vii
TABLE OF CONTENTS
CHAPTER
1
TITLE
PAGE NO.
TITLE
i
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENT
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
xii
LIST OF FIGURES
xiv
LIST OF SYMBOLS
xvii
LIST OF ABBREVIATIONS
xviii
INTRODUCTION
1.1
Introduction
1
1.2
Problem Statement
3
1.3
Objective
4
1.4
Scope of Study
4
viii
2
LITERATURE REVIEW
2.1
Introduction
6
2.2
System Identification
8
2.3
System Identification Procedures
11
2.4
Model Structure
11
2.4.1
ARMAX Model
12
2.4.2
NARMAX Model
12
2.5
Parametric Identification
13
2.5.1
Recursive Least Square
13
2.5.2
Genetic Algorithm
14
2.5.2.1
Differences between GA
and Traditional Methods
2.5.2.2
2.6
16
Population Representation
and Initialization
17
2.5.2.3
Fitness Functions
18
2.5.2.4
Selection
18
2.5.2.5
Crossover
19
2.5.2.6
Mutation
20
2.5.2.7
Termination Strategy
20
Nonparametric Identification
21
2.6.1
21
Artificial Neural Networks
2.6.1.1
Definition of Artificial
Neural Networks
2.6.1.2
The Structure of Neural
Networks (NNs)
2.6.1.3
2.6.1.4
2.6.3
22
23
Multi-layer Perceptron Neural
Networks
24
Elman Neural Network
26
Adaptive Neuro-Fuzzy Inference
System
2.6.3.1
28
ANFIS Architecture
29
ix
3
SYSTEM IDENTIFICATION APPROACHES
3.1
Introduction
34
3.2
Modeling
34
3.3
Model Structure
35
3.3.1 Parametric Model Structure
36
3.3.2 Nonparametric Model Structure
37
3.4
Parametric Model Estimation
38
3.4.1 Modeling Using Recursive Least
Square
3.5
38
3.4.2 Modeling Using Genetic algorithm
40
3.4.2.1 Control parameters of GA
42
Nonparametric model estimation
42
3.5.1 Modeling Using Multi-layer Perceptron
3.5.2
Neural Networks
43
Modeling Using Elman Neural Networks
45
3.5.3 Modeling Using Adaptive Neuro-Fuzzy
Inference System
3.6
4
46
Model Validation
47
3.6.1 One Step-Ahead Prediction
47
3.6.2 Mean Squared Error
48
3.6.3 Correlation Test
48
EXPERIMENTAL STUDY
4.1
Introduction
50
4.2
Data Acquisition System (DAQ)
50
4.2.1 Flow of Information in DAQ
52
Test Equipment
54
4.3.1 Rectangular Plate
54
4.3
x
4.3.2 Function Generator Type (TG1010A)
54
4.3.3 Amplifier Type (2706)
55
4.3.4 Electromagnetic Shaker
57
4.3.5 Piezo-beam Type Accelerometer
(Kistler-8636C5)
4.3.6 NI Compact-data Acquisition Unit
4.4
5
58
59
4.3.6.1 NI-9234 Module
60
4.3.7 Processer with LabVIEW
61
Experimental Setup
62
4.4.1
63
Experiment Procedure
IMPLEMENTATION AND RESULTS
5. 5.1
Experimental Results
64
5. 5.2
Modeling Using Recursive Least Square (RLS)
70
5 5.3
Modeling Using Genetic algorithm (GA)
73
5.4
Modeling Using Multilayer Perceptron Neural
Network (MLP-NN)
77
5.5
Modeling Using Elman Neural Network (ENN)
80
5.6
Modeling Using Adaptive Neuro-Fuzzy
5.7
Inference System (ANFIS)
83
Comparative Assessment and Discussion
87
5.7.1 RLS Performance
87
5.7.2 GA Performance
88
5.7.3 MLP-NN Performance
90
5.7.4 ENN Performance
91
5.7.5 ANFIS Performance
93
5.7.6 Overall comparison
94
xi
6
REFERENCES
CONLUSION AND FURTHER WORK
6.1
Conclusion
97
6.2
Further Work
98
99
xii
LIST OF TABLES
TABLE NO
TITLE
5.1
Plate specifications
5.2
First five natural frequencies of the plate
PAGE NO.
64
with C-C-C-C- boundary condition detected
at observation point
5.3
Performance of RLS with different numbers of
model order
5.4
92
Performance of ENN with different model
structures
5.11
91
Performance of ENN with different numbers of
model order
5.10
90
Performance of MLP-NN with different model
structure
5.9
89
Performance of MLP-NN with different numbers
of model order
5.8
88
Performance of GA with different numbers of
population size
5.7
88
Performance of GA with different numbers of
generation
5.6
87
Performance of RLS with different numbers of
forgetting factor
5.5
67
92
Performance of ANFIS with different number of
membership function for model order 2
93
xiii
5.12
Performance of ANFIS with different number of
membership function for model order 4
5.13
94
summary of the best Performance achieved in
parametric and nonparametric modelling
96
xiv
LIST OF FIGURES
FIGURE NO
TITLE
PAGE NO.
