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APPLICATION OF STATISTICAL AND NEURAL NETWORK MODEL FOR
OIL PALM YIELD STUDY
AZME BIN KHAMIS
Faculty of Science
Universiti Teknologi Malaysia
DECEMBER 2005
5
APPLICATION OF STATISTICAL AND NEURAL NETWORK MODEL FOR
OIL PALM YIELD STUDY
AZME BIN KHAMIS
A thesis submitted in fulfilment of the
requirements for the award of the degree of
Doctor of Philosophy
Faculty of Science
Universiti Teknologi Malaysia
DECEMBER 2005
7
ACKNOWLEDGEMENTS
بسم اهللا الرحمن الرحيم
In the name of Allah, the most Beneficent and the most Merciful.
I would like to express my gratitude to my supervisor, Associate Professor
Dr. Zuhaimy Hj Ismail for his encouragement, patience, constant guidance,
continuous support and assistance all through out the period. Most of his invaluable
comments and suggestion would be preciously valued. His dedication to work and
perfectionism will be always be remembered and learnt as a basic necessity of a
successful scholar. I am also very grateful to my co-supervisor, Dr. Khalid Haron
from Malaysian Oil palm Board (MPOB), Kluang Station for his, comments,
suggestions and sincere support during this endeavour. I also would like to thank
Haji Ahmad Tarmizi Mohammed from MPOB Bangi for his motivation, fruitful
discussion and valuable comments.
I am especially grateful to my beloved wife, Hairani Razali, for her patience,
encouragement and constant support she gives. She is my ‘co-pilot’ and this study
would not possible without her. To my two lovely sons, Amirul Fikri and Amirul
Farhan, and my lovely daughter Amirah Afiqah: you’re daddy’s source of
inspiration. Many thanks go to my beloved parents, who constantly and remotely
gave me encouragement and advice.
I am grateful to the Kolej Universiti Teknologi Tun Hussein Onn and
Malaysian Government for the sponsorship given. Lastly, many thanks go to those
who have contributed directly and indirectly to the completion of my work in the
Universiti Teknologi Malaysia.
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ABSTRACT
This thesis presents an exploratory study on modelling of oil palm (OP) yield
using statistical and artificial neural network approach. Even though Malaysia is one
of the largest producers of palm oil, research on modelling of OP yield is still at its
infancy. This study began by exploring the commonly used statistical models for
plant growth such as nonlinear growth model, multiple linear regression models and
robust M regression model. Data used were OP yield growth data, foliar
composition data and fertiliser treatments data, collected from seven stations in the
inland and coastal areas provided by Malaysian Palm Oil Board (MPOB). Twelve
nonlinear growth models were used. Initial study shows that logistic growth model
gave the best fit for modelling OP yield. This study then explores the causality
relationship between OP yield and foliar composition and the effect of nutrient
balance ratio to OP yield. In improving the model, this study explores the use of
neural network. The architecture of the neural network such as the combination
activation functions, the learning rate, the number of hidden nodes, the momentum
terms, the number of runs and outliers data on the neural network’s performance
were also studied. Comparative studies between various models were carried out.
The response surface analysis was used to determine the optimum combination of
fertiliser in order to maximise OP yield. Saddle points occurred in the analysis and
ridge analysis technique was used to overcome the saddle point problem with several
alternative combinations fertiliser levels considered. Finally, profit analysis was
performed to select and identify the fertiliser combination that may generate
maximum yield.
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ABSTRAK
Tesis ini mempersembahkan kajian penerokaan terhadap pemodelan hasil
kelapa sawit melalui pendekatan statistik dan rangkaian neural buatan. Malaysia
adalah negara pengeluar minyak kelapa sawit terbesar, namun begitu penyelidikan
mengenai pemodelan hasil kelapa sawit masih berada diperingkat awal. Kajian ini
dimulakan dengan penerokaan terhadap model statistik yang popular untuk
pertumbuhan pokok seperti model pertumbuhan taklinear, analisis regresi linear
berganda dan analisis regresi-M teguh. Data hasil kelapa sawit, data kandungan
nutrien dalam daun dan data ujikaji pembajaan yang dikumpulkan daripada tujuh
buah stesen di kawasan pedalaman dan tujuh buah stesen di kawasan tanah lanar
pantai telah disediakan oleh Lembaga Minyak Sawit Malaysia (MPOB). Dua belas
model pertumbuhan taklinear telah dipertimbangkan. Kajian awal menunjukkan
model pertumbuhan taklinear logistik adalah yang terbaik untuk memodelkan
pertumbuhan hasil kelapa sawit. Kajian ini diteruskan dengan menerokai hubungan
di antara hasil kelapa sawit dengan kandungan nutrien dalam daun dan nisbah
keseimbangan nutrien. Bagi mempertingkatkan keupayaan model, kajian ini
menerokai penggunaan rangkaian neural. Kajian ini juga mengkaji kesan rekabentuk
rangkaian neural seperti gabungan fungsi penggiat, kadar pembelajaran, bilangan nod
tersembunyi, kadar momentum, bilangan larian dan data lampau terhadap prestasi
rangkaian neural. Kajian perbandingan di antara beberapa model yang dikaji telah
dilakukan. Analisis satah sambutan telah digunakan untuk menentukan nisbah baja
yang paling optimum bagi menghasilkan hasil kelapa sawit yang maksimum.
Masalah titik pelana berlaku di dalam analisis dan analisis permatang telah
digunakan untuk mengatasi masalah tersebut dengan ia menyediakan beberapa
pilihan kombinasi baja yang boleh dipertimbangkan. Akhir sekali, analisis
keuntungan dilakukan untuk memilih dan mengenalpasti kombinasi baja yang boleh
menghasilkan keuntungan maksimum.
