Wavelet decomposition in predicting
suspended sediment transport rate
Yousef Hassanzadeh
Mohammad Amir Rahmani
Peyman Yousefi
Department of Civil Engineering, University of Tabriz, Tabriz, Iran
1
[email protected]
[email protected]
[email protected]
2
Introduction
Importance of sediment transport rate prediction in
engineering
Most hydrometric station are newly accomplished
Estimating dead volume of reservoirs and sediment
entered to them
3
Time- and cost-consuming procedure of measuring
4
Data-driven methods
Data-driven methods
M5 tree model
Artificial neural networks (ANN)
5
Gene expression programming (GEP)
M5 Tree model
An alternative to linear regression
6
Splitting data into subsets and fitting a linear equation to
each subset
Artificial neural networks (ANN)
Inspired by the neural structure of the human brain
7
Extract the patterns between input and output data
through training a network
8
Artificial neural networks (ANN)
Gene expression programming (GEP)
GA (Holland, 1960
1 st
100101011001001
2nd
110110010111001
GP (Cromer,1985)
î
1
X
x2 1
X
GEP (Frierra,1999)
Q
î
a
b
c
d
a b u c d 9
+
Wavelets
Time and
Frequency
Resolution
Wavelets
More
Functions
11
High
Accuracy
Wavelets
Convert a signal into a series of wavelets
Provide a way for analyzing waveforms, bounded in
both frequency and duration
Allow signals to be stored more efficiently than by
Fourier transform
Be able to better approximate real-world signals
12
Well-suited for approximating data with sharp
discontinuities
Wavelet decomposition
2
1
Original time-series
0
0
50
100
150
200
0,5
Approximation
0
0
50
100
150
0
50
100
150
200
0,5
Detail 1
0
200
-0,5
0,5
0
0
50
100
150
200
0
50
100
150
200
Detail 2
-0,5
0,5
0
Detail 3
13
-0,5
Hybrid models
Daily data of discharge and suspended sediment
transport rate, Mississippi River, USA.
Design1: S(t+1)=f(Q(t))
Design2: S(t+1)=f(Q(t), S(t))
14
Design3: S(t+1)=f(Q(t-1), Q(t), S(t-1), S(t-1))
Results (non-decpmposed inputs)
Training
0.469
552664
0.982
89602
0.980
88299
0.352
463400
0.960
128780
0.981
87863
0.693
370139
0.982
87428
0.988
72132
Verification
0.530
541605
0.979
48753
0.979
48211
0.384
347500
0.955
189111
0.980
47582
0.534
608536
0.980
46953
0.982
45424
15
M5
ANN
GEP
Model Design Fitness
R2
1
RMSE
R2
2
RMSE
R2
3
RMSE
R2
1
RMSE
R2
2
RMSE
R2
3
RMSE
R2
1
RMSE
R2
2
RMSE
R2
3
RMSE
Results (wavelet decomposed inputs)
Training
0.678
400510
0.995
57869
0.993
57027
0.681
378303
0.960
51512
0.995
49620
0.910
200281
0.988
61306
0.994
50580
Verification
0.551
536607
0.991
32078
0.991
32345
0.568
575548
0.966
53109
0.991
33407
0.405
779050
0.988
33739
0.990
32640
16
WAVE - M5 WAVE » ANN WAVE » GEP
Model Design Fitness
R2
1
RMSE
R2
2
RMSE
R2
3
RMSE
R2
1
RMSE
R2
2
RMSE
R2
3
RMSE
R2
1
RMSE
R2
2
RMSE
R2
3
RMSE
(Improvements in methods by wavelet)
Method
Design
Design 1
Absolute
Relative
improvement improvement
in R2 (%)
in RMSE (%)
0.922813
0.021
Wave-GEP Design 2
34.20302
0.012
Design 3
32.9095
0.012
Design 1
-65.6253
0.184
Wave-ANN Design 2
71.91649
0.011
Design 3
29.79068
0.011
Design 1
-28.0204
-0.129
Design 2
28.14304
0.008
Design 3
28.14371
0.008
Wave-M5
17
Results
Results
(Improvements in methods by wavelet)
ANN-Design 3
2000000
1500000
Observe
1000000
ANN
500000
0
1
201
401
601
801
1001
1201
1401
1601
1801
Day
18
Sediment transport rate (ton/day)
2500000
Results
(Improvements in methods by wavelet)
Wave-ANN-Design 3
2000000
1500000
Observe
1000000
Wave-ANN
500000
0
1
201
401
601
801
1001
1201
1401
1601
1801
Day
19
Sediment transport rate (ton/day)
2500000
Results
(Improvements in methods by wavelet)
GEP-Design 3
2000000
1500000
Observe
1000000
GP
500000
0
1
201
401
601
801
1001
1201
1401
1601
1801
Day
20
Sediment transport rate (ton/day)
2500000
Results
(Improvements in methods by wavelet)
Wave-GEP-Design 3
2000000
1500000
Observe
1000000
Wave-GEP
500000
0
1
201
401
601
801
1001
1201
1401
1601
1801
Day
21
Sediment transport rate (ton/day)
2500000
Results
(Improvements in methods by wavelet)
M5-Design 3
2000000
1500000
Observe
1000000
M5
500000
0
1
201
401
601
801
1001
1201
1401
1601
1801
Day
22
Sediment transport rate (ton/day)
2500000
Results
(Improvements in methods by wavelet)
Wave-M5-Design 3
2000000
1500000
Observe
1000000
Wave-M5
500000
0
1
201
401
601
801
1001
1201
1401
1601
1801
Day
23
Sediment transport rate (ton/day)
2500000
Conclusions
Data-driven techniques have sufficient performance in
predicting SSTR in Design 2 and 3.
Wavelet improves performances of data-driven
techniques.
Wavelets improves performances of Design 1 most.
Hybrid models of Design 2 and 3 do not have
priority to each other BY R2 and RMSE measures.
24
Hybrid model of Wavelet-M5 predicts peak rates
better.