1.1
The flow chart of the project
5
2.1
Schematic of ARMAX model
12
2.2
Working principle of GA
15
2.3
Schematic of how artificial neural networks work
22
2.4
Connectives within a node
23
2.5
Multiple layers of feedfoward neural network
25
2.6
Structure of the ENN Model
27
2.7
ANFIS process
29
2.8
Type-3 fuzzy reasoning
30
2.9
Structure of type-3 ANFIS
30
3.1
System Identification procedure
35
3.2
Schematic of ARX model
36
3.3
Diagrammatic representation of the RLS algorithm
40
3.4
Diagrammatic representation of the GA algorithm
41
3.5
Diagrammatic representation of the MLP-NN algorithm
43
3.6
Diagrammatic representation of the ENN algorithm
45
3.7
Diagrammatic representation of the ANFIS algorithm
46
4.1
Block diagram of data acquisition system
51
4.2
Experimental setup layout
53
xv
4.3
Function generator of type (TG1010A)
55
4.4
Amplifier type (2706)
56
4.5
Electromagnetic shaker
57
4.6
Piezo-beam type accelerometer (Kistler-8636C5)
59
4.7
NI compact-data acquisition unit
60
4.8
NI-9234 module
61
4.9
Processer with LabVIEW
62
4.10
Experimental setup
62
5.1
Schematic of the plate with all edges clamped
boundary conditions
65
5.2
Input force applied at point x=0.25𝑎 m and y=0.25𝑏 m
66
5.3
Lateral deflection detected at x=0.75a, and y=0.75b
in time domain
5.4
Lateral deflection detected at x=0.75a, and y=0.75b
in frequency domain
5.5
68
Lateral deflection detected at x=0.75a, and
y=0.75b point ( Y )
5.7
67
Schematic of the plate with all edges clamped boundary
conditions for the development of AVC
5.6
66
69
Lateral deflection detected at x=0.75a, and y =0.25b
point ( Z )
69
5.8
Actual and predicted RLS output
71
5.9
Error between actual and predicted RLS output
71
5.10
Correlation tests of RLS
72
5.11
Actual and predicted GA output
74
5.12
Error between actual and predicted GA output
75
5.13
The best and mean fitness values in each generation
75
5.14
Correlation tests of GA
76
5.15
Actual and predicted MLP-NN output
77
5.16
Error between actual and predicted NLP-NN output
78
5.17
Mean-squared error vs. number of training passes
78
5.18
Correlation tests of MLP-NN
79
5.19
Actual and predicted ENN output
80
xvi
5.20
Error between actual and predicted ENN output
81
5.21
Mean-squared error vs. number of training passes
81
5.22
Correlation tests of ENN
82
5.23
Initial membership functions of the input variable
83
5.24
Final membership functions of the input variable
84
5.25
Actual and predicted ANFIS output
84
5.26
Error between actual and predicted ANFIS output
85
5.27
Correlation tests of ANFIS
86
xvii
LIST OF SYMBOLS
A z −1
Polynomials parameters of autoregressive
B z −1
Polynomials parameters of exogenous
C z −1
Polynomials parameters of moving average
𝑦(𝑘)
System output at time sample k
𝑢 𝑘
System input at time sample k
𝜉 𝑘
White noise at time sample k
𝑦
𝑛𝑦 , 𝑛𝑢 ,𝑛𝑒
Pc
Estimation output at time t
Model orders
Crossover probability
𝑃1 , 𝑃2
GA parents strings
𝑂1 , 𝑂2
GA offspring strings
𝐴𝑖 , 𝐵𝑖
Linguistic label of ANFIS structure
𝑧 −1
𝜆
𝜙𝑢𝑒 𝜏
𝑂𝑘 , 𝑂𝑗 , 𝑂𝑖
𝑤𝑘𝑗
𝑤𝑗𝑖
Back-shift operator
Forgetting factor
Cross-correlation function between u(t ) and e (t)
Output values at the output, hidden and input layers
Connection weight from unit j at the hidden layer to unit k at
the output layer
Connection weight from unit i at the input layer to unit j at the
hidden layer
𝛼
Momentum factor
𝜂
Learning rate
δk
The error signal from the NN output to the hidden layer
δj
The error signal from the hidden layer to the input layer
xviii
LIST OF ABBREVIATIONS
RLS
Recursive Least Square
GA
Genetic Algorithm
MLP-NN
Multi-layer Perceptron Neural Networks
ENN
Elman Neural Networks
ANFIS
Adaptive Neuro-Fuzzy Inference System
NI
National Instrumentation
OSA
One step ahead
MSE
Mean squared error
NNs
Neural networks
TRMS
Twin rotor multi-input multi-output system
FD
Finite Difference
ARMAX
Autoregressive moving average model with exogenous inputs
NARMAX
Non-linear autoregressive moving average model with
exogenous inputs
ARX
Auto Regressive with exogenous inputs
NARX
Non-linear Auto Regressive with exogenous inputs
FL
Fuzzy Logic
RBF
Radial-Basis Function
BP
Backpropagation
RNNs
Recurrent Neural Networks
FIS
Fuzzy Inference System
SISO
Single-Input Single-Output
DAQ
Data Acquisition System
xix
A/D
An analog to digital converter
D/A
Digital to an analog converter