10
TABLE OF CONTENTS
CHAPTER
1
TITLE
PAGE
TITLE
i
DECLARATION
ii
ACKNOWLEDGEMENTS
iii
ABSTRACT
iv
ABSTRAK
v
TABLE OF CONTENTS
vi
LIST OF FIGURES
xii
LIST OF TABLES
xvii
LIST OF SYMBOLS
xxi
LIST OF APPENDICES
xxv
INTRODUCTION
1.1 Introduction
1
1.2 Research Background
1
1.3 Brief History of Oil Palm Industry in Malaysia
3
1.4 Problem Descriptions
7
1.5 Research Objectives
8
1.6 Scope of The Study
9
1.6.1 Data Scope
9
1.6.2 Model Scope
11
1.6.3 Statistical Testing Scope
12
1.7 Data Gathering
13
1.8 Leaf Analysis
14
1.9 Research Importance
17
1.10 Research Contribution
18
1.11 Thesis Organisation
19
11
2
REVIEW OF THE LITERATURE
2.1 Introduction
21
2.2 Oil Palm Yield Modelling
21
2.3 Nonlinear Growth Model
27
2.4 Application of Neural Network Modelling
30
2.4.1 Neural Network in Science and Technology
31
2.4.2 Neural Network in Economy
32
2.4.3 Neural Network in Environmental and
34
Health
35
2.4.4 Neural Network in Agriculture
2.5 Response Surface Analysis
2.6
3
37
38
Summary
RESEARCH METHODOLOGY
3.1 Introduction
43
3.2 Data Analysis
43
3.3 Modelling
45
3.3.1 Nonlinear Growth Models
3.3.1.1 Nonlinear Methodology
3.3.2 Regression Analysis
3.3.2.1 Least Squares Method
45
47
51
51
3.3.3 Robust M-Regression
53
3.3.4 Neural Networks Model
55
3.3.4.1 Introduction to Neural Network
56
3.3.4.2 Fundamentals of Neural Network
57
3.3.4.3 Processing Unit
58
3.3.4.4 Combination Function
58
3.3.4.5 Activation Function
59
3.3.4.6 Network Topologies
62
12
3.3.4.7 Network Learning
64
3.3.4.8 Objective Function
65
3.3.4.9 Basic Architecture of Feed-Forward
Neural Network
3.3.5 Response Surface Analysis
66
72
3.3.5.1 Introduction
73
3.3.5.2 Response Surface: First Order
73
3.3.5.3 Response Surface: Second Order
76
3.3.5.4 Stationary Point
77
3.3.5.5 Ridge Analysis
79
3.3.5.6 Estimate the standard error of
predicted response
3.4 Summary
4
80
81
MODELLING OIL PALM YIELD GROWTH
USING NONLINEAR GROWTH MODEL
4.1 Introduction
4.2 The Nonlinear Model
4.3 The Method of Estimation
4.4 Partial Derivatives for The Nonlinear Models
4.5 Results and Discussion
4.6 Conclusion
5
MODELLING OIL PALM YIELD USING
MULTIPLE LINEAR REGRESSION AND
ROBUST M-REGRESSION
5.1 Introduction
82
84
85
87
93
104
13
5.2 Model Development
105
5.3 Results and Discussion
105
5.3.1 Multiple Linear Regression
107
5.3.2 Residual Analysis for MLR
107
5.3.3 Robust M-Regression
110
5.3.4 Residual Analysis for RMR
115
5.4 Conclusion
116
119
6
NEURAL NETWORK MODEL FOR OIL PALM
YIELD
6.1 Introduction
122
6.2 Neural Network Procedure
123
6.2.1 Data Preparation
123
6.2.2 Calculating Degree of Freedom
124
6.3 Computer Application
125
6.4 Experimental Design for Neural Network
129
6.4.1 Experiment 1
131
6.4.2 Experiment 2
131
6.4.3 Experiment 3
132
6.5 Results and Discussion
133
6.5.1 Statistical Analysis
133
6.5.2 Neural Network Performance
138
6.5.3 Residual Analysis
146
6.5.4 Results of Experiment 1
149
6.5.5 Results of Experiment 2
149
6.5.6 Results of Experiment 3
149
6.6 Comparative Study on Oil Palm Yield Modelling
155
6.7 Conclusion
167
14
7
THE APPLICATION OF RESPONSE SURFACE
ANALYSIS IN MODELLING OIL PALM YIELD
7.1 Introduction
7.2 Response Surface Analysis
7.3 Data Analysis
7.4 Numerical Analysis
7.4.1 Canonical Analysis for Fertilizer Treatments
7.4.2 Ridge Analysis for Fertilizer Treatments
7.5 Economic Analysis
7.5.1 Profit Analysis
7.6 Conclusion
8
169
169
172
173
174
179
186
187
195
SUMMARY AND CONCLUSION
8.1 Introduction
196
8.2 Results and Discussion
196
8.2.1 Initial Exploratory Study
197
8.2.2 Modelling Using Neural Network
201
8.2.3 Modelling Using Response Surface Analysis
208
8.3 Conclusion
211
8.4 Areas for Further Research
211
REFERENCES
214
Appendices A - U
231
15
LIST OF TABLES
TITLE
TABLE NO.
