matric no.: 4580 has been read and certified by of hydraulic jump using artificial neural...
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Final Year Project Report below:
Title : Length of Hydraulic Jump Using Artificial Neural Network
Author : Boon Chun Wui
Matric No.: 4580
has been read and certified by:
t' ý'
_ T
(Assoc. Prof. Dr. Nabil Bessaih) Date Supervisor
Y'usat Khiclmat Makiurnat Akaslenm ÜNIVE Il;; {'1'' MALAYSIA SARAVAE
P. KHIDMATMAKLUMATAKADEMIK U N IMAS
NIIIIIIIIIIIýIIIIIIIIII 1000125787
LENGTH OF HYDRAULIC JUMP USING ARTIFICIAL NEURAL NETWORK
BOON CHUN WUI
This project is submitted in partial fulfilment of the requirements for the degree of Bachelor of Engineering with Honours
(Civil Engineering)
Faculty of Engineering UNIVERSITI MALAYSIA SARAWAK
2004
Acknowledgement
I owe much to my Final Year Project supervisor, Assc. Prof. Dr Nabil
Bessaih for his valuable time in guiding me from the commence to the end of this
project. My thanks also go to UNIMAS lectures who guided me in the process of
pursuing engineering knowledge and skills along my Bachelor degree course. The
engineering knowledge and skills I gained have been fully utilized in the
preparation of this project.
Finally, I owe many thanks to my family and friends for their constant
support and encouragement.
i
Abstract
A relatively new tool, artificial neural network (ANN), was applied to
simulate the relative length of hydraulic jump of the Natural stilling basin with
horizontal floor (Basin 1). A set of data which was obtain from previous research
were used as the input and target to train the neural networks. The trained model
was used to generate the relative length of jump (L/D2). Different combinations of
variables and parameters have been tested on 2 different networks (Feedforward
Backpropagation and Recurrent) to find the best result by using Regression
Analysis.
Coefficient of Regression, R2 is the indicator of how good fit of the
simulated L/D2 compare to the recommended curve. Feedforward Backpropagation
Networks (R2=0.789) and Recurrent Networks (R2=0.825) can produce the relative
length of the jump (L/D2) with better accuracy than the recommended curve
(R`=0.782).
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Abstrak
Sebagai salah satu kaedah yang baru, " Artificial Neural Network (ANN)",
digunakan untuk meramal panjang sesuatu lompatan hidraulik bagi suatu kawasan
tadahan semula jadi dengan dasar yang mendatar ("Basin 1"). Satu set data yang
diperolehi daripada penyelidikan dahulu telah digunakan sebagai input dan sasaran
untuk kalibrasian rangkaian. Model kalibrasi yang digunakan untuk menghasilkan
panjang lompatan (L/D, ). Kombinasi pembolehubah dan parameter yang berbeza
telah diuji melalui pengunaan 2 rangkaian berbeza (Feedforward Backpropagation
dan Recurrent) untuk mendapat keputusan yang terbaik dengan menggunakan
"Regression Analysis".
"Coefficient of Regression", R2 ialah penunjuk yang menunjukkan betapa
sesuainya L/D, yang dihasilkan berbanding dengan lengkungan yqng disyorkan.
Rangkaian Feedforward Backpropagation (R2=0.789) dan Rangkaian Recurrent
(R2=0.825) dapat menghasilkan panjang lompatan relatif dengan lebih tepat
berbanding dengan lengkungan yang disyorkan (R`'=0.782).
