time series flow forecasting using artificial neural networks for brahmaputra river
DESCRIPTION
TRANSCRIPT
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