1.1
PAGE
The optimum value of nutrient balance ratio, NBR for
foliar analysis
17
2.1
The summary of the literature reviews in this study
39
3.1
Nonlinear mathematical models considered in the study
50
3.2
Summary of the data set types and research approaches
considers in this study
4.1
Partial derivatives of the Logistic and Gompertz and von
Bertalanffy growth models
4.2
4.4
87
Partial derivatives of the Negative exponential,
Monomolecular, log-logistic and Richard’s growth models
4.3
81
88
Partial derivatives of the Weibull, Schnute and MorganMercer-Flodin growth models
89
Partial derivatives of the Champan-Richard and Stannard
90
growth models
4.5
Parameter estimates of the logistic, Gompertz, negative
exponential, monomolecular, log-logistic, Richard’s and
Weibull growth models for yield-age relationship
94
16
4.6
Parameter estimates of the MMF, von Bertalanffy,
Chapman-Richard and Stannard growth models for yieldage relationship
4.7
Asymptotic correlation for each nonlinear growth models
fitted
4.8
95
96
The actual and predicted values of FFB yield, the
associated measurement error and correlation coefficient
between the actual and predicted values for Logistic ,
Gompertz, von Bertalanffy, negative exponential, mono
molecular and log-logistic growth models
4.9
98
The actual and predicted values of FFB yield, the
associated measurement error and correlation coefficient
between the actual and predicted values for Richard’s ,
Weibull, MMF, Chapman-Richard, Chapman-Richard*
(with initial) and Stannard growth models
4.10
99
The parameter estimates an asymptotic correlation for von
Bertalanffy and Chapman-Richard when an initial growth
response data point is added
4.11
The number of iteration and the root mean squares error for
nonlinear growth models consider in this study
5.1
119
The regression equation for the inland and coastal station
using MNC and NBR as independent variables
5.3
104
The regression equations and R2 values for the inland and
coastal areas
5.2
103
Regression equation using robust M-regression for the
114
17
inland and coastal areas
6.1
The F statistics value for ANOVA for different activation
functions used for inland area
6.2
137
Mean squares error for training, validation, testing and
average of the neural networks model in the inland area
6.6
136
Duncan test for the average of MSE for homogeneous
subsets for the inland and coastal areas
6.5
135
The Chi-Square value of MSE testing for the inland and
coastal areas
6.4
134
The F statistics value for ANOVA for different activation
functions used for the coastal area
6.3
116
138
Mean squares error for training, validation, testing and
average of the neural networks model in the coastal area
139
6.7
The correlation coefficient of the neural network model
140
6.8
The MAPE values of the neural network model
141
6.9
The t-statistic values in the training data
152
6.10
The t-statistic values for the test data
155
6.11
The MSE, RMSE, MAE and MAPE for MLR, MMR and
neural networks performance for inland
6.12
157
The MSE, RMSE, MAE and MAPE for MLR, MMR and
neural networks performance for coastal area
158
18
6.13
The correlation changes from the MLR and MMR models
to neural network model
6.14
The performance changes of the MAPE from the MLR and
MMR to the neural network model
7.1
175
The eigenvalues and predicted FFB yield at stationary
point for each critical fertilizer level in inland area
7.4
174
The average of FFB yield, MSE, RMSE and R2 values for
coastal area
7.3
164
The average of FFB yield, MSE, RMSE and R2 values for
inland area
7.2
163
176
The eigenvalues, the predicted FFB yield at the stationary
points and critical values of fertiliser level for CLD1 and
CLD2 stations
7.5
177
The eigenvalues, the predicted FFB yield at the stationary
points and critical values of fertiliser level for CLD3,
CLD4, CLD5, CLD6 and CLD7
7.6
The estimated FFB yield and fertiliser level at certain
radius for stations ILD3 and ILD4 in the inland area
7.7
181
The estimated FFB yield and fertiliser level at certain radii
for station ILD7
7.9
180
The estimated FFB yield and fertiliser level at certain
radius for stations ILD5 and ILD6 in the inland area
7.8
178
The estimated FFB yield and fertiliser level at certain radii
182
19
for stations CLD1 and CLD2 in the coastal area
7.10
The estimated FFB yield and fertiliser level at the certain
