

4

5

6

Wat

er le

vel (

m)

Training

200 400 600

Validation

100 200 300 400 500

Testing

ObeservedPredicted

200 400 600 800

1

2

3

4

5

6

Wat

er le

vel (

m)

200 400 600 100 200 300 400 500

Time (-10min)

BPNN

NARX


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t+1 t+2 t+3 t+4 t+5 t+60.00

0.05

0.10

0.15

0.20

0.25

0.30

0.09

0.16

0.19

0.220.24 0.24

0.10

0.16

0.19

0.230.25 0.26

0.09

0.14

0.190.21

0.23 0.23

BPNN ELMAN NARX

RM

SE (m

)

BPNN ELMAN NARX

Time lag

RMSE (m) CE Gbench

RMSE (m) CE Gbench

RMSE (m) CE Gbench

10 min 0.095 0.93 0.02 0.095 0.93 0.01 0.087 0.94 0.1820 min 0.156 0.80 0.06 0.155 0.80 0.07 0.145 0.83 0.1930 min 0.190 0.70 0.17 0.189 0.70 0.18 0.188 0.70 0.1940 min 0.219 0.59 0.19 0.229 0.55 0.11 0.214 0.61 0.2150 min 0.237 0.52 0.20 0.251 0.46 0.11 0.227 0.55 0.2560 min 0.245 0.48 0.23 0.262 0.41 0.12 0.228 0.55 0.32


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t+1 t+2 t+3 t+4 t+5 t+60.40

0.50

0.60

0.70

0.80

0.90

1.00 0.94

0.83

0.70

0.610.55 0.55

BPNN ELM NARX

CE

BPNN ELMAN NARX

Time lag

RMSE (m) CE Gbench

RMSE (m) CE Gbench

RMSE (m) CE Gbench



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Results and DiscussionBPNN ELMAN NARX

Time lag

RMSE (m) CE Gbench

RMSE (m) CE Gbench

RMSE (m) CE Gbench


t+1 t+2 t+3 t+4 t+5 t+60.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.02

0.06

0.170.19

0.200.23

0.01

0.07

0.18

0.11 0.110.12

0.18 0.19 0.190.21

0.25

0.32

BPNN ELM NARX

Gbe

nch

N

tii

N

tii

dd

yd

1

21

1

2

1Gbench =


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ConclusionsIntelligent real-time water level forecast models are developed to forecast the 10-60 min-ahead front pool water levels by utilizing the current rainfall and water level.

The results indicate that all of the forecasts are good, which can well capture the trend of the flooding hydrograph.

The NARX network produces the best performance in terms of RMSE, CE and G-bench values.


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24Department of Bioenvironmental Systems Engineering, National Taiwan University

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THANK YOU FORYOUR ATTENTION

Intelligent Real-time Water Level Forecast Models for Pumping Stations

Engineering

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