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TABLE OF CONTENTS
CHAPTER TITLE PAGE
1
TITLE
DECLARATION
ACKNOWLEDGEMENTS
ABSTRACT
ABSTRAK
TABLE OF CONTENTS
LIST OF FIGURES
LIST OF TABLES
LIST OF SYMBOLS
LIST OF APPENDICES
INTRODUCTION
1.1 Introduction
1.2 Research Background
1.3 Brief History of Oil Palm Industry in Malaysia
1.4 Problem Descriptions
1.5 Research Objectives
1.6 Scope of The Study
1.6.1 Data Scope
1.6.2 Model Scope
1.6.3 Statistical Testing Scope
1.7 Data Gathering
1.8 Leaf Analysis
1.9 Research Importance
1.10 Research Contribution
1.11 Thesis Organisation
i
ii
iii
iv
v
vi
xii
xvii
xxi
xxv
1
1
3
7
8
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9
11
12
13
14
17
18
19
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2 REVIEW OF THE LITERATURE
2.1 Introduction
2.2 Oil Palm Yield Modelling
2.3 Nonlinear Growth Model
2.4 Application of Neural Network Modelling
2.4.1 Neural Network in Science and Technology
2.4.2 Neural Network in Economy
2.4.3 Neural Network in Environmental and
Health
2.4.4 Neural Network in Agriculture
2.5 Response Surface Analysis
2.6 Summary
21
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30
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3
RESEARCH METHODOLOGY
3.1 Introduction
3.2 Data Analysis
3.3 Modelling
3.3.1 Nonlinear Growth Models
3.3.1.1 Nonlinear Methodology
3.3.2 Regression Analysis
3.3.2.1 Least Squares Method
3.3.3 Robust M-Regression
3.3.4 Neural Networks Model
3.3.4.1 Introduction to Neural Network
3.3.4.2 Fundamentals of Neural Network
3.3.4.3 Processing Unit
3.3.4.4 Combination Function
3.3.4.5 Activation Function
3.3.4.6 Network Topologies
43
43
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51
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55
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58
58
59
62
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3.3.4.7 Network Learning
3.3.4.8 Objective Function
3.3.4.9 Basic Architecture of Feed-Forward
Neural Network
3.3.5 Response Surface Analysis
3.3.5.1 Introduction
3.3.5.2 Response Surface: First Order
3.3.5.3 Response Surface: Second Order
3.3.5.4 Stationary Point
3.3.5.5 Ridge Analysis
3.3.5.6 Estimate the standard error of
predicted response
3.4 Summary
64
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81
4
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
82
84
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93
104
5
MODELLING OIL PALM YIELD USING
MULTIPLE LINEAR REGRESSION AND
ROBUST M-REGRESSION
5.1 Introduction
13
5.2 Model Development
5.3 Results and Discussion
5.3.1 Multiple Linear Regression
5.3.2 Residual Analysis for MLR
5.3.3 Robust M-Regression
5.3.4 Residual Analysis for RMR
5.4 Conclusion
105
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119
6
NEURAL NETWORK MODEL FOR OIL PALM
YIELD
6.1 Introduction
6.2 Neural Network Procedure
6.2.1 Data Preparation
6.2.2 Calculating Degree of Freedom
6.3 Computer Application
6.4 Experimental Design for Neural Network
6.4.1 Experiment 1
6.4.2 Experiment 2
6.4.3 Experiment 3
6.5 Results and Discussion
6.5.1 Statistical Analysis
6.5.2 Neural Network Performance
6.5.3 Residual Analysis
6.5.4 Results of Experiment 1
6.5.5 Results of Experiment 2
6.5.6 Results of Experiment 3
6.6 Comparative Study on Oil Palm Yield Modelling
6.7 Conclusion
122
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129
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138
146
149
149
149
155
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
169
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186
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195
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SUMMARY AND CONCLUSION
8.1 Introduction
8.2 Results and Discussion
8.2.1 Initial Exploratory Study
8.2.2 Modelling Using Neural Network
8.2.3 Modelling Using Response Surface Analysis
8.3 Conclusion
8.4 Areas for Further Research
REFERENCES
Appendices A - U
196
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201
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214
231
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LIST OF TABLES
TABLE NO. TITLE
PAGE
1.1 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
81
4.1 Partial derivatives of the Logistic and Gompertz and von
Bertalanffy growth models
87
4.2 Partial derivatives of the Negative exponential,
Monomolecular, log-logistic and Richard’s growth models
88
4.3 Partial derivatives of the Weibull, Schnute and Morgan-
Mercer-Flodin growth models
89
4.4 Partial derivatives of the Champan-Richard and Stannard
growth models
90
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 yield-
age relationship
95
4.7 Asymptotic correlation for each nonlinear growth models
fitted
96
4.8 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
98
4.9 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
99
4.10 The parameter estimates an asymptotic correlation for von
Bertalanffy and Chapman-Richard when an initial growth
response data point is added
103
4.11 The number of iteration and the root mean squares error for
nonlinear growth models consider in this study
104
5.1 The regression equations and R2 values for the inland and
coastal areas
119
5.2 The regression equation for the inland and coastal station
using MNC and NBR as independent variables
114
5.3 Regression equation using robust M-regression for the
17
inland and coastal areas
116
6.1 The F statistics value for ANOVA for different activation
functions used for inland area
134
6.2 The F statistics value for ANOVA for different activation
functions used for the coastal area
135
6.3 The Chi-Square value of MSE testing for the inland and
coastal areas
136
6.4 Duncan test for the average of MSE for homogeneous
subsets for the inland and coastal areas
137
6.5 Mean squares error for training, validation, testing and
average of the neural networks model in the inland area
138
6.6 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
157
6.12 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
163
6.14 The performance changes of the MAPE from the MLR and
MMR to the neural network model
164
7.1 The average of FFB yield, MSE, RMSE and R2 values for
inland area
174
7.2 The average of FFB yield, MSE, RMSE and R2 values for
coastal area
175
7.3 The eigenvalues and predicted FFB yield at stationary
point for each critical fertilizer level in inland area
176
7.4 The eigenvalues, the predicted FFB yield at the stationary
points and critical values of fertiliser level for CLD1 and
CLD2 stations
177
7.5 The eigenvalues, the predicted FFB yield at the stationary
points and critical values of fertiliser level for CLD3,
CLD4, CLD5, CLD6 and CLD7
178
7.6 The estimated FFB yield and fertiliser level at certain
radius for stations ILD3 and ILD4 in the inland area
180
7.7 The estimated FFB yield and fertiliser level at certain
radius for stations ILD5 and ILD6 in the inland area
181
7.8 The estimated FFB yield and fertiliser level at certain radii
for station ILD7
182
