Posted: October 20th, 2022

ANN Application in Maritime Industry: Baltic Dry Index Forecasting & Optimization of the Number of Container Cranes

ANN Application in Maritime Industry:
Baltic Dry Index Forecasting & Optimization
of the Number of Container Cranes
By
CUI HAN
The People’s Republic of China
A dissertation submitted to the World Maritime University in Partial
Fulfillment of the requirement for the award of the degree of
MASTER OF SCIENCE
In
MARITIME AFFAIRS
(SHIPPING AND PORT MANAGEMENT)
2012
Copyright Cui Han, 2012
i
DECLARATION
I certify that all the material in this dissertation that is not my own work has been
identified, and that no material is included for which a degree has previously been
conferred on me.
The contents of this dissertation reflect my own personal views, and are not
necessarily endorsed by the University.
Signature:
Date:
Supervised by: DR. Aykut I. Ölcer
Associate Professor
WORLD MARITIME UNIVERSITY
Malmö, Sweden

Assessor: DR. Ilias Visvikis
Associate Professor
WORLD MARITIME UNIVERSITY
Malmö, Sweden
Co-assessor: DR. Osman Turan
Professor
UNIVERSITY OF STRATHCLYDE
Glasgow, UK
ii
ACKNOWLEDGEMENTS
I would like to thank World Maritime University for offering me the
opportunity to study and pursue my Master’s degree in Malmo, Sweden.
I want to give my special thanks to Professor Aykut Olcer, my supervisor.
He guided me, leading me through this work, providing me useful and
invaluable advice. This dissertation benefits from his profound
knowledge in the AI field. I also want to thank Ms. Anne Pazaver, who
Helped me in the linguistic part of the work.
I also appreciate Librarian Chris Hoebeke and Anna Volkova, who helped
me a lot in searching books and databases.
Finally, I am grateful to my beloved parents, who fully supported me
during my studies.
iii
ABSTRACT
Title of Dissertation: ANN application in Maritime Industry:
Baltic Dry Index Forecasting &
Optimization of the Number of
Container Crane
Degree: MSc
This dissertation is a study of dry bulk freight index forecasting and port planning,
both based on Artificial Neural network application.
First the dry bulk market is reviewed, and the reason for the high fluctuation of freight
rates through the demand-supply mechanism is examined. Due to the volatile BDI, the
traditional linear regression forecasting method cannot guarantee the performance of
forecasting, but ANN overcomes this difficulty and gives better performance
especially in a short time. Besides, in order to improve the performance of ANN
further, wavelet is introduced to pre-process the BDI data. But when the noise (high
frequency parts) is stripped, the hidden useful data may also be eliminated. So the
performance of different degrees of de-noising models is evaluated, and the best one
(most suitable de-noising model) is chosen to forecast BDI, which avoids over
de-noising and keeps a fair ability of forecasting.
In the second case study, the collected container terminals and ranked, and the
throughput of each combination (different crane number) is estimated by applying a
trained BP network. The BP network with DEA output is combined, simulating the
efficiency of each combination. And finally, the optimal container crane number is
fixed due to the highest efficiency and practical reasons.
The Conclusion and Recommendation chapter gives some further advice, and many
recommendations are given.
KEY WORDS: FORECASTING, WAVELET DECOMPOSITION, ARTIFICIAL
NEURAL NETWORK, DATA ENVELOPMENT ANALYSIS, PORT EFFICIENCY
iv
TABLE OF CONTENTS
DECLARATION i
ACKNOWLEDGEMENT ii
ABSTRACT iii
TABLE OF CONTENTS iv
LIST OF TABLES viii
LIST OF FIGURES ix
LIST OF ABREVIATIONS xii
CHAPTER 1: INTRODUCTION 1
1.1 MOTIVIATION 1
1.2 GOAL 2
1.3 OBJECTIVES 2
1.4 STRUCTURE OF THE DISSERTATION 3
CHAPTER 2: LITERATURE REVIEW 4
2.1 DRY BULK MARKET 4
2.1.1 THE DEVELOPMENT OF CONTEMPORARY SHIPPING INDUSTRY 5
2.1.2 THE CURRENT ISSUES INFLUENCING SHIPPING 4
2.1.3 THE OVERVIEW OF DRY BULK MARKET 7
2.2 FORECASTING 11
2.2.1THE SHIPPING MARKET CYCLES 11
2.2.2 THE DEFINITION OF FORECASTING 14
v
2.2.3 THE MAIN FORECASTING METHODS IN THE DRY BULK MARKET 15
2.2.4 THE ANN-BASED FORECASTING METHODS 20
2.3 DATA ENVELOPMENT ANALYSIS 21
CHAPTER 3: METHODOLOGY 23
3.1 ARTIFICIAL NEURAL NETWORK 23
3.1.1 INTRODUCTION OF ARTIFICIAL NEURAL NETWORK 23
3.1.2 DEFINITION AND TERMINOLOGY 25
3.1.3 THE NEURAL STRUCTURE AND ACTIVATION FUNCTION 26
3.1.4 MEMORIZATION AND GENERALIZATION ABILITY AND
LEARNING RULES 27
3.1.5 SINGLE LAYER AND MULTIPLE-LAYER NEURAL NETWORK 28
3.1.6 THE BACK-PROPAGATION NETWORK 29