III
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Table of Content Acknowledgement
Abstract ii
Abstrak i i i
Table of Content iv
List of Figures vi
List of Tables vii
List of Appendix viii
Topic 1 Introduction
1.1 Background
1.2 Artificial Neural Networks 3
1.3 Project Objective 4
Topic 2 Literature Review 5
2.1 Hydraulic Jump 5
2.2 Types of jump 6
2.3 Length of hydraulic jump 8
2.4 Artificial Neural Networks 9
2.5 The Artificial Neuron 10
2.6 Layers 12
2.7 Communication and types of connections 13
2.8 Inter-layer connections 14
2.8.1 Feedforward 15
iv
2.9 Intra-layer connections
2.9.1 Elman Network
2.10 Learning
2.11 Learning laws
2.12 Neural Network For hydrology analysis
Topic 3 Methodology
3.1 Training of ANN
3.2 Data Structure
3.3 Type of Network Used
3.4 Software Used
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V
Page
Topic 4 Result And Discussion 33
4.1 Introduction 33
4.2 Number Of Neurons In The Hidden Layer 33
4.2.1 Influence of training algorithm on number of 35 neurons for BP
4.2.2 Influence of training algorithm on number of neurons for Recurrent Network 38
4.3 Training Styles 42
4.4 Learning rates 47
4.5 Epoch 49
4.5.1.1 Influence of epoch in MSE for BP Networks 50
4.5.1.2 Influence of epoch in MSE for Recurrent Networks (Elman Networks) 51
4.5.2.1 Influence of epoch in R2(Training) for BP Networks 52
4.5.2.2 Influence of epoch in R2(Training) for recurrent Networks (Elman Networks) 53
4.5.3.1 Influence of epoch in R2(Testing) for BP Networks 54
4.5.3.2 Influence of epoch in R2(Testing) for Recurrent Networks 55
Topic 5 Conclusion And Suggestion 57
5.1 Conclusion 57
5.2 Suggestion For Future Research 58
vi
Reference 59
Appendix 60
List of Figures
Figure 1.1 Length of jump in terms of D2 (Basin I)
Figure 2.1 Hydraulic jump
Figure 2.2 Length of jump in terms of sequent depth D2 of jumps
Figure 2.3 Artificial Neuron
Figure 2.4 Different layers in Neuron Network
Figure 2.5 Example of 2-layer tansig / purelin Feedforward neural network
Figure 2.6 Elman Network
Figure 2.7 Observed and Computed Discharge Using Curve Fitting and ANN-Jamtara Site by S. K. Jain and D. Chalisgaonkar (2000)
Figure 2.8 Fitting Loop Rating Curve Using ANN
Figure 4.1
Figure 4.2
Figure 4.3
Performance of Neuron Networks in MSE, R2 (training), R2 (testing) in trainrp for BP
Page
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6
9
II
12
15
18
25
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35
Performance of Neuron Networks in MSE, R2 (training), R` (testing) in trainscg for BP 36
Performance of Neuron Networks in MSE, R` (training), R` (testing) in trainoss for BP 37
vii
Figure 4.4
Figure 4.5
Figure 4.6
Figure 4.7
Figure 4.8
Figure 4.9
Figure 4.10
Figure 4.1 1
Figure 4.12
Figure 4.13
Figure 4.14
Figure 4.15
Figure 4.16
Figure 4.17
Performance of Neuron Networks in MSE, R` (training), R2 (testing) in trainrp for RC
Performance of Neuron Networks in MSE, R 2 (training), R2 (testing) in trainscg for RC
Performance of Neuron Networks in MSE, R` (training), R2 (testing) in trainoss for RC
Simulation of length of jump using BP Networks with trainrp, trainscg, trainoss algorithm compare with the observed length of jump and the recommended curve.
Simulation of length of jump using Recurrent Networks with , trainscg, trainoss algorithm compare with the observed length of jump and the recommended curve.
Simulation of length of jump using BP Networks and Recurrent Network(RC) with trainrp method compare with the observed relative length of jump and recommended curve.
Performance of neural networks according to learning rate using trainrp in BP Network
Performance of neural networks according to learning rate using trainrp in Recurrent Networks (Elman Networks)
Influence of epoch
Influence of epoch
Influence of epoch
Influence of epoch
Influence of epoch
Influence of epoch
in MSE (BP)
in MSE (RC)
in R`' (Training)(BP)
in R'` (Training)(RC)
in R2 (Testing)(BP)
in R`(Testing)(RC)
VIII
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List of Tables
Table 3.1 Data Structure
Table 4.1 Number of neurons needed (Optimum) according to training algorithm
Table 4.2 Performance of neural networks according to learning rate using trainrp in BP Network.
Table 4.3 Performance of neural networks according to learning rate using trainrp in Recurrent Networks (Elman Networks).
List of Appendixes
Page
29
41
47
49
Appendix A Performance of neural networks using BP Network 60
Appendix B Performance of neural networks using Recurrent 69 Network
IX
Topic 1
Introduction
1.1 Background
The Length of hydraulic jump is defined as the distance measured from the
front face of the jump to a point on the surface immediately downstream from the
roller. This length has been investigated experimentally by many hydraulicians. The
best known and most widely accepted curve for length of jump is that of
Bokhmeteff and Matzke (curve 1 in Figure 1.1) which was determined from
experiment made at Columbia University at 1936.
