TIME SERIES FLOW FORECASTING USING A.N.N.

AT SELECTIVE STATIONS OF BRAHMAPUTRA

FIRST RESEARCH PROGRESS SEMINAR

For Ph.D. Thesis at N.I.T.K., Surathkal,

By Aniruddha Banhatti,

Part Time Ph.D. Student,

Registration Number: AM08P05

2

IMPORTANCE OF STREAM FLOW FORECASTING

Hydrologic StructuresIrrigationFlood ControlHydrologic PlanningFlood Relief

3

NATURE OF STREAM FLOW DATA

Time Series DataShow following characteristics:

TrendSeasonalityCyclic NatureIrregular Fluctuations – Outliers and Noise

4

ALGORITHM USED:

BACK PROPAGATION ALGORITHM

IS FOUND TO BE BEST SUITED FOR

TIME SERIES DATA

AND MOST OF THE

HYDROLOGIC MODELING PROBLEMS.

5

SCHEMATIC OF BP ALGORITHM

6

CHARACTERISTICS OF HYDROLOGIC TIME SERIES

Non-stationary Auto correlated Cross related Chronological dependance These characteristics manifest as

Trend Seasonality Cyclic nature Irregular fluctuations

7

STUDY AREA

Gauging stations at Pandu and Pancharatna along Brahmaputra River at Guwahati is taken as the study area.

Daily stream flow data for twenty year period

1st January 1980 to 31st December 1999 will be used for the present study.

8

MAP OF STUDY AREA

9

MAP OF STUDY AREA

10

DATA PRE-PROCESSING TECHNIQUES

Raw Values – for control group Normalization – De-trending Logarithmic transform Logarithmic plus First Difference Logarithmic plus Second Difference

11

OBJECTIVES

USING DIFFERENT PRE-PROCESSING TECHNIQUES

OBSERVING EFFECT OF PRE-PROCESSED DATA ON PERFORMANCE OF ANNs

COMPARITIVE PERFORMANCE OF DIFFERENT ARCHITECTURES OF ANNs

IDENTIFICATION OF BEST CONFIGURATION FOR PREDICTION OF STREAMFLOW

12

ARCHITECTURES OF ANN

According to Activating Function

According to Number of Neurons

According to Algorithm Used

13

ARCHITECTURES USED

According to Activation Function

TANSIG

LOGSIG

PURELIN These architectures will be used

14

PRE-PROCESSING TECHNIQUES USED

Following techniques will be used :

RAW DATA

LOG TRANSFORMED DATA

LOG TRANSFORMED DATA WITH FIRST DIFFEREBCES

15

DATA SETS No. of lagged terms Dataset Lagged terms Data Matrix

Input Output

1 Raw values Log Log + first difference

yt = xt

 yt = log xt

 yt = log xt + first diff.

y1

y2

y3

…..yt

y2

y3

y4

…..yt-1

2 Raw values Log Log + first difference

yt = xt

 yt = log xt

 yt = log xt + first diff.

y1, y2

y2, y3

.…. yt-1, yt

y3

y4

.…. 

yt-2

3 Raw values Log Log + first difference

yt = xt

 yt = log xt

 yt = log xt + first diff.

y1, y2, y3

y2, y3, y4

…..…..yt-2, yt-1,

yt

y4

y5

…..….. yt-3

16

ROLE OF ACTIVATION FUNCTIONS

TRANSFER OF DATA BETWEEN NEURONS

SUMMING UP OR INTEGRATION OF DATA RECEIVED AT A NEURON

INCORPORATING BIAS WITH THE INTEGRATED DATA

PASSING THE SIGNAL FORWARD IN THE NETWORK

17

WORK DONE SO FAR

VISUAL OBSERVATION OF DATA

PREPARATION OF DATA SETS

CONSTRUCTING ANNs FOR RAW DATA

TRAINING AND TESTING ANNs FOR ONE DAY LAG RAW DATA TWO DAY LAG RAW DATA THREE DAY LAG RAW DATA

EVALUATION OF RESULTS

18

VISUAL OBSERVATION OF DATA

7 567 112716872247280733673927448750475607616767270

10000

20000

30000

40000

50000

60000

70000

1980-1999

Time (days)

Str

eam

flow

(cu

mes

)

19

4 300 596 892 1188148417802076237226682964326035560

10000

20000

30000

40000

50000

60000

70000

1980-1989

Time (days)

Str

eam

flow

(cu

mec

s)

203 262 521 780 103912981557181620752334259328523111

0

10000

20000

30000

40000

50000

60000

70000

1990-1999

Time (days)

Str

eam

flow

(cu

mec

s)