7.9 The estimated FFB yield and fertiliser level at certain radii
19
for stations CLD1 and CLD2 in the coastal area
183
7.10 The estimated FFB yield and fertiliser level at the certain
radii for stations CLD4 and CLD5 in the coastal area
184
7.11 The estimated FFB yield and fertiliser level at the certain
radii for stations CLD5 and CLD6 in the coastal area
185
7.12 The estimated FFB yield and fertiliser level at the certain
radii for station CLD7 in the coastal area
186
7.13 The fertiliser level, average estimated of FFB yield and
total profit for the inland and coastal areas
189
7.14 The estimated FFB yield and the foliar nutrient
composition levels in (%) for inland area
192
7.15 The estimated FFB yield and the foliar nutrient
composition levels in (%) for the coastal area
193
8.1 The adequacy of fit measurement used for the nonlinear
growth models
198
8.2 The RMSE, MAPE and R2 values for the MLR and MMR
modeling for the inland and coastal areas
199
8.3 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
202
8.5 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
204
8.7 The comparison of the MAPE values and the correlation
values among the MLR, MMR and NN models for inland
and coastal areas
205
8.8 The accuracy of the MLR, MMR, NN models and the
accuracy changes for the inland area
207
8.9 The accuracy of the MLR, MMR, NN models and the
accuracy changes for the coastal area
207
8.10 The fertiliser level, average estimated of FFB yield and
total profit for the inland area
209
8.11 The fertiliser level, average estimated of FFB yield and
total profit for the coastal area
209
8.12 The average estimated of the FFB yield and the foliar
nutrient composition levels for the inland and coastal areas
210
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LIST OF FIGURES
FIGURE NO. TITLE
PAGE
1.1 Annual production of crude palm oil (1975-2003)
including Peninsular Malaysia, Sabah and Sarawak
4
1.2 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 re-
exporting country (*)
6
1.6 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
100
4.2 Residual plot for Richard’s, Weibull, Morgan-Mercer-
Flodin, Chapman-Richard, Chapman-Richard* and
Stannard growth models
101
5.1 The error distribution plots of MLR model in coastal
stations
111
5.2 The error distribution plots of MLR model in inland
stations
112
5.3 The error distribution plots of RMR model in inland
stations
117
5.4 The error distribution plots of RMR model in coastal
stations
118
5.5 The R2 value for each model proposed for inland area
119
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5.6 The R2 value for each model proposed for coastal area
120
6.1 Three layers fully connected neural networks with five
input nodes and one output node
125
6.2 The early stopping procedure for feed-forward neural
network
128
6.3 The mean squares error for training, validation and
testing
128
6.4 The correlation coefficient between the actual and
predicted value
129
6.5 The three layers fully connected neural networks with
nine input nodes and one output node
130
6.6 The actual and predicted FFB yield for ILD1, ILD2 and
ILD3 stations using the NN model
142
6.7 The actual and predicted FFB yield for ILD4, ILD5,
ILD6 and ILD7 stations using the NN model
143
6.8
The actual and predicted FFB yield for ILDT, CLD1,
CLD2 and CLD3 stations using the NN model
144
6.9 The actual and predicted FFB yield for CLD4, CLD5,
CLD6 and CLD7 using the NN model
145
6.10 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
147
6.12 The error distribution plots of neural network model for
the coastal stations
148
6.13 The MSE values for different levels of the percentage-
outliers in the training data
150
6.14 The MSE values for different levels of the magnitude-
outliers in the training data
151
6.15 The MSE values for different levels of the percentage-
outliers in the test data
153
6.16 The MSE values for different levels of the magnitude-
outliers in the test data
153
6.17 The correlation coefficient from the MLR, MMR and
NN models for inland area
159
6.18 The correlation coefficient from the MLR, MMR and
NN models for coastal area
160
6.19 Comparison of the MAPE values between MLR, MMR
and NN for inland area
160
6.20 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
166
6.24 The percentage changes of the models accuracy for
coastal area
166
7.1 The response surface plots for fertiliser treatments in
ILD1 and ILD2 stations in inland and CLD2 and CLD7
stations in coastal area
171
7.2 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
192
7.6 The foliar nutrient composition levels for each station
in the coastal area
194
7.7 Comparison between the N and K fertiliser level needs
by oil palm for the coastal and inland areas
194
8.1 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
240
G The parameters estimate using multiple linear
regression for MNC as independent variables for
inland area
255
H The parameters estimate using multiple linear
regression for MNC as independent variables for
coastal area
256
I Normal probability plot of multiple linear regression
for the inland area
257
J 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
259
L 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
263
P Graphical illustration for the best regression line
fitting for inland stations
266
Q Graphical illustration for the best regression line
fitting for coastal stations
270
R The MSE, RMSE, MAE and MAPE values for each
neural network model in the inland area
274
S The MSE, RMSE, MAE and MAPE values for each
neural network model in the coastal area
276
T The calculation of total profit (RM) for the inland
stations according to each radius
278
U The calculation of total profit (RM) for the coastal
stations in the coastal areas according to each radius
281
29
CHAPTER 1
INTRODUCTION
1.1 INTRODUCTION
This chapter presents the introduction to this thesis. It begins by describing
the overall research background followed by a brief history of the oil palm industry
in Malaysia. Research objectives, the scope of this study, research framework and
discussion on the research contribution are also given. Finally, the brief of each
chapter is outlined.
1.2 RESEARCH BACKGROUND
In the oil palm industry, modelling plays an important role in understanding
various issues. It is used in decision making and the advance in computer technology
has created new opportunity for the study of modelling. Modelling can be
categorised into statistical and heuristic modelling. Statistical modelling is defined
as the analysis of the relationship between multiple measurements made on groups of
subjects or objects, and the model usually contains systematic elements and random
effects. As a mathematical aspect, statistical modelling can be defined as a set of
probability distributions on the sample space. Modelling involves the appropriate
application of statistical analysis techniques with certain assumptions on hypothesis
testing, data interpretation, and applicable conclusion.