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Figure 1.1 Length of jump in terms of D2 (Basin 1)
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A general investigation of the hydraulic jump on horizontal aprons (Basin
1) has been carried out. It was done in all six test flumes (A, B, C, D, E, F) which
involved about 125 tests for discharges of I to 28 c. f. s. However, the length of
jump obtained from the two smaller flumes, A and F, was consistently shorter than
that observed for the larger flumes. It was found that results form Flume F,
contained 3 points which are given the symbol ® and fall short of the
recommended curve as shown in the figure 1. 1. Besides, a lot of the data (dots) are
also tabulated away and quite far from the recommended line as shown in the figure
2
l. l. Therefore, other approach has to be used to improve the prediction of the
length of jump.
1.2 Artificial Neural Networks (ANNs)
Attempts have been made to develop a technique that that can solve the
problem of modeling. One such technique is known as neurocomputing, and the
networks laid out with many parallel processing elements to do this
neurocomputing are called artificial neural networks (ANNs). The ANNs try to
mimic the functioning of the human brain, which contains billions of neurons and
their interconnections. The human brain is able to rapidly recognize patterns and
learn from past experiences.
The potential of ANNs as a modeling tool for stage and discharge
relationship in developing a rating curve is presented in S. K. Jain and D.
Chalisgaonkar (2000). Based on the efficiency of their research, this project tries to
investigate capability of ANN to improve the curve for length of hydraulic jump.
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1.3 Objective
The objective of this project is to produce an ANN to give the relative
length of the jump (L/D2) with better accuracy than the recommended curve shown
in Figure I. 1.
4
Topic 2
Literature Review
2.1 Hydraulic jump
The hydraulic jump was first investigated experimentally by Bidone in
1818. This led Belanger (1828) to distinguish between subcritical and supercritical
slopes, since he had observed that in steep channels hydraulic jump is frequently
produced by a barrier in originally uniform flow. Thereafter, a lot of researches
were made and the results were quoted by many writers. Outstanding contributors
were Bresse (1860), Gibson (1913), Smetana (1934), Bakhmeteff and Matzke
(1936), Nebbia (1940), Forster and Skrinde (1950) and others.
A hydraulic jump is formed whenever flow changes from supercritical flow
to subcritical flow. In this transition from supercritical to subcritical flow, water
surface rises abruptly, surface rollers are formed, intense mixing occurs, air is
entrained, and a large amount of energy is usually dissipated. The Figure 2.1 as
5
shown below show the hydraulic jump. The V;, is the velocity at initial depth, y,
while the V0 is the velocity at Sequent depth, Y2-
- - - - - - - - - - - - - - - -
i - i Y2 V out
- - --- - - - - - - - -
Figure 2. l Hydraulic jump
The practical applications of hydraulic jump are many. It can he used to
dissipate energy in water flowing over dams, weirs, and other hydraulic structures
and thus prevent scouring. It also can be used to recover head or raise the water
level on the downstream side of a measuring flume and thus maintain high water
level in the channel for irrigation or water distribution systems. Sometime it is also
used for mixing chemicals used for water purification and aerates water for city
water supplies.
2.2 Types of jump
Hydraulic jumps on horizontal floor are of several distinct types. According
to studies of the U. S Bureau of Reclamation, these types can be conveniently
classified according to the Froude number F, of the coming flow as follows:
6
For F1 = I, the flow is critical, and hence no jump can form.
For F, = I to 1.7, the water surface shows undulations, and the jump is
called an undular jump.
For F, = 1.7 to 2.5, a series of small rollers develop on the surface of the
jump, but the downstream water surface remains smooth. The velocity throughout
is fairly uniform, and the energy loss is low. This jump may called a weak jump.
For F, = 2.5 to 4.5, there is an oscillating jet entering the jump bottom to
surface and back again with no periodicity. Each oscillation produces a large wave
of irregular period which, very commonly in canals, can travel for miles doing
unlimited damage to earth banks and ripraps. This jump may be called an
oscillating jump.
For F1 = 4.5 to 9.0, the downstream extremity of the surface roller and the
point at which the high-velocity jet tends to leave the flow occur at practically the
same vertical section, the action and position of this jump are least sensitive to
variation in tailwater depth. The jump is well-balanced and the performance is at its
best. The energy dissipation ranges from 45 to 70 %. This jump may be called a
steady jump.