3.1.7 THE RADIAL BASIS FUNCTION (RBF) NETWORK 29
3.2 DATA ENVELOPMENT ANALYSIS (DEA) 32
3.3 WAVELET TRANSFORMATION (PRE-PROCESSING DATA IN
BDI FORECASTING MODEL) 34
3.3.1 DATA TRANSFORMATION 34
3.3.2 FOURIER TRANSFORMATION 35
3.3.3 WAVELET TRANSFORMATION 36
CHAPTER 4: CASE STUDY ONE: FORECASTING BALTIC DRY INDEX 39
4.1 INTRODUCTION OF BALTIC DRY INDEX (BDI) 39
vi
4.1.1 THE FREIGHT RATE INDEX 39
4.1.2 BALTIC DRY INDEX 40
4.1.3 BDI, RESULT OD DRY BULK DEMAND-SUPPLY MECHANISM 41
4.1.4 THE BDI DEVELOPMENT 48
4.2 THE GOAL OF THIS CASE STUDY AND DATA COLLECTING 49
4.3THE APPLICATION OF WAVELET NEURAL NETWORK TO
BDI FORECASTING 50
4.3.1 THE WHOLE PROCESS ILLUSTRATION 50
4.3.2 TRANSFORMING BDI DATA BY WAVELET 50
4.3.3 THE APPLICATION OF RBF NETWORK 53
4.3.4 FORECASTING 61
4.4 DISCUSSION 62
CHAPTER 5: CASE STUDY TWO: OPTIMATION OF NUMBER
OF CONTAINER CRANES 63
5.1 BACKGROUND: THE OVERVIEW OF DEVELOPMENT
OF CONTAINERIZATION 63
5.1.1 CONTAINERIZATION ON SHIP SIDE 63
5.1.2 CONTAINERIZATION ON PORT SIDE 65
5.2 THE GIVEN SPECIFICATION OF THE NEW CONTAINER TERMINAL
AND GOAL 67
5.3 THE APPLICATION OF DEA-ARTIFICIAL NEURAL NETWORK MODEL 67
5.3.1 THE OVERVIEW OF DEA-BP MODEL 67
vii
5.3.2 DATA COLLECTION AND ANALYSIS 67
5.3.3 THE EFFICIENCY RANKING OF THE TERMINALS BY APPLYING
DEA MODEL 70
5.3.4 FORECASTING OF TERMINAL THROUGHPUT BY APPLYING
BP NETWORK 72
5.3.5 SEARCHING THE OPTIMAL NUMBER OF CRANE BY
APPLYING DEA-BP MODEL 76
5.3.6 DISCUSSION 78
5.3.7 THE FINAL OPTIMAL COMBINATION 79
CHAPTER 6: CONCLUSION & RECOMMENDATION 80
6.1 FORECASTING BALTIC DRY INDEX 80
6.2 OPTIMIZATION OF THE NUMBER OF CONTAINER CRANES 82
REFERENCE LIST 84
APPENDEX A: THE COMMON USED WAVELET FUNCTIONS 92
viii
LIST OF TABLES
Table 2.1 Cost sharing scheme 8
Table 2.2 Correlation between BDI, Voyage Volume and Period Volume 9
Table 2.3 Shipping market fundamental analysis 13
Table 2.4 Summary of Forecasting methods 16
Table 2.5 Literature review of various DEA-based Models 21
Table 3.1 Neural Network Glossary 25
Table 4.1 Iron ore freight difference between Brazil-China and W-Australia 43
Table 4.2 Summary of Output error and Curve error 60
Table 4.3 Forecasting BDI from 2012.7.23 to 2012.9.03 61
Table 5.1 Statistical description of the container terminals 70
Table 5.2 Ranking of container terminals (CCR and BCC) 70
Table 5.3 Throughput Simulation based on BP network and M-regression models73
Table 5.4 The Throughputs of each combination (25-40 cranes) based on BP
network and M-regression models 75
Table 5.5 Simulated efficiency of each combination (25-40 cranes) based on BP
network and M-regression models 77
Table 5.6 Final optimal combination 79
ix
LIST OF FIGURES
Figure 2.1 Indices for world GDP, the OECD Industrial Production Index, world
merchandise trade and world seaborne trade (1975–2011) (1990=100) 4
Figure 2.2 Illustration of international seaborne trade from 2005 to 2011,
Millions of tons loaded 5
Figure 2.3 World MFO 380 bunker price from 1992 to 2012 5
Figure 2.4 Volume of voyage chartering and time chartering Vs. BDI 9
Figure 2.5 Dry bulk cycle 1741-2007 13
Figure 2.6 Illustration of Regression analysis 19
Figure 3.1 Illustration of Biological Neuron 24
Figure 3.2 Constitution of a neuron 26
Figure 3.3 Illustration of gradient descent 28
Figure 3.4 Illustration of Multiple-layer neural network 28
Figure 3.5 The procedure of BP network training 29
Figure 3.6 Illustration of Radial basis function neural network 30
Figure 3.7 Illustration of Radial Basis Function 30
Figure 3.8 The procedure of RBF neural network training 31
Figure 3.9 Comparison between CRS and VRS efficiency 33
Figure 3.10 Illustration of measuring efficiency of point ‘A’ 34
Figure 3.11 Example of Flourier Transformation 35
Figure 3.12 Illustration of Fourier wave and wavelet wave 36
Figure 4.1 Dry bulk demand from 2001-2010 42
Figure 4.2 Dry Bulk fleet age Distribution, million dwt. July-2012 42
Figure 4.3 BDI Vs. New building price of Capesize Vessel 44
Figure 4.4 BDI Vs. Broken-up tonnage, 1K tonnage 45
Figure 4.5 Dry Bulker Laying up Tonnage, Million Tonnage from 1992 to 2012 46
x
Figure 4.6 Dry Bulk Supply from 1992 to 2012 47
Figure 4.7 Demand-Supply mode 48
Figure 4.8 Statistic analysis of BDI (2005.12.07-2012.07.20) by MATLAB 48
Figure 4.9 Illustration of the procedure of wavelet neural network 50
Figure 4.10 Haar 3 Low-frequency part of BDI reconstruction by MATLAB 51
Figure 4.11 Sym5, 3 Low-frequency part of BDI reconstruction by MATLAB 51
Figure 4.12 Coif3, 3 low-frequency part of BDI reconstruction by MATLAB 51
