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).

I

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

16

17

18

20

23

27

27

29

31

32

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

7

6

9

II

12

15

18

25

26

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

38

39

40

43

44

45

47

48

50

51

52

53

54

55

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.

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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.

12

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.

13