radii for stations CLD4 and CLD5 in the coastal area
7.11
198
The RMSE, MAPE and R2 values for the MLR and MMR
modeling for the inland and coastal areas
8.3
193
The adequacy of fit measurement used for the nonlinear
growth models
8.2
192
The estimated FFB yield and the foliar nutrient
composition levels in (%) for the coastal area
8.1
189
The estimated FFB yield and the foliar nutrient
composition levels in (%) for inland area
7.15
186
The fertiliser level, average estimated of FFB yield and
total profit for the inland and coastal areas
7.14
185
The estimated FFB yield and fertiliser level at the certain
radii for station CLD7 in the coastal area
7.13
184
The estimated FFB yield and fertiliser level at the certain
radii for stations CLD5 and CLD6 in the coastal area
7.12
183
199
The RMSE, MAPE and R2 values for the MLR and MMR
modeling for the coastal area
200
8.4
The F values of the analysis of variance for different
activation functions for the inland and coastal areas
8.5
202
The MAPE values and the correlation of the neural
network models for the inland and coastal areas
203
20
8.6
The F value of analysis of variance for Experiment 1, 2 and
3
8.7
204
The comparison of the MAPE values and the correlation
values among the MLR, MMR and NN models for inland
and coastal areas
8.8
The accuracy of the MLR, MMR, NN models and the
accuracy changes for the inland area
8.9
209
The fertiliser level, average estimated of FFB yield and
total profit for the coastal area
8.12
207
The fertiliser level, average estimated of FFB yield and
total profit for the inland area
8.11
207
The accuracy of the MLR, MMR, NN models and the
accuracy changes for the coastal area
8.10
205
209
The average estimated of the FFB yield and the foliar
nutrient composition levels for the inland and coastal areas
210
21
LIST OF FIGURES
TITLE
FIGURE NO.
1.1
Annual production of crude palm oil (1975-2003)
including Peninsular Malaysia, Sabah and Sarawak
1.2
PAGE
4
Oil palm planted area: 1975 – 2003 (hectare) including
Peninsular Malaysia, Sabah and Sarawak
5
1.3
Annual export of palm oil: 1975 – 2003 (in tonnes)
5
1.4
World major producers of palm oil (‘000 tonnes)
6
1.5
World major exporter of palm oil and including reexporting country (*)
1.6
6
Summary of research framework and research
methodology used in this study
10
3.1
Data analysis procedure used in this study
44
3.2
FFB yield growth versus time (year of harvest)
46
3.3
Processing unit
58
3.4
Identity function
60
3.5
Binary step function
60
22
3.6
Sigmoid function
61
3.7
Bipolar sigmoid function
61
3.8
Feed-forward neural network
62
3.9
Recurrent neural network
63
3.10
Supervised learning model
65
3.11
Backward propagation
70
3.12
The descent vs. learning rate and momentum
72
4.1
Residual plot for Logistic, Gompertz, von Bertalanffy,
Negative exponential, Monomolecular and Log logistic
growth models
4.2
100
Residual plot for Richard’s, Weibull, Morgan-MercerFlodin, Chapman-Richard, Chapman-Richard* and
Stannard growth models
5.1
The error distribution plots of MLR model in coastal
stations
5.2
5.5
112
The error distribution plots of RMR model in inland
stations
5.4
111
The error distribution plots of MLR model in inland
stations
5.3
101
117
The error distribution plots of RMR model in coastal
stations
118
The R2 value for each model proposed for inland area
119
23
5.6
The R2 value for each model proposed for coastal area
6.1
Three layers fully connected neural networks with five
input nodes and one output node
6.2
144
The actual and predicted FFB yield for CLD4, CLD5,
CLD6 and CLD7 using the NN model
6.10
143
The actual and predicted FFB yield for ILDT, CLD1,
CLD2 and CLD3 stations using the NN model
6.9
142
The actual and predicted FFB yield for ILD4, ILD5,
ILD6 and ILD7 stations using the NN model
6.8
130
The actual and predicted FFB yield for ILD1, ILD2 and
ILD3 stations using the NN model
6.7
129
The three layers fully connected neural networks with
nine input nodes and one output node
6.6
128
The correlation coefficient between the actual and
predicted value
6.5
128
The mean squares error for training, validation and
testing
6.4
125
The early stopping procedure for feed-forward neural
network
6.3
120
145
The actual and predicted FFB yield for CLDT using the
NN model
146
24
6.11
The error distribution plot of neural network model for