Figure 4.13 Bior2.4, 3 low-frequency part of BDI reconstruction by MATLAB 52
Figure 4.14 db5, 3 low-frequency part of BDI reconstruction by MATLAB 52
Figure 4.15 Illustration of decomposition by db3, 2 wavelet by MATLAB 53
Figure 4.16 The process of training, testing, and Assessment 55
Figure 4.17 Comparison between reconstructed a5 curve and BDI 55
Figure 4.18 Training curve and Error curve of a5 RBF network 56
Figure 4.19 Comparison among network output a5, target, and original BDI 56
Figure 4.20 Comparison between reconstructed a4 curve and BDI 56
Figure 4.21 Training curve and Error curve of d5 RBF network 56
Figure 4.22 Comparison among network output a4, target, and original BDI 57
Figure 4.23 Comparison between reconstructed a3 curve and BDI 57
Figure 4.24 Training curve and Error curve of d4 RBF network 57
Figure 4.25 Comparison among network output a3, target, and original BDI 57
Figure 4.26 Comparison between reconstructed a2 curve and BDI 58
Figure 4.27 Training curve and Error curve of d3 RBF network 58
Figure 4.28 Comparison among network output a2, target, and original BDI 58
Figure 4.29 Comparison between reconstructed a1 curve and BDI 58
Figure 4.30 Training curve and Error curve of d2 RBF network 59
Figure 4.31 Comparison among network output a1, target, and original BDI 59
xi
Figure 4.32 Training curve and Error curve of d1 RBF network 59
Figure 4.33 Comparison among network output, and original BDI 59
Figure 4.34 Illustration of output MSE, Curve MSE, and Summation 60
Figure 5.1 Development of container ship size 64
Figure 5.2 Container ship number, DWT, TEU capacity development 64
Figure 5.3 The Capacity of container fleet and new building vessels,
2011-September 64
Figure 5.4 World container trade (tonnage) and GDP 65
Figure 5.5 Top 5 container port throughput from 2006 to 2011, 1000TEU 66
Figure 5.6 Specification of given terminal area 67
Figure 5.7 The procedure of DEA-BP model 67
Figure 5.8 Brief illustration of container terminals 68
Figure 5.9 Container terminals efficiency ranking: CCR V.s BCC 72
Figure 5.10 Selection of Inputs and Targets in BP network 72
Figure 5.11 Comparison among outputs based on BP network and M-regression 73
Figure 5.12 Comparison of throughput simulation based on BP network and
M-regression 74
Figure 5.13 Interval of cranes counting 75
Figure 5.14 Selection of Input and targets in BP-DEA model 76
Figure 5.15 Structure of BP-DEA model and training curve by MATLAB 77
Figure 5.16 output of efficiency of each combination based on BP network and
M-regression and Throughput 78
xii
LIST OF ABBREVIATIONS
AGV Automatic Guided Vehicle
AI Artificial Intelligent
ANN Artificial Neural network
AR Autoregression
ARIMA Autoregressive Integrated Moving Average
ARMA Autoregressive Moving Average model
ARMAX
Autoregressive Moving Average Model with
EXogenous inputs model
BCC Banker,Charnes, and Cooper
BCI Baltic Capesize Index
BDI Baltic Dry Index
BFI Baltic Freight Index
BHMI Baltic Handymax Index
BP Back-Propagated
BPI Baltic Panamax Index
C/P Charter Party
CCR Charnes, Cooper, and Rhodes
CCV central clustering vector
CGT Compensated Gross Tonnage
CRS Constant Return Scale
db wavelet Daubechies wavelet
DEA Data Envelopment Analysis
DMU Decision Making Unit
DWT Dead Weight Tonnage
ECA Emission Control Area
EMA Exponential Moving Average
GDP Gross Domestic Product
GHG Green House Gas
xiii
HARPEX HARPEX Shipping Index
HK convention Hong Kong Convention
IEA International Energy Agency
ISL ISL shipping statistics yearbook
LMS Least mean square
LNG Liquid Nature Gas Carrier
MARPOL
International Convention for the Prevention
of Pollution from Ships
MATLAB Matrix Laboratory
MFO Marine Fuel oil
M-Regression Multiple-Regression
MSE Mean Square Error
OECD
Organisation for Economic Co-operation and
Development
OLS Ordinary Least Square
RBF Radial basis function
SFA Stochastic Frontier Analysis
SH ship Second-Hand ship
SSE Sum of Squared Error
sym wavelet Symlets wavelet
T/C Time Charter
TEU Twenty-foot Equivalent Unit
UNCTAD
United Nations Conference on Trade and
Development
VAR Vector Autoregression
VLOC Very Large Ore Carrier
VRS Various Return Scale
WMU World Maritime University
WTO World Trade Organization
1
CHAPTER 1
INTRODUCTION
1.1 Motivation
 Baltic Dry Index (BDI) forecasting
After the financial crisis in 2008, the world economic situation gradually recovered
from the extreme downtrend. But in 2011, and the first half of 2012, the regional war,
debt crisis, fiscal austerity and the natural disasters result in the development rate
slowing down again.