21

22

Training Testing

Transfer function

Hidden Neurons

R2 RMSE Transfer function

Hidden Neurons

R2 RMSE

TANSIG

1 0.982 1496.001

TANSIG

1 0.984 1242.234

2 0.568 17698.154 2 0.59 18086.14

3 0.988 1212.973 3 0.989 1035.06

4 0.418 18998.347 4 0.478 19205.17

5 0.908 1520.735 5 0.958 2025.234

6 0.328 20221.132 6 0.358 22653.14

LOGSIG

1 0.982 1495.589

LOGSIG

1 0.985 1236.576

2 0.988 1217.794 2 0.989 1044.269

3 0.987 1185.740 3 0.989 1020.269

4 0.985 1220.235 4 0.989 1024.234

5 0.899 1622.786 5 0.989 1221.256

6 0.651 4231.124 6 0.979 1740.432

PURELIN

1 0.987 16014.26

PURELIN

1 0.988 16359.87

2 0.965 2121.192 2 0.971 1709.439

3 0.965 2121.199 3 0.971 1707.383

4 0.951 3112.256 4 0.961 1812.269

5 0.851 3314.453 5 0.961 2020.12

6 0.623 3412.431 6 0.961 2415.57

Table1. Details of 1 Day Lag Data

23

Training TestingTransfer function

Hidden Neurons

R2 RMSE Transfer function

Hidden Neurons

R2 RMSE

TANSIG

1 0.985 1373.054

TANSIG

1 0.987 1612.482

2 0.689 17782.041 2 0.702 24812.564

3 0.087 17216.041 3 0.268 25131.428

4 0.072 17216.115 4 0.258 26409.237

5 0.052 18508.786 5 0.203 30301.458

6 0.048 20201.639 6 0.155 40599.342

LOGSIG

1 0.985 1371.891

LOGSIG

1 0.987 1621.350

2 0.991 1051.939 2 0.991 1300.590

3 0.231 14329.328 3 0.194 20207.788

4 0.22 15333.134 4 0.184 21201.234

5 0.15 16789.326 5 0.155 25553.578

6 0.142 16600.348 6 0.155 25541.256

PURELIN

1 0.967 2060.171

PURELIN

1 0.972 2361.536

2 0.967 1058.066 2 0.973 2349.156

3 0.621 14760.164 3 0.634 21909.903

4 0.528 16785.223 4 0.588 24356.245

5 0.522 16987.254 5 0.535 26788.903

6 0.522 17001.235 6 0.501 30101.423

Table 2. Details of 2 Day Lag Data

24

Training TestingTransfer function

Hidden Neurons

R2 RMSE Transfer function

Hidden Neurons

R2 RMSE

TANSIG

1 0.985 1374.042

TANSIG

1 0.987 1137.619

2 0.022 17817.061 2 0.16 18252.136

3 0.346 9507.908 3 0.374 8261.156

4 0.018 20123.876 4 0.255 8344.231

5 0.258 9987.231 5 0.231 8557.254

6 0.016 22244.563 6 0.018 20867.231

LOGSIG

1 0.985 1373.682

LOGSIG

1 0.987 1147.415

2 0.976 1777.61 2 0.972 1796.500

3 0.991 1031.746 3 0.991 902.309

4 0.991 1031.876 4 0.972 1147.325

5 0.975 1182.432 5 0.887 1252.254

6 0.689 2217.237 6 0.865 1288.987

PURELIN

1 0.843 15808.829

PURELIN

1 0.85 16107.087

2 0.968 2051.830 2 0.972 1664.678

3 0.968 2050.582 3 0.972 1668.799

4 0.753 2231.342 4 0.785 2298.341

5 0.233 10113.452 5 0.685 3244.243

6 0.185 17722.237 6 0.553 3876.231

Table.3 Details of 3 Day Lag Data

25

1 2 3 4 5 6

Traning 0.982 0.568 0.988 0.418 0.908 0.328

Testing 0.984 0.59 0.989 0.478 0.958 0.358

0.1

0.3

0.5

0.7

0.9

1.1

1dl TANSIGR2

26

1 2 3 4 5 6

Training 0.982 0.988 0.987 0.985 0.899 0.651000000000

001

Testing 0.985 0.989 0.989 0.989 0.989 0.979

0.1

0.3

0.5

0.7

0.9

1.1

1dl LOGSIGR2

27

1 2 3 4 5 6

Training 0.987 0.965 0.965 0.951 0.851 0.623

Testing 0.988 0.971 0.971 0.961 0.961 0.961

0.1

0.3

0.5

0.7

0.9

1.1

1dl PURELINR2

28

1 2 3 4 5 6

Train-ing

1496.001 17698.154

1212.973 18998.347

1520.735 20221.132

Test-ing

1242.234 18086.14 1035.06 19205.17 2025.234 22653.14

2500

7500

12500

17500

22500

1dl TANSIGRM

SE

29

1 2 3 4 5 6

Train-ing

1495.589 1217.794 1185.74 1220.235 1622.786 4231.124

Test-ing

1236.576 1044.269 1020.269 1024.234 1221.256 1740.432

250

750

1250

1750

2250

2750

3250

3750

4250

1dl LOGSIGRM

SE

30

1 2 3 4 5 6

Train-ing

16014.26

2121.192

2121.199

3112.256

3314.453

3412.431

Test-ing

16359.87

1709.439

1707.383

1812.269

2020.12 2415.57

1000

3000

5000

7000

9000

11000

13000

15000

17000

1dl PURELINRM

SE

31

1 2 3 4 5 6