Statistical analysis requires careful selection of analytical techniques,
verification of assumptions and verification of the data. In conducting statistical
30
analysis, it is normal to begin with the descriptive statistics, graphs, and relationship
plots of the data to evaluate the legitimacy of the data, identify possible outliers and
assumption violations, and form preliminary ideas on variable relationships for
modelling.
The heuristic approach is defined as pertaining to the use of general
knowledge based on experimentation, evaluating possible answers or solutions, or
trial-and-error methods relating to solving problems by experience rather than theory.
Heuristic is also the problem-solving procedure that involves conceiving a
hypothetical answer to a problem at the outset of an inquiry for purposes of giving
guidance or direction to the inquiry. One of the heuristic approaches is the neural
network model, which is based on the rules of thumb and widely used in various
fields. A very important feature of neural networks is their adaptive nature where
‘learning by example’ replaces ‘programming’ in solving problems. This feature
renders these computational models very appealing in application domains, where
one has little or incomplete understanding of the problem to be solved, but where
training data or examples are available.
Neural networks are viable and very important computational models for a
wide variety of problems. These include pattern classification, function
approximation, image processing, clustering, forecasting and prediction. It is
common practice to use the trial and error method to find a suitable neural networks
architecture for a given problem. A number of neural networks are successfully used
and reported in literature (Zuhaimy and Azme, 2001; Zuhaimy and Azme, 2002).
Neural network also has been applied in various fields such as in environmental
(Corne et al., 1998; Hsieh and Tang, 1998; Navone and Ceccatto, 1994), in
economy and management (Boussabaine and Kaka, 1998; Franses and Homelen,
1998; Garcia and Gency, 2000; Indro et al., 1999; Klein and Rossin, 1999b; Tkacz
and Hu, 1999; Yao et al., 2000) and in agronomy (Shearer et al., 1994; Drummond
et al., 1995; Liu et al., 2001; Kominakis et al., 2002; Shrestha and Steward, 2002).
There are different types of the network are perceptron network, multiple
layer perceptron, radial basis function network, Kohonen network, Hopfield network
etc. However, the multiple layer perceptron is widely reported and used neural
31
networks in application. The most popular architecture, in the class of multiple layer
perceptron, is the feedforward neural network.
The developments of models for agriculture are normally divided into three
steps. The first step is to develop a preliminary model, which is inadequate. This
preliminary model does not have to be a good model but it acts as a basis. This leads
to further research, to develop a comprehensive model incorporating all the processes
that appear to be important. Such a model is valuable for research, but far too
complex for everyday use. To overcome this, a set of summary models is produced,
each containing enough detail to answer limited questions. For example, there might
be a summary model to predict the response to fertilisers on different soil types.
Another model might be used to predict cyclic variation in yield. Modelling helps to
make predictions more accurate. There is no doubt that modelling will maintain its
importance in oil palm research as the problems set more complex and difficult. This
study proposes the development of statistical model and neural network in modelling
oil palm yield.
1.3 BRIEF HISTORY OF OIL PALM INDUSTRY IN MALAYSIA
Oil palm (Eleais guineensis. Jacq.), is a plant of African origin and is grown
commercially in Africa. In the early 19th century the oil palm was brought into this
country by the British. The oil palm was first planted in 1848 in Bogor-Indonesia
and in Malaysia in 1870, at the same time rubber seeds were brought in (Hartley,
1977). Due to lower profitability of oil palm in comparison to rubber, the
development of oil palm industry was rather slower. The first commercial planting
of oil palm in Malaysia took place in 1917, six years after its systematic cultivation
in Sumatera. The early planting was undertaken by European plantations, including
Tannamaran Estate in Selangor and Oil Palm Malaya Limited. The 1960s and 1970s
were marked by extensive development of oil palm undertaken largely by private
32
plantations and the Federal Land Development Authority (FELDA). In addition, a
number of State Agriculture Development Corporations (SADC) became involved in
oil palm cultivation after learning about its good prospects. The Rubber Industry
Smallholders’ Development Authority (RISDA) and the Federal Land Consolidation
and Rehabilitation Authority (FELCRA) were also involved in cultivating abandoned
and idle rubber and paddy areas with oil palm (Teoh, 2000).
From year 1975 to year 2000, the worldwide area planted with oil palm
(Elaeis guineensis Jacq.) has increased by more than 150 percent. Most of this
increase has taken place in Southeast Asia, with a spectacular production increase in
Malaysia and Indonesia. The production of crude palm oil (CPO) in 2003 increased
markedly, by 12.1 percent or 1.4 million tonnes to 13.35 million tonnes from 11.91
million tonnes in 2002 (Figure 1.1) (Teoh, 2000).
0
500000
1000000
1500000
2000000
2500000
3000000
3500000
4000000
19751977
19791981
19831985
19871989
19911993
19951997
19992001
2003
Year
Hect
are
Figure 1.1: Oil palm planted area: 1975 – 2003 (hectares) including Peninsular
Malaysia, Sabah and Sarawak
(Source: Department of Statistics, Malaysia: 1975-1989; MPOB: 1990-2003)
33
The production of crude palm kernel also rose substantially by 11.6 percent in
to 1.6 million tonnes year 2003 from 1.47 million tonnes in year 2002. The increase
was mainly attributed to the expansion in the matured area (Figure 1.2), favourable
weather conditions and rainfall distribution as well as constant sunshine throughout
the year. Exports of palm oil increased by 12.5 percent or 1.36 million tonnes to
12.25 million tonnes from 10.89 million tonnes in 2002 (Figure 1.3) (MPOB, 2003).