Trade and economies depend on each other indivisibly. And it is known that a 1%
downtrend in economies will cause around 10% downtrend in trade.1
To some degree,
trade is the main engine of the economies.
Shipping is derived from international trade, and international trade needs shipping to
transport cargo. The main demand countries: Europe, America, and Japan are facing
post-crisis depression, performing so weakly. And the biggest exporting country,
China, is also carrying out economic reform to change the industry structure.
Although in 2010 shipping the sector had a very strong rebound, giving people hope,
the next 2 years seemed to break people’s hope again. Shipping has returned to a
low-cycle, and shipping lines, ship owners are suffering from low freight rates. Many
small ship building yards, even worse, are closing due to bankruptcy.
During2002-2008, many banks flooded into the shipping financial market for
investment or speculation, but now shipping is the last industry that they are interested
in. Recently some Banks claimed they quit shipping finance definitely due to the
extremely bad performance. Besides, regulations and new laws came into force, for

1
See REVIEW OF MARTIME TRANSPORT 2011 (page 4). UNCTAD
2
example, the arrest of ships, and the GHG emission control, affecting the margin of
profitability. In conclusion, it is a tough time for shipping but where there is crisis,
there is opportunity. So forecasting will play a very important role in the coming years
because people want to survive and grow in the uncertain time.
 Port planning
The port sector plays an important role in the economic development of the whole
country, connecting the shipping industry to inland transport. In addition, the maritime
container industry, as a predominant mode of inter-continental cargo traffic, has been
developing significantly. In order to achieve a better efficiency by adopting
economies of scales, the size of container ships has been enlarged by several times in
the last several decades. Accordingly, the port, as the connection, has to adapt to the
dramatic change of container ships, to meet the increasing demand. But for new ports,
especially for those pioneer ports, there is no existing example of port planning,
which is involved in huge investment/risks. Besides, the competition between ports
has become more and more fierce, focusing on cost-efficiency, time-keeping, and
throughput. So appropriate port planning can save a lot in both investment and time.
1.2 Goal
By applying Artificial Neural network, it is intended to forecast the future trend of
BDI in the first case study, and obtain the optimal crane number in the second case
study.
1.3 Objectives
Due to the two different case studies, there are two separate objectives but based on
the same technology: Artificial neural network.
 The Baltic Dry Index forecast
As is known, the dry bulk market is full of uncertainty, the BDI was 17000 high in
June of -2008, but fell to 900 low in November after the “free fall”. The high
fluctuation will result in high risk for shipping companies and other organizations, but
this can be controlled by appropriate forecasting, helping people avoid losses and
3
improve profitability.
 Port planning optimization
With the development of containerization, the port, as the interface of sea and inland
transport has to face increasing demand and competition. So expansion becomes a
good choice, but the expansion of a port requires huge investment, which will involve
investors in high uncertainty and risk. So combination method is developed to
measure the efficiency in order to seek the optimal combination of crane number in
port planning.
1.4 Structure of the dissertation
The dissertation consists of Introduction (Motivation, Goal, Objectives, and Structure),
Literature review (Dry Bulk market, Forecasting, and Data envelopment Analysis),
Methodology (Artificial Neural network, Data Envelopment analysis, and wavelet
transformation), Case study 1: Forecasting Baltic Dry Index, Case study 2:
Optimization of number of container crane, and Conclusion and Recommendations.
4
CHAPTER 2
LITERATURE REVIEW
2.1 Dry Bulk Market
2.1.1 The development of contemporary shipping industry
Figure2.1 Indices for world GDP, the OECD Industrial Production Index, world
merchandise trade and world seaborne trade (1975–2011) (1990=100)
Source: Review of Maritime Transport 2011, UNCTAD
Since 1950, World exports have grown on average 2.4 times faster than world GDP.
As we know, GDP growth depends on industrial production, and trade is driven and
affected by GDP. From Figure 2.1, the gap between trade and GDP has become wider.
The main reasons are globalization, which improves manufacture and service,
including transportation. Recently, the developing and transition economies have
played a more and more important role in merchandise trade. If we look at the
proportion of these economies, in 1997, they accounted for 34% of the global
merchandise trade, but in 2007, it became 40%. No doubt, these countries, BRIC
countries2
are new emerging powers, and will continue take away a share of the trade
from the OECD countries.

2
BRIC countries mean Brazil, Russian, India and China.
World GDP
OECD
Production
5
Ninety% of international cargo volume is transported by sea because shipping is the
best cost-efficient way to carry the huge volume of cargo over long distances.
Although high value cargo is mostly carried by plane or train, the value proportion of
sea transport is growing gradually. In Figure 2.1 , we can find that seaborne trade is
still dominated by raw material, intermediate products, and finished products, which
all had a strong rebound in 2010. Although in 2011, and 2012*, the world economies
slowed down, affecting the recovery of the seaborne trade. In the long term, it will
continue to grow, with shifting trade patterns from higher labor cost countries to
comparative low labor cost countries.
Figure 2.2 Illustration of international seaborne trade from 2005 to 2011, Millions of
tons loaded
Source: Review of Maritime Transport 2011, UNCTAD and various data
2.1.2 The current issues influencing shipping
When we look at shipping, it is a mixture of cost, benefit, environment, regulation,
safety and security. Shipping is not only affected by the whole economic situation, but
also reshaped by many other emerging issues. For example, the high bunker price, the
new regulations about cutting CO2 emissions, and piracy.