the inland stations
6.12
The error distribution plots of neural network model for
the coastal stations
6.13
160
Comparison of the MAPE values between MLR, MMR
and NN for inland area
6.20
159
The correlation coefficient from the MLR, MMR and
NN models for coastal area
6.19
153
The correlation coefficient from the MLR, MMR and
NN models for inland area
6.18
153
The MSE values for different levels of the magnitudeoutliers in the test data
6.17
151
The MSE values for different levels of the percentageoutliers in the test data
6.16
150
The MSE values for different levels of the magnitudeoutliers in the training data
6.15
148
The MSE values for different levels of the percentageoutliers in the training data
6.14
147
160
Comparison of the MAPE values between MLR, MMR
and NN for coastal area
161
6.21
Comparison of the accuracy of models for inland area
165
6.22
Comparison of the accuracy of models for coastal area
165
25
6.23
The percentage changes of the model accuracy for
inland area
6.24
The percentage changes of the models accuracy for
coastal area
7.1
166
166
The response surface plots for fertiliser treatments in
ILD1 and ILD2 stations in inland and CLD2 and CLD7
stations in coastal area
7.2
171
Data analysis procedure in obtaining the optimum level
of fertiliser level and foliar nutrient composition
172
7.3
The fertiliser levels for each station in the inland area
190
7.4
The fertiliser levels for each station in the coastal area
191
7.5
The foliar nutrient composition levels for each station
in the inland area
7.6
The foliar nutrient composition levels for each station
in the coastal area
7.7
8.1
192
194
Comparison between the N and K fertiliser level needs
by oil palm for the coastal and inland areas
194
The factors that contribute to oil palm yield production
213
26
LIST OF SYMBOLS
FFB
-
Fresh Fruit Bunches
FELDA
-
Federal Land Development Authority
RISDA
-
Rubber Industry Smallholders Development Authority
SADC
-
State Agriculture Development Corporations
FELCRA
-
Federal Land Consolidation and Rehabilitation Authority
LSU
-
Leaf Sampling Unit
NN
-
Neural Network
MLR
-
Multiple Linear Regression
RMR
-
Robust M-Regression
RSA
-
Response Surface Analysis
MSE
-
Mean Square Error
RMSE
-
Root Mean Square Error
MAPE
-
Mean Absolute Percentage Error
N
-
Nitrogen
P
-
Phosphorus
K
-
Potassium
Ca
-
Calcium
Mg
-
Magnesium
TLB
-
Total Leaf Basis
NBR
-
Nutrient Balance Ratio
CLP
-
Critical Leaf Phosphorus Concentration
MNC
-
Major Nutrient Component
AS
-
Ammonium Sulphate
CIRP
-
Christmas Island Rock Phosphate
KIES
-
Kieserite
27
LIST OF APPENDICES
APPENDIX
TITLE
PAGE
A
The list of oil palm experimental stations
231
B
The rate and actual value of fertiliser (kg/palm/year)
232
C
Summary of macro nutrients needed by plants
234
D
The list of paper published from 2001 until Now
236
E
The ridge analysis
239
F
Nonlinear least squares iterative phase, nonlinear
least squares summary statistics and normal
probability plot for the nonlinear growth models
G
240
The parameters estimate using multiple linear
regression for MNC as independent variables for
255
inland area
H
The parameters estimate using multiple linear
regression for MNC as independent variables for
256
coastal area
I
Normal probability plot of multiple linear regression
for the inland area
J
257
Normal probability plot of multiple linear regression
for the coastal area
258
28
K
The parameters estimate using multiple linear
regression using MNC and NBR as independent
variables for the coastal area
L
259
The parameters estimate using multiple linear
regression using MNC and NBR as independent
variables for the inland area
260
M
The Q-Q plot for inland stations
261
N
The Q-Q plot for coastal stations
262
O
Example of the Matlab programming for neural
network application
P
Graphical illustration for the best regression line
fitting for inland stations
Q
276
The calculation of total profit (RM) for the inland
stations according to each radius
U
274
The MSE, RMSE, MAE and MAPE values for each
neural network model in the coastal area
T
270
The MSE, RMSE, MAE and MAPE values for each
neural network model in the inland area
S
266
Graphical illustration for the best regression line
fitting for coastal stations
R
263
278
The calculation of total profit (RM) for the coastal
stations in the coastal areas according to each radius
281