0
2000000
4000000
6000000
8000000
10000000
12000000
14000000
16000000
1975
1977
1979
1981
1983
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
Year
Cru
de p
alm
oil
(tonn
es)
Figure 1.2: Annual production of crude palm oil (1975-2003) including Peninsular
Malaysia, Sabah and Sarawak. (Source: Department of Statistics, Malaysia: 1975-
1989; MPOB: 1990-2003)
0
2000000
4000000
6000000
8000000
10000000
12000000
14000000
1975
1977
1979
1981
1983
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
Year
Palm
oil
(tonn
es)
Figure 1.3: Annual export of palm oil: 1975 – 2003 in tonnes. (Source: MPOB)
34
Malaysia is the major producer and exporter of palm oil in the world (Teoh,
2000). Figure 1.4 shows Malaysian production of palm oil compared to Indonesia
and other countries from 1999 to 2003. It shows that Malaysia and Indonesia
recorded an increase in production every year. While Figure 1.5 presents the world’s
major palm oil exporters of palm oil from year 1999 to 2003, it also indicates that
Malaysia and Indonesia also recorded the higher volume. In 2003, the Malaysian
palm oil exporting industry has increased by around 12.5 percent to 12,248 million
tonnes, from 10,886 million tones the previous year. Indonesia only recorded a 7.07
percent increase over the same period. The development of the oil palm industry is
growing at a fast rate and requires a lot of research. This study took the challenge to
contribute our knowledge to the development of the oil palm industry.
02000400060008000
1000012000140160
Msia Indon Nigeria Colomb C-d'Ivoeir
PNG Thai Other
World countries
Prod
uctio
n ('0
00 to
nne 00
00
s
1999 2000 2001 2002 2003
Figure 1.4: World major producers of palm oil (‘000 tonnes)
Source: Oil World (December 12, 2003), Oil World Annual (1999-2003)
35
0
2000
4000
6000
8000
10000
12000
14000
Msia Indon PNG C-d'Ivoeir
Colomb Sing* HK* Other
World countries
Exp
ort (
'000
tonn
es)
1999 2000 2001 2002 2003
Figure 1.5: World major exporter of palm oil, including re-exporting country (*)
ing
d
r of planting. The yield will then increase at a low increment until the
enty-fifth year. From our exploratory study on modelling practices, little work has
been re
t
ar
Source: Oil World (December 12, 2003), Oil World Annual (1999-2003)
1.4 PROBLEM DESCRIPTIONS
The problem in modelling oil palm yield growth is that it does not follow a
linear model. It normally follows a nonlinear growth curve. In modelling a
nonlinear curve, the complexity of the problem increases with the increase in the
number of independent variables. The function of a growth curve has a sigmoid
form, ideally its origin is at (0,0), a point of inflection occurring early in the
adolescent stage and either approaching a maximum value, an asymptote or peak
and falling in the senescent stage (Philip, 1994). Normally, oil palm can be harveste
after three years of planting. The oil palm yield will increase vigorously until the
tenth yea
tw
ported on modelling the oil palm yield growth (Corley and Gray, 1976).
In most cases, researchers focused their study on the effect of environmental
factors, such as evapotranspiration, moisture and rainfall to the oil palm growth.
Chan et al. (2003) conducted a study on the effect of climate change to fresh frui
bunches (FFB) yield, and found that climate change has significantly affected oil
palm yield. The most popular method used in the oil palm industry is multiple line
36
regression. This model is used to investigate the causal effect of the independent
variables to the dependent variable. The literature shows that the foliar nutr
composition can be used as an indicator to estimate the oil palm yield. Nevertheless
the foliar nutrient composition is also dependent on several factors, such as climate,
soil nutrients, fertilisers, pest and diseases, but little had been done on modelling
these factors. This study explores the possibility of improving the model but in
particular, in improving the level of accuracy it can produce. The proposed model
should give smaller error values than previous model (Multiple Linear Regression,
MLR).
ient
actors
e
a
lationship between the response variable (oil palm yield) and the four fertiliser
us (P), potassium (K) and magnesium
(Mg). The expected yield can be described as a continuous function of the
applica
r
sers
f
ried
may still be estimated.
whether the solution gives a maximum, minimum or saddle point of the
sponse curve. From our exploratory study on the use of response surface analysis,
ther le. This study will propose to use
g
The response surface analysis is the technique used to model the relationship
between the response variable (Fresh Fruit Bunch yield, FFB) and treatment f
(fertilisers). The factor variables are sometimes called independent variables and ar
subject to the control by the experimenter. In particular, response surface analysis
also emphasises on finding a particular treatment combination, which causes the
maximum or minimum response. For example, in the oil palm industry there is
re
treatments, namely nitrogen (N), phosphor
tion level of fertiliser used. A continuous second-degree-function (N2, P2, K2
or Mg2) is often a sufficient description of the expected yield over the range of facto
levels applied (Verdooren, 2003). If the fertiliser application rates are greater or
smaller than the optimum application rate it may result in reduced yields. Fertili
are wasted if the amount applied is more than the optimum rate. The advantage o
this technique is that the effects of treatment combinations that have not been car
out in the experiment
The use of response surface analysis is necessary to obtain the optimum level
of fertiliser requirements. In response surface analysis, the eigenvalues will
determine
re
e is no solution if the stationary point is a sadd
rid e analysis as an alternative solution to overcome the saddle point problem.
37
1.5 RESEARCH OBJECTIVES
Even though Malaysia is the largest producer of palm oil in the world, studies
a recent phenomenon for decades. Literature reviews on research
onducted in this field are confined to simple models. The oil palm industry is
urrently under going a structural change and is becoming more complex due to
chnological advances, agricultural management, product demand and planting
l
We further refine the objectives as follows:-
To study current modelling and estimating practices in the oil palm industry.
To explore and propose the best model for oil palm yield growth.
of neural network to model oil palm yield.
To optimise fertiliser level which will generate optimum yield.
d
.6 SCOPE OF THE STUDY
s
on modelling yields have been very limited. The modelling of Malaysian oil palm
yield has been
c
c
te
areas (Teoh, 2000).
This research is an attempt to present a proper methodology for modelling oi
palm yield. The model may then be used for estimating and managing the oil palm
industry.
•
•
• To explore the use
•
These objectives will be achieved by following the research framework as presente
in Figure 1.6.