 The bunker price and slow steaming
0
5000
10000
2005 2006 2007 2008 2009 2010 2011
container other dry five major bulks crude oil and products
$0
$200
$400
$600
$800
Nov…
Sep…
Jul-…
Ma…
Ma…
Jan-…
Nov…
Sep…
Jul-…
Ma…
Ma…
Jan-…
Nov…
Sep…
Jul-…
Ma…
Ma…
Jan-…
Nov…
Sep…
Jul-…
Ma…
Ma…
Jan-…
BUNKER
PRICE
6
Figure 2.3 World MFO 380 bunker price from 1992 to 2012
Source: Data collected from Shipping Statistics yearbook 2011, and www.bunkerindex.com
With the development of the world, the imbalance between oil demand and supply is
becoming more and more unstable, and “The IEA estimates that some $60 billion
must be invested in global oil production capacity every year in order to meet global
demand3
”. In shipping, the cost of bunker accounts for 60% of the operating cost,
undoubtedly, the rise of bunker prices will affect the transport cost, finally paid by
clients. Since 2004, the era of cheap oil ended, and its price began to rise together
with the trade volume. Some studies show: altering the oil price will affect the freight
rate in the short term, but in the long term, it will change the trade pattern.
In order to deal with the high oil prices, many shipping companies have decided to
use slow-steaming since the financial crisis. The direct effect is cutting down fuel
consumption because fuel consumption ∝ 3
. At the same time, slow-steaming,
which absorbs the overcapacity due to the slower speed, will result in a need for more
ships in the route to keep the service. In addition, it will cut down emissions. But it
also generates more transit time.
We cannot subjectively say that slow-steaming is 100% good for shipping because
different ships, routes, and cargoes will lead to different answers. However, as a direct,
reactive response to the fragile freight and high bunker prices, slow-steaming makes
sense.
 The emission-control regulation and climate change
No doubt, MARPOL73/78 Annex VI, concerning NOx, SOx, and Ozone depleting
substances has already begun to control the harmful emissions. The new ECA will
extend to the U.S. and Canada apart from the original Baltic and North Sea areas.4
Roughly, the global shipping industry accounts for 3% of CO2 emissions. And so far,
many proposals are submitted concerning cutting down emissions, including

3
Retrieved from IEA website
https://monkessays.com/write-my-essay/iea.org/publications/worldenergyoutlook/pressmedia/quotes/23/
4
IMO. North American ECA. Retrieved from
https://monkessays.com/write-my-essay/imo.org/mediacentre/pressbriefings/pages/44-marpol-amends.aspx
7
operational, design, and market-based frameworks. It is very important to make the
shipping industry aware of the social responsibility, which can push new regulations
on the “lazy shipping companies and ship owners”. With climate change, the sea level
will rise, many ports will have to modify their infrastructures and even some trade
patterns will significantly change.
However, as the icecap increasingly melts, arctic navigation will no longer be an
“impossible mission”. For example, in the last year, around 30 vessels passed the
arctic area together with ice breakers in the summer time. It is still a long way to
explore the new route, not only about the geographical restriction, but also about the
matched Helping industries: ship design, class, regulation, and insurance. Besides,
controlling pollution in the fragile polar area is also a big issue.
The regulation will force shipping companies to spend more money on caring about
environment, but in the long run, people cannot survive without sustainability, let
alone the shipping.
 Piracy, Maritime security
In the last several years, many piracy cases have occurred off the coast of Somalia.
And in 2009, 600 nm away from Mogadishu, pirates carried out the attacks. It seems
like a plier to pinch global shipping due to the crucial important position. For crews,
their lives and property are severely threatened. For shipping companies, they have to
pay more for insurance, manning costs, safe guards, and equipment, if they want to
transit this area. Alternatively, if they decide to avoid this area, it will increase the
bunker, hire. Of course, all increased cost will be passed to the shipper through higher
freight rates.
Now, shipping is in a downtrend with negative profit, so actually, the frequency of the
service in a specific route is maintained at a low level. But if one day demand for
maritime transport picks up, what will piracy cost? It is always better to cure earlier
than later.
2.1.3 Overview of the dry bulk market
Dry bulk transportation plays an important role in the global shipping market,
8
accounting for approximately 33% of the total sea transportation volume. With the
container ship rising up, the general cargo ship, the representative of “low-handling
efficiency, high cargo damage rate” has gradually faded out from the major shipping
routes. But compared with the rapid declining of general cargo ships, the dry bulk
cargo ships are still expanding because the major dry bulk cargo are mostly low-value,
huge-volume, long-distance, crucial raw materials of manufacture, infrastructure,
and energy, which cannot be substituted. In 2009, the total volume of dry cargo was
5.2 billion tons, and in 2010, it rose to 5.7 billion tons.5
 The components of the dry bulk market
The dry bulk market is a combination of the shipper, carrier, and dry bulk cargo.
Historically, the shipper was the carrier, even the captain, to carry their own cargo.
Although a few extremely strong cargo owners begin to develop their own fleets to
carry their own cargo, most of the dry bulk shipping is done in the form of chartering
due to various reasons.
Chartering contains time chartering, voyage chartering, contract of affreightment (a
little similar to voyage charter) and bareboat chartering. The different forms of
chartering mean different cost sharing schemes.
Table 2.1 Cost sharing scheme
Bareboat Time charter Voyage charter
Capital cost Owner Owner Owner
Operation cost Charter Owner Owner
Voyage cost Charter Owner Flexible
Source: Shuo Ma (2011). Maritime Economics. (Page 118). World Maritime University.
In dry bulk shipping, Voyage chartering (V/C) and Time Chartering(T/C) are both
popular. In V/C the ship owner will pay for all the expenses except the cargo handling
cost (flexible), carrying the cargo from port A to port B, and finally charge the shipper
the freight. The freight is based on the amount of the cargo they negotiated in advance

5
Review of Maritime Transport 2011. UNCTAD.