Training 0.985 0.689 0.087 0.072 0.052 0.048

Testing 0.987 0.702 0.268 0.258 0.203 0.155

0.05

0.15

0.25

0.35

0.45

0.55

0.65

0.75

0.85

0.95

2dl TANSIGR2

32

1 2 3 4 5 6

Training 0.985 0.991 0.231 0.22 0.15 0.142

Testing 0.987 0.991 0.194 0.184 0.155 0.155

0.05

0.15

0.25

0.35

0.45

0.55

0.65

0.75

0.85

0.95

2dl LOGSIGR

2

33

1 2 3 4 5 6

Training 0.967 0.967 0.621 0.528 0.522 0.522

Testing 0.972 0.973 0.634000000000001

0.588 0.535 0.501

0.050.150.250.350.450.550.650.750.850.95

2dl PURELINR

2

34

1 2 3 4 5 6

Train-ing

1373.054 17782.041

17216.041

17216.115

18508.786

20201.639

Test-ing

1612.482 24812.564

25131.428

26409.237

30301.458

40599.342

2500

7500

12500

17500

22500

27500

32500

37500

42500

2dl TANSIGR

MS

E

351 2 3 4 5 6

Training 1371.891 1051.939 14329.328 15333.134 16789.326 16600.348

Testing 1621.35 1300.59 20207.788 21201.234 25553.578 25541.256

2500

7500

12500

17500

22500

27500

2dl LOGSIGR

MS

E

36

1 2 3 4 5 6

Training

2060.171

1058.066

14760.164

16785.223

16987.254

17001.235

Test-ing

2361.536

2349.156

21909.903

24356.245

26788.903

30101.423

2500

7500

12500

17500

22500

27500

32500

2dl PURELINR

MS

E

37

1 2 3 4 5 6

Training 0.985 0.022 0.346 0.018 0.258 0.016

Testing 0.987 0.16 0.374 0.255 0.231 0.018

0.1

0.3

0.5

0.7

0.9

1.1

3dl TANSIGR2

38

1 2 3 4 5 6

Training 0.985 0.976 0.991 0.991 0.975 0.689

Testing 0.987 0.972 0.991 0.972 0.887 0.865

0.1

0.3

0.5

0.7

0.9

1.1

3dl LOGSIGR2

39

1 2 3 4 5 6

Training 0.843 0.968 0.968 0.753 0.233 0.185

Testing 0.85 0.972 0.972 0.785 0.685 0.553

0.1

0.3

0.5

0.7

0.9

1.1

3dl PURELINR2

40

1 2 3 4 5 6

Train-ing

1374.042

17817.061

9507.907999999

99

20123.876

9987.230999999

99

22244.563

Test-ing

1137.619

18252.136

8261.155999999

99

8344.230999999

99

8557.254

20867.231

2500

7500

12500

17500

22500

3dl TANSIGRM

SE

41

1 2 3 4 5 6

Train-ing

1373.682

1777.61 1031.746

1031.876

1182.432

2217.237

Test-ing

1147.415

1796.5 902.309 1147.325

1252.254

1288.987

250

750

1250

1750

2250

3dl LOGSIGRM

SE

42

1 2 3 4 5 6

Train-ing

15808.829

2051.83 2050.582

2231.342

10113.452

17722.237

Test-ing

16107.087

1664.678

1668.799

2298.341

3244.243

3876.231

10003000500070009000

1100013000150001700019000

3dl PURELINRM

SE

43

SOME TYPICAL SCATTERS

0 10000 20000 30000 40000 50000 600000

10000

20000

30000

40000

50000f(x) = 1.00168311671782 x − 156.429701466132R² = 0.984969086166063

1dl LS 1n

Observed (cumecs)

Pre

dic

ted

(cu

mec

s)

440 10000 20000 30000 40000 50000 60000

0

10000

20000

30000

40000

50000

60000

f(x) = 0.998606325863701 x + 36.3951065709443R² = 0.989059583751233

1dl LS 2n

Observed (cumecs)

Pre

dic

ted

(cu

mec

s)

450 10000 20000 30000 40000 50000 60000

0

10000

20000

30000

40000

50000

60000

f(x) = 0.992880272898286 x + 190.666717894135R² = 0.989510819234754

1dl LS 3n

Observed (cumecs)

Pre

dic

ted

(cu

mec

s)

460 10000 20000 30000 40000 50000 60000

0

1000

2000

3000

4000

5000

6000

7000

8000

f(x) = − 0.0735695374594739 x + 5737.2337795381R² = 0.590304968740329

1dl TS 2n

Observed (cumecs)

Pre

dic

ted

(cu

mec

s)

470 10000 20000 30000 40000 50000 60000 70000

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

f(x) = 0.0268024038212196 x + 3669.16835090227R² = 0.0874664306895823

2dl TS 3n tr

Observed (cumecs)

Pre

dic

ted

(cu

mec

s)

48

WORK TO BE DONE MAKING ANNs FOR LOG TRANSFORMED DATA

MAKING ANNs FOR REMAINING DATA SETS

CONSIDERING MODULAR APPROACH

CONSIDERING MANUALLY ALTERING WEIGHTS AND BIAS FOR ANNs

49

THANK YOU