1
This section is divided into three subsections. The first section will discus
the scope of the data, followed by a discussion on the model scope, and finally the
discussion on statistical testing deployed in this study.
38
1.6.1 Data Scope
For modelling oil palm yield growth data used in this study is secondary data
taken from research done by Foong (1991; 1999). The research was conducted at
Serting Hilir in Negeri Sembilan with relatively wet weather. The annual rainfall in
this area is between 1600 mm to 1800 mm with two distinct droughts in January to
March and June to August. The data used here is the average fresh fruit bunches
(tonnes/hectare) from 1979 to year 1997.
The Malaysian Palm Oil Board (MPOB) provided us with a data set taken
from several estates in Malaysia. The factors included in the data set were foliar
composition, fertiliser treatments and FFB yield. The variables in foliar composition
include percentage of nitrogen concentration N, percentage of phosphorus
concentration P, percentage of potassium concentration K, percentage of calcium
concentration Ca, and percentage of magnesium concentration Mg. The fertiliser
treatments included N, P, K and Mg fertilisers, and they were measured in kg per
palm per year, example 3.7 kg N fertilisers were needed for one palm per year. The
foliar composition data was presented in the form of measured values while the
fertiliser data in ordinal levels, from zero to three.
39
Research Design Review
Secondary DATA GATHERING MPOB Data
DATA MINING
DATA ANALYSIS
MODELLING
Oil Palm Yield Foliar Composition Fertiliser Data Growth Data
Nonlinear Growth Response Surface Curve Analysis MLR RMR Neural Network
Goodness of Fit Testing
No Yes
Comparative Study
No Yes
Oil Palm Yield Model
Figure 1.6: Summary of research framework and research methodology used in this
study
40
1.6.2 Model Scope
This study will confine the scope of models, namely the nonlinear growth
model (NLGM), multiple linear regression (MLR), robust M-regression (RMR),
response surface analysis (RSA) and neural network (NN) models. The nonlinear
growth model will be used to model the data of oil palm yield growth. Using foliar
analysis data we employ the multiple linear regression and robust M-regression to
estimate the oil palm yield. In the MLR model the independent variables are N, P,
K, Ca and Mg concentration (or as we call it, major nutrient component, MNC) and
the dependent variable is fresh fruit bunches (FFB) yield. Aside from MNC
concentration, we also introduce the use of nutrient balance ratio (NBR), critical leaf
phosphorus concentration (CLP), total leaf basis (TLB), deficiency of K (defK) and
deficiency of Mg as independent variables in the second part in MLR. In MM
regression we only consider N, P, K, Ca and Mg concentration as independent
variables and FFB yield as the dependent variable.
We propose the use of the neural network to model oil palm yield. The
discussion on the selection of neural network architecture and some statistical
analysis will be given in Chapter 6. Chapter 7 will describe the use of response
surface analysis to obtain the optimum fertiliser rate to produce an optimum FFB
yield. Following this is a simple economic analysis to select the best combination of
fertilisers input that generates the maximum profit.
1.6.3 Statistical Testing Scope
In this study we considered several statistical tests. They are the error model,
sum of squares error (SSE), root mean squares error (RMSE), determination
coefficient (R2), coefficient of correlation (r), t-test, F test and chi-square test. The
discrepancy between the predicted value from the model fitted, i and actual value yy i
is used to measure the model goodness of fit. The difference between the actual and
the estimated value as known as the model error, and can be written as follows;
ei = yi - i = 1, 2,…, n iy
41
where ei is the model error in observation i. yi is the actual observation i, and i is
the estimated value at i observation. If the model performance is ‘good’, the model
error will be relatively sm
y
all.
)
(ii) Mean Squares Error, MSE =
For the purposes of measuring the accuracy of model fitting, we consider the
four measurements commonly used in any research on model fitting. Namely sum
squares error, root mean squares error, determination coefficient R2 and correlation
coefficient. All formulas are given below;
(i) Sum Squares Error, SSE = , i = 1, 2,…, n (∑=
−n
1i
2ii yy
( )n
yyn
iii∑ −
=1
2ˆ, i = 1, 2,…, n
( )
n
yyn
1i(iii) Root Mean Squares Error, RMSE =
2ii∑
=
− 2,…, n
(iv) Determination of coefficient, R2 = 1-
, i = 1,
( )
( )2n
n
1i
2ii yy∑
=
− , i = 1, 2,…, n
1ii yy∑
=
−
and
(v) Coefficient of correlation, r = ∑=
i
−−n
i
i
yVarxVaryyxx
1 )()())((
, i = 1, 2,…, n
where y observed value, y predicted value, n number of observation, x and y are
the me
xplain
ation coefficient is used to identify the strength of the
relationship between any two variables.
In the case of more then two samples, one-way analysis of variance (anova)
can be used to test the different between the groups using F-test. The anova F-test is
an of xi observation and yi observation, respectively, var(x) is the variance of X
and var(y) is the variance of Y. SSE, MSE and RMSE are used to measure the model
accuracy. The R2 value is a measure of how well the explanatory variables e
the response variable. Correl
42
calculated by dividing an estimate of the variability between the groups by the
variability within the groups;
F = upsithion groVariance wupsetween groVariance b
A high value of F, therefore, is evidence against the null hypothesis of equality of all
population means. If the test shows the mean difference be
tween groups to be
tatistically significant, the Multiple Duncan test can be used to examine which
groups e-
h
The model performance will be measured using sum squares error, mean
quares error, mean absolute, root mean squares error, mean absolute percentage
d coefficient of correlation.
n
nts
s
te
in
and differs for each experiment. We study
urteen experimental stations (including Peninsular Malaysia and East Malaysia),
seven s
s
are different to each other (Montgomery, 1991). Another alternative to on
way analysis of variance is the Chi-square test, which is a nonparametric test whic
can be used when assumption of normality is not needed.
s
error, coefficient of determination an
1.7 DATA GATHERING
The Malaysian Palm Oil Board (MPOB) provided data from the MPOB
database of oil palm fertiliser treatments, which have been carried out from fourtee
oil palm estates. All the data from each estate has been collected, recorded and
compiled by MPOB researchers in the Research Database Center. All treatme
were based on a factorial design with at least three levels of N, P and K fertiliser
rates. Although different types of fertiliser were used in the treatments, the rate
quoted in the final analysis will be equalized to the amounts of ammonium sulpha
(AS), muriate of potash (KCI), Christmas Island Rock Phosphate (CIRP) and
kieserite (Kies). Cumulative yields obtained over a period of two to five years
each trial were analyzed. The data of this study is experimental basic and was
collected for a certain period of time
fo
tations in inland areas and seven stations in coastal areas. Appendix A
presents the background of the experimental stations including age of oil palm, soil
type and the location of the station.