9
in the C/P.
Another popular charter is Time-Charter: the charterer will use the ship not
necessarily for performing a particular voyage but for a fixed period of time. And in
return, the charterer will pay the ship owner the hire. At the same time, the charterer
has to carry the burden of the bunker cost. Bareboat Charter is similar to T/C.
Figure 2.4 Volume of voyage chartering and time chartering Vs. BDI
Source: data collected from. The Drewry Monthly (1999-2012). Drewry Shipping Consultant.
Table 2.2 Correlation between BDI, Voyage Volume and Period Volume
BDI voyage volume period volume
BDI 1
voyage volume -0.4535 1
period volume 0.429304 0.196997436 1
This is the correlation among BDI, T/C volume, and Voyage charter volume. BDI vs
V/C is negative, but BDI vs T/C is positive. This is because when BDI gets higher and
higher, charterers will tend to T/C a ship in order to get a relatively low hire rate, but
when BDI is dropping, the charterer will try to V/C or short T/C a ship so as to finish
the contract to get a lower freight rate in the downtrend.
 The structure of the dry bulk market
The dry bulk market is close to a perfect competitive market.
The ship owner may be a very strong regional leader or a single-ship company, and
the charterer maybe a big importer/exporter or a small sub-charterer company. Both
sides constitute the basic demand and supply mechanism. In present times, with the
0
5000
10000
15000
0
20000
40000
60000
voyage volume period volume BDI
10
help of modern communication, the information flow between demand and supply can
be easily exchanged, even in international business. If a shipper wants to send a cargo
to a specific port at a specific time in a specialized ship, the requirement can be spread
to most ship owners` ears quickly.
Most shipping lines are rather strong and control several routes and ports. In contrast,
due to relatively low standard of entering, a lot of people flood into the dry bulk
market, with a loaned ship and several crews. Most companies in the dry bulk market
are rather small. At the same time, consolidation for those companies is not an easy
thing because of the number of companies, and their small size. But we should also
notice that a lot of political influence and man-made interference will affect and
control the market. For example, before the 2008 collapse, one strong company
chartered a large number of bulkers, and held them not to put them in the market
resulting in a shortage of supply, and freight rates went up at once. So we can define
the dry bulk market as very close to a perfect competitive market, but not.
In a perfect competitive market, the price is determined by the balance of the demand
and supply. In the dry bulk market, the freight reflects the relationship between
demand and ship supply.
 The 5 major dry bulk cargo
According to the types and volume of the dry bulk cargo, we can classify them into 5
major bulks: Iron ore, Coal, Grain, Bauxite/Alumina, and Phosphate.
First, in many countries, coal is the major source of energy, called “steam coal”. The
other kind of coal is “thermal coal”, which is mainly used in the production of steel.
Obviously, iron ore and coal are strongly related, and in many cases, the trend of
iron ore and coal shipments are rather similar, which is decided by the major producer
and exporter due to the imbalanced distribution of natural resources. From 1984-2010,
the annual growth of iron ore and coal were both 5%, especially the share of iron ore
within the 5 major dry bulk cargoes rose from 36.8% in 1984 to 42.3% in 2010. We
have to mention that China, as the biggest developing country, is expanding its
infrastructure to satisfy the booming domestic demand. Although China is changing
the industry structure under the recession of the financial crisis, the huge population
11
and urbanization will continue to stimulate the growth of the two major cargoes.
Besides, other emerging countries like India, Brazil, and Russia will also maintain the
continuous growth with the same demands, which will support the long-haul dry bulk
cargo transport. The major carriers are Panamax, Capesize, and VLOC vessels.
Second, grain is mostly affected by the weather. However, other factors are also give
pressure upon the volume, structure and patterns of grain shipments. There are 4
major influences (a) the shift in demand and usage (e.g. industrial purposes vs. feed);
(b) environmental and energy policies that promote the use of alternative energy
sources such as biofuels; (c) the evolution in consumption and demand patterns (e.g.
higher meat consumption in emerging developing countries leads to more grain
shipments for feedstock); and (d) trade measures aimed at promoting or restricting
trade flows6
. The major exporters are Argentina, Australia, Canada, the European
Union and the United States, but the major importers are the European Union, Russia,
Asia, and Africa, which are mostly developing countries. The long distance between
those countries gives the bulk carrier employment. The trade of grain will have an
impact on the handymax and handy vessels.
Third are Alumina and Phosphate; Alumina is the major raw material of industry.
Experiencing the decline of 2008, the export and import of Alumina rebounded,
indicating the recovery of the industry. Another reason, also related to the emerging
developing countries, is that stimulus funding and rapid pace of industrialization
increases consumption. For Phosphate, because it is the raw material of the compound
fertilizer, grain exporters are the major buyer. In 2011, the export remained steady
reflecting further consolidation in the economic recovery and demand for grains. But
expansion in Russia and Asia may cause a new round of price competition, affecting
the shipments. The major carriers are handymax, handysize vessels.
2.2 Forecasting
2.2.1 The shipping market cycles
Before reviewing forecasting, the foundation of the decomposition: shipping cycles,

6
Review of Maritime Transport 2009 (Page 34). UNCTAD
12
which is strongly related to forecasting, is introduced.
“In the fifty-year period following the Second World War, the seven dry cargo freight
cycles were shorter, averaging 6.7 years each.”
7
– Martin Stopford.