7
For F1 = and larger. the high-velocity jet grabs intermittent slugs of water
rolling down the front face of the jump, generating waves downstream, and a rough
surface can prevail. The jump action is rough but effective since the energy
dissipation may reach 85%. This jump may be called a strong jump.
2.3 Length of hydraulic jump
The length of the jump is the distance measured from the front face of the
jump to a point on the surface immediately downstream from the roller.
The length of a jump is needed to select the apron length and height of the
side walls of a stilling basin. To determine the length of a jump during laboratory
investigations, it is difficult to mark the beginning and the end of a. jump because of
highly turbulent flow surface, formation of rollers and eddies, and air entrainment.
In addition, the surface disturbances are of random nature, and the time-averaged
quantities may not always give consistent results. The length of the roller may be
taken to the point where the flow velocity at the top reverses and the jet continues.
The experimental data on length of. jump can be plotted with the Froude
number F against a dimensionless ratio f., /D,, L/D,. The plot of F, vs 111), is
probably the best, for the resulting curve can best defined by the data. For practical
purposes, however, the plot of F, vs L/D, is desirable, because the resulting curve
8
shows regularity or a fairly flat portion for the range of well-established jumps. The
Figure 2.2 shows the length of hydraulic jump.
5
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2.4 Artificial Neural Networks (ANN)
S.
Artificial Neural Network is a system loosely modeled on the human brain.
The field goes by many names, such as connectionism, parallel distributed
processing, neuro-computing, natural intelligent systems, machine learning
algorithms, and artificial neural networks. It is an attempt to simulate within
9
specialized hardware or sophisticated software, the multiple layers of simple
processing elements called neurons. Each neuron is linked to certain of its
neighbors with varying coefficients of connectivity that represent the strengths of
these connections. Learning is accomplished by adjusting these strengths to cause
the overall network to output appropriate results.
2.5 The Artificial Neuron
The basic unit of neural networks, the artificial neurons, simulates the four
basic functions of natural neurons. Artificial neurons are much simpler than the
biological neuron; the figure below shows the basics of an artificial neuron.
1= Z w x i Summation
Y = f(I) Transferxo
Transfer
2.3 Artificial Neuron
10
Note that various inputs to the network are represented by the mathematical
symbol, x(n). Each of these inputs are multiplied by a connection weight, these
weights are represented by w(n). In the simplest case, these products are simply
summed, fed through a transfer function to generate a result, and then output.
Even though all artificial neural networks are constructed from this basic
building block the fundamentals may vary in these building blocks and there are
differences.
2.6 Layers
Biologically, neural networks are constructed in a three dimensional way
from microscopic components. These neurons seem capable of nearly unrestricted
interconnections. This is not true in any man-made network. Artificial neural
networks are the simple clustering of the primitive artificial neurons. This
clustering occurs by creating layers, which are then connected to one another. I low
these layers connect may also vary. Basically, all artificial neural networks have a
similar structure of topology. Some of the neurons interface the real world to
I I
receive its inputs and other neurons provide the real world with the network's
outputs. All the rest of the neurons are hidden form view.
HIDDEN LAYER (there may be several
hidden layers)
Figure 2.4 Different layers in Neuron Network
As the 2.4 above shows, the neurons are grouped into layers The input
layer consist of neurons that receive input form the external environment. The
output layer consists of neurons that communicate the output of the system to the
user or external environment. There are usually a number of hidden ! ayers between
these two layers; the 2.4 above shows a simple structure with only one hidden
layer.
When the input layer receives the input its neurons produce output. which
becomes input to the other layers of the system. The process continues until a
certain condition is satisfied or until the output layer is invoked and tires their
output to the external environment.
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To determine the number of hidden neurons the network should have to
perform its best, one are often left out to the method trial and error. If increase the
hidden number of neurons too much it will be over fitted that is the net will have
problem to generalize. The training set of data will be memorized, making the
network useless on new data sets.
2.7 Communication and types of connections
Neurons are connected via a network of paths carrying the output of one
neuron as input to another neuron. These paths is normally unidirectional, there
might however be a two-way connection between two neurons, because there may
be an another path in reverse direction. A neuron receives input from many
neurons, but produce a single output, which is communicated to other neurons.
The neuron in a layer may communicate with each other, or they may not
have any connections. The neurons of one layer are always connected to the
neurons of at least another layer.
2.8 Inter-layer connections
There are different types of connections used between layers, these
connections between layers are called inter-layer connections.
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