43
Fresh fruit bunches (FFB) yield data used in this study was measured in
tonnes per hectare per year or the average of FFB yield in one year. Foliar analysis
was only done once a year and the samples are taken either on March or July every
year. For example, if this year foliar analysis conducted in July, the next
sample also
conducted in July next year, and so on. The type of FFB yield data and foliar
nalysis data is continuous, and a fertiliser input is in coded form (0, 1, 2, and 3). If
code data is needed, the coded value will be recoded to the exact value (Appendix
analysis procedure is presented in section 1.8.
and
s
) deficiency may be the result of a lack of Mg in the soil or due to
ect with excessive K levels or both of these conditions. It also shows
hidden
f sampling the appropriate frond is correctly sampled for each leaf
sampling unit (LSU). Frond 17 is sampled from the labeled reference LSU palm in
some o ll
a
re
B). The detail of the leaf
1.8 LEAF ANALYSIS
The best method of determining the kind and amount of fertiliser to apply to
fruit trees is by leaf analyses. It effectively measures macro and micronutrients
indicates the need for changes in fertiliser programs (Cline, 1997). Leaf analyse
integrate all the factors that might influence nutrient availability and uptake. The
essentials of macronutrients to oil palm tree were listed in Appendix C. However,
leaf analysis indicates the nutritional status of the crop at the time of sampling
(Pushparajah, 1994). It also shows the balance between nutrients for example,
magnesium (Mg
antagonistic eff
or incipient deficiencies. Adding N, for example, when K is low may result
in a K deficiency because the increased growth requires more K (Fairhurst and
Mutert, 1999).
The leaf analysis was conducted to determine the nutritional status of leaflets
from frond 9 on immature palms and frond 17 on mature palms (Corley, 1976). This
is conducted to assist the preparation of annual fertiliser programmes. In each
nominated lea
r all fields in a LSU and prepared for analysis. Cleanliness is essential at a
44
stages to prevent sample contamination and sampling time between 6.30 am and
12.00 noon.
A frond 17 is identified by counting from the first fully open frond in the
center of the crown (frond 1) (and moved three steps downward (frond 1, 9, 17) with
the same stack) and removed with a sickle. The frond is cut into approximately thre
equal sections (to get the average of the nutrient concentration). The top and ba
sections are discarded and placed in the frond stack. Twelve leaflets are selected an
e
se
d
moved from each frond. Six leaflets are cut from each site at the mid-point of the
frond s
e 20-30 cm
id-section; it is not necessary to wash the leaves. The mid-rib of each leaflet’s
section re
e
leaflets are placed in a labeled plastic bag. Half of the
ample retained as a backup for future reference (stored in a cool, dry place) while
the oth ry are
s.
re
ection (Corley, 1976). Ensure that the 12 leaflets comprise of three from the
upper rank and three from the lower rank from each side of the rachis. The leaflets
samples from each field (or smaller area if required) are put together in a large
labeled plastic bag. About 500 leaflets are collected from each field of 30 hectare.
The samples are then sent to the estate laboratory or sample preparation room
for further preparation. The leaflets are bundled and trimmed to retain th
m
is removed and discarded. The remaining parts of the leaflet’s (lamina) a
then cut into small pieces 2 cm long and placed on aluminium trays to be dried. Th
leaflets are dried in a fan-assisted oven for 48 hours (650C) or 24 hours (1050C). The
leaf N concentration will be reduced if the temperature exceeds 1050C.
After drying, the
s
er is submitted for analysis. The LSU sample results from the laborato
then formatted as a spreadsheet and the variability is calculated. Leaf samples are
analyzed for N, P, K, Ca and Mg. Other nutrients may be included for palms planted
on particular soil types.
Leaf sampling is carried out once each year. Sampling is frequently
conducted to examine specific areas or to investigate particular nutritional problem
Leaf sampling should be done at the same time each year and not during wet or very
dry periods. Complete the sampling procedure in the shortest possible time.
45
Because of the synergism between nitrogen (N) and phosphorus (P) uptake,
leaf c
chs, 1981). This is due to the constant ratio between N and P in protein compounds
found i
39
oncentration must be assessed in ratio to leaf N concentration (Ollagnier and
O
n plant tissue (Fairhurst and Mutert, 1999). A critical curve has been
developed where CLCp is defined as;
Critical Leaf P concentration, CLCP = 0.0487 x Leaf N concentration + 0.0
A different approach to determine whether potassium (K) and magnesium
(Mg) are deficient taking into account the relative concentrations of the leaf cations
,
00
K Mg and calcium (Ca). First, the total amount of bases in leaf (TLB) is calculated
and K and Mg are assessed as a percentage of TLB (Foster 1999). TLB can be
derived from equation below;
TLB (cmol/kg) = (% leaf K/39.1 + % leaf Mg/12.14 + % leaf Ca/20.04) x 10
roughly, K and Mg deficiency can then be assessed individually, based on their
percentage of TLB. The deficiency of K and Mg can then be obtained
as 100x⎟⎠⎞
⎜⎝⎛
TLBX , where X is partial to TLB of K and Mg. The K and Mg deficiency
can be rated into three categories; If the value is below than 25 the rating is
deficient, a low rating is between 25 to 30 d a rating more than 30 is considered
sufficient. Nutrient Balance Ratio, NBR is defined as the ratio between the foliar
nutrient composition and another foliar nutrient composition. For example, the NBR
between N and K in foliar, is defined as the ratio between N and K concentration.