Researchers have studied the shipping market cycles, for example, Stopford. He
thinks that a shipping market cycle can be dismantled into 3 components: Long
shipping cycles, short cycles, and seasonal cycles.
 For the long cycles, it is thought that they are driven by technical innovation,
economic development or regional change. In other words, these factors give the
cycles a backbone, although itis not easy to detect.
 For the short cycles, it is easier to identify the periodical stages. “The short cycles
shot up and down, and are easy, indeed conspicuous to see.”
8 We can take China
for example. After the 9/11 attacks, industry production in Europe and the U.S.
declined, and hire and freight went down accordingly. But since 2002, China, due
to entering the WTO in 2001 and reducing the trade barrier, is moving into a high
speed development era. In particular, steel production is booming to feed the high
speed expansion. So the market should have been weak in 2007, but the Chinese
factor supported the market to extend to 2008 after the Beijing Olympics, and free
drop from the peak.
 For the seasonal cycles, it happens very frequently, with repeating similar
fluctuations in consecutive years. For example, Chinese New year, varying from
January to February, has a strong impact on the container ship market, because
people in Asia will celebrate this festival rather than continue working in the
factories, which will definitely cause a decrease in manufacturing and decline of
container transport. Another example, in the winter of the northern hemisphere,
people there will need more heating, causing more importing of coal and oil, which
will push up the bulk market temporarily.
From the statistics, in the last 50 years, the average shipping cycles are 8 years,
varying from 5 years to 9 years, but no two cycles are similar. From Stopford’s theory,

7 Martin Stopford (2009). Maritime Economics (page 118)
8 Martin Stopford (2009). Maritime Economics (page 96)
13
he divides the cycles into 4 kinds:
Table 2.3 Shipping market fundamental analysis
Demand growth Supply growth
Prosperity Very fast Shortage
Competitiveness Fast Expansion
Weakness Fast Overcapacity
Depression Falling Overcapacity
Source: Martin Stopford (2009). Maritime Economics (3rd edition)
Figure 2.5 Dry Bulk cycles 1741-2007
Source: Martin Stopford (2009). Maritime Economics (3rd edition).
Normally, the freight rates are decided by the demand-supply model, but in the
shipping market, the demand is inelastic, meaning some kinds of cargo cannot be
transported by other substitutes. The lead time of ship building also means that
fast-growing demand cannot be satisfied at once, and the long process of ship
recycling blocks technological updating. Besides, many ship owners tend to invest in
new ships in the prosperous market, not considering the uncertainty and overcapacity
but the expectation of high freight. And if we come into details of the market, we have
to face the massive relations among the new-building market, scrapping market (the
first 2 markets will be strongly affected by the steel price, which is related to iron ore
and coal,.), the second-hand market (mainly decided by the expectation of the freight),
the world trade volume (following the international trade, driven by global economy,),
14
and definitely the freight market (we can call it lever).
Sometimes, other than the factors above, an unexpected shock will also lead the
market into different directions. For example, the oil crisis, the Suez Canal closing,
and the 9/11 attacks. Because of these shocks, the market will develop in an uncertain
direction, with huge fluctuation.
2.2.2 The definition of forecasting
Forecasting is the process of making statements about events whose actual outcomes
(typically) have not yet been observed. A commonplace example might be the
estimation of some variable of interest at some specified future date. Prediction is a
similar, but more general term. Both might refer to formal statistical methods. Finally,
forecasting will help people make practical decisions.
For most shipping investors forecasting plays a very important role in the whole
business. It is how they earn their living. No matter whether they decide to buy a new
ship/second hand ship, or choose a certain kind of charter, the more precisely they
predict the future, the more profit they will earn. This not only includes the ship
owners and shipping companies who are making the prediction, but also bankers who
will decide to finance the ship, shipyards who will update the design, engineering
companies who are selling the ship equipment, rating agencies who will evaluate the
risk, the port authority which needs to follow the newest trend to develop their
facilities, forecasting can give a more accurate future to help them to be a better
position.
Maritime forecasting is part of economic forecasting. We should see that the shipping
market is an extremely complicated market, which is decided by a mixture of 4 basic
factors. They contain economic and trade factors, regional regulations and political
reasons, influence from upstream and downstream markets, and some unexpected
shocks. So it is more complex to forecast the shipping markets.
Historically, shipping forecast has had a poor reputation. If we look at the forecasts
made in the 1960s and 1970s, most of them failed, few succeeded. This is especially
true for long-term forecasting because people will ignore some little clues resulting in
15
missing the huge influence later. Although the unpredictable elements always exist in
the shipping markets, people are still eager to forecast the future. For example, when
the future of the market is not clear, the investors will employ people to forecast the
cargo volume, the fleet capacity, and so on. But when the forecasting result comes out,
who can say this is 100% right?
Except the bad record of forecasting, when we are forecasting, it is essential to
identify the goal, and collect the correct information. Shipping investors know that
they are not playing with certainty, but just due to the uncertainty, making the whole
shipping game meaningful. With the accumulation of experience, the investors or
forecasters can narrow down the possibility, making the right decision, although they
have made a lot of wrong decisions before. In addition, the right information can lead
the decision-maker through the unclear future, reducing the risk.9
2.2.3 The main forecasting methods in the dry bulk market
 The goal of forecasting
Everything occurring in the dry bulk market can be forecasted, but there are three
dominant goals. Of course, except the 3 major goals, we also can forecast the bunker
price, and crew market situation.
 Forecasting the cargo volume
Cargo volume forecasting is demand forecasting. It contains cargo flow volume
(Tonnage x distance), structure of the cargo flow, source and distribution of cargo
flow. In this system, we should consider comprehensive information from the global
view, combined with the development of global economics and trade.