The range of the NBR values for oil palm presented in Table 1.1.
an
46
Table 1.1: The op value of nutrient balance ratio (NBR) for foliar analysis
nt ratio
timum
Nutrie NBR
N/K 2.50 – 3.00
N/Mg
N/P
N/C
K/Ca
14.00– 18.00
11.00 – 17.00
4.00 – 9.00
4.00 – 10.00
2.00 – 5.00
K/Mg
Mg/Ca 0.25 – 0.55
1.9 RESEARCH IMPORTANCE
The nonlinear growth models are used in modelling the nonlinear
henomenon. Since the nonlinear growth model has not yet been explored in oil
palm in
l
ss
the
r the additional relevance of the independent
ariable to the model. In these sense, multiple linear regression is rather flexible.
Our stu
rly all
p
dustry (Foong, 1999 and Ahmad Tarmizi et al., 2004), we proposed the use
of the nonlinear growth model in the oil palm yield growth study. Here we wil
provide some mathematical basis in parameter estimation for modelling oil palm
yield growth. Then from the results and analysis we can study the biological proce
of oil palm yield growth.
Multiple linear regression can be used to find the relationship between
dependent variable and the independent variable. There can be more than one
independent variable, which allows fo
v
dy emphasizes the proposed new independent variables into the model, an
area yet to be explored by researchers. In real life, nothing seems to work linea
the time. Data are sometime inclusive of outlier or unusual observation. We
proposed the use of multiple robust regression to overcome the negative impact of
outlier to the model’s development.
47
To improve the models, there are various new heuristic methods suggested in
this literature. We explore the flexibility of the neural networ
k to improve the
timated performance and the model’s accuracy. Previous studies in oil palm
topped when the stationary point was saddle (Ahmad Tarmizi, 1986). This caused
id not make allowances for the possibility an incomplete inference from the model
aused difficulties in implementing
improvements in practice outcomes. This study proposes the use of ridge analysis
whe
0
is study. Since it is an area of high
cate
•
• ural networks model to predict the oil palm yield and NN
•
The findings indicated that the combination activation and number
This study investigates the effects of outliers on NN performance. The findings
The response surface analysis when combined with the ridge analysis was used
to obtain the optimum level of foliar nutrient composition and fertiliser input to
produce optimum oil palm yield.
es
s
d
than produce inefficient decision. It also c
n the stationary point is saddle to improve data analysis.
1.1 RESEARCH CONTRIBUTION
There are many contributions in th
importance for the sustainability of the oil palm industry, the contributions can be
gorized as follows;
• Identifying several nonlinear growth models for oil palm yield growth.
The investigation on the relationship between foliar nutrient composition and
yield was conducted using MLR and RMR. A practical model and procedure
were developed for this purpose.
Development of ne
results more reliable compared with the MLR and RMR models.
This study proposes statistical testing to evaluate the factors that influence NN
performance.
of hidden nodes have a significant effect on the NN performance. However, the
learning rate, momentum term and number of runs do not give any effect on the
NN performance.
•
show that percentage-outliers and magnitude-outliers significantly affect the NN
performance.
•
48
Several of the contribution demonstrated above has been published in various form
as desc
1.11 HESIS ORGANISATION
f description on the
usage of the data in this research.
in several fields, such as economic, management and
gronomy. A summary is included at the end of the chapter.
e neural networks model. This chapter also proposes
e research framework
yield
e partial
and
Chapter 5 discusses the development of multiple linear regression and robust
M-regression to investigate the relationship between fresh fruit bunch and the
nutrien
re
ribed in Appendix D
T
This thesis contains eight chapters. Chapter 1 is the introduction. This
chapter gives an introduction to the problem’s description, research objectives,
research scopes, research importance, research data and a brie
Chapter 2 is the Literature Review. This chapter contains a discussion on the
current and past research on oil palm yield. Here we present the application of
neural network modelling
a
Four main models used in the thesis are explained in Chapter 3. It discusses
the statistical methods such as nonlinear growth models, multiple linear regression,
response surface analysis and th
th
In Chapter 4 the use of the nonlinear growth curve to model the oil palm
growth is considered. Twelve nonlinear growth models are presented and th
derivative for each models are provided. Comparisons among the model is done
given at the end of the chapter.
t foliar composition. The use of nutrient balance ratio, deficiency of
magnesium, deficiency of potassium and critical leaf phosphorus as independent
variables are proposed in this chapter. The numerical results from both methods a
presented and compared in terms of modelling performance.
49
Chapter 6 presents the development of neural network to oil palm yield
modell
al
ss of fit and model accuracy.
umerical results of the foliar nutrient composition and fertiliser treatments
perform
simple economics analysis to generate the optimum
rtilisers level in order to maximise the profit.
Chapter 8 concludes the relevant and important findings from this research.
ecommendations on areas related to the findings and possible directions for future
search are presented.
ing. The experimental design is conducted to investigate the effect of the
number of hidden nodes, the number of runs, momentum terms learning rate and
outliers data to the NN performance. The results and conclusion of model selection
have been carried out. The results from multiple regression analysis and neur
network model are compared in terms of goodne
N
ed by response surface analysis are reported in Chapter 7. The use of ridge
analysis is discusses to overcome the ‘saddle point’ problem at the stationary point.
This chapter ends with a
fe
R
re
242
ience, 26(2): 165-176.
Ahmad Tarm
berkesan. Prosiding Persidangan Kebangsaan Pekebun Kecil Sawit 2002:
Ahmad
. No. 22.
t and validation of PORIM fertilizer
17.
Ahmad at and Ariffin
Ahmad Tarmizi Mohammed, Zin Zawawi Zakaria, Mohd Tayeb Dolmat and Ariffin
Darus (2004). Oil palm fertilizer programme: A proposal for higher yield.
Presented in Mesyuarat Plan Tindakan MPOB dan RISDA, at Prime City,
Kluang.
Ahmad Tarmizi Mohmmed, Zin Zawawi Zakaria, Mohd Tayeb Dolmat, Foster, H.
L., Hamdan Abu Bakar and Khalid Haron (1991). Relative efficiency of urea
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