 Forecasting the capacity of fleet
This is the opposite of cargo volume forecasting. When we consider these questions,
many factors will affect the capacity, including average speed, average haul,
efficiency of port handling facilities, and the level of management. Besides, delivery
of new building ships, scrapping of the old ships, and lying up of ships also will affect
the supply of shipping markets.

9 Martin Stopford (2009). Maritime Economics 3rd edition, page 697-702
16
 Forecasting the freight rate
This is the most complex part of the forecasting. In reality, the demand and supply
will change dynamically, causing the freight, as the representative of the market to
fluctuate.
 The method of forecasting
Generally speaking, we can categorize the forecast models by nature: they are
qualitative model, quantitative model, and combination model. Examples of
qualitative forecasting methods are: informed opinion and judgment, the Delphi
method, market research, historical life-cycle analogy. Examples of quantitative
forecasting methods are: last period demand, simple and weighted moving averages
(N-Period), simple exponential smoothing, and multiplicative seasonal indexes.
Table 2.4 Summary of Forecasting methods
Time-series forecast
Moving average
Weighted moving average
Exponential smoothing
Autoregressive moving average (ARMA)
Autoregressive integrated moving average (ARIMA),
e.g. Box-Jenkins
Extrapolation
Linear prediction
Trend estimation
Growth curve
Causal / econometric
forecasting methods
Regression analysis
Autoregressive moving average with exogenous inputs
(ARMAX)
Judgmental methods
Composite forecasts
Statistical surveys
Delphi method
17
Scenario building
Technology forecasting
Forecast by analogy
Artificial intelligence
methods
Artificial neural networks
Group method of data handling
Support vector machines
Other methods
Simulation
Prediction market
Probabilistic forecasting and Ensemble forecasting
Source: various sources
The most commonly used methods are moving average, single/multiple regression,
ARMA and its extension, VAR. There are several brief introductions of common-used
forecast models.
 The moving average
This method shows that the latest data affects the next data mostly. The importance of
the previous data affecting the next data will decrease with the increasing interval
between those two data. The extent may vary from linear to exponential, depending
on which kind of moving average is applied.
This is the formula of weighted moving average.
n is the weight of pM, (n-1) is the weight of pM-1, and so on.
This is exponential moving average. The weighting for each older datum point
decreases exponentially, never reaching zero.
Yt is the value at a time period t.
St is the value of the EMA at any time period t.
18
The coefficient α represents the degree of weighting decrease, a constant smoothing
factor between 0 and 1. A higher value of α discounts older observation faster.
The moving average is a very convenient way to smooth the data and roughly forecast
the trend. It does not apply to that if the data is increasing or decreasing dramatically
because the average data is worked out restricted in the past data, impossible to break
the limitation. If seasonal cycles exist, the number of items should be roughly equal to
the seasonal cycles, otherwise this method cannot eliminate the seasonal cycles.
 Regression analysis
This method mainly focuses on the relationship between the dependent variable and
single/multiple independent variables. When we apply regression analysis, the data
must satisfy three checking conditions.
This is an example of single regression.
Y is dependent variable, x is independent variable, β1 and β2 are coefficients, and
εis residual, which is the difference between the value of the dependent variable
predicted by the model.
One method of estimation is ordinary least squares. This method obtains parameter
estimates that minimize the sum of squared residuals, SSE.
Minimization of this function results in a set of normal equations, a set of
simultaneous linear equations in the parameters, which are solved to yield the
parameter estimators
where x is the mean (average) of the x values and ȳ is the mean of the y values.
19
Figure 2.6 Illustration of Regression analysis
In the more general multiple regression model, there are p independent variables:
Where x are independent variables, and y is dependent variable, εis also the
residual.
Generally speaking, when modeling a simple thing, single regression is more
appropriate than multiple-regression, because the estimation of coefficient and
selection of corresponding curve is much easier. When it comes to a complicated
model, the single/multiple regression will not be so competent. The ability of fitting
and generalization will be restricted, especially when the data is not following a
pastime repeating, simple and regular pattern.
 Auto-regression and Auto-regression-moving-average
Autoregressive (AR) model is a type of random process which is often used to model
and predict various types of natural phenomena. The autoregressive model is one of a
group of linear prediction formulas that attempt to predict an output of a system based
on the previous outputs.
where are the parameters of the model, is a constant (often omitted
for simplicity) and is white noise.
ARMA is the combination of AR and MA, sometimes called Box–Jenkins models
after the iterative Box–Jenkins methodology usually used to estimate them, are
typically applied to auto-correlated time series data.
20
The notation ARMA (p, q) refers to the model with p autoregressive terms and q
moving-average terms. This model contains the AR (p) and MA (q) models
where the θ1, …, θq are the parameters of the model, μ is the expectation of (often
assumed to equal 0), and the , ,… are again, white noise error terms.
ARMA is appropriate when a system is a function of a series of unobserved shocks
(the MA part) as well as its own behavior. For example, stock prices may be shocked
by fundamental information as well as exhibiting technical trending and
mean-reversion effects due to market participants.
2.2.4 The ANN-based forecasting methods
 Artificial Neural Network
D.V. Lyridis (2004) applied ANN in different lags10 to forecast the market and it
gave better performance than M-regression model. He got several useful conclusions
to help people to construct ANN.
Başak introduced a special trend factor into the input variables, which follows the
classical supply-demand model, showing a combination of demand-supply theory
and ANN.
Wang Dong (2009) gave some good advice in selection of neuron number in hidden
layer, and functions.
 Combination of artificial neural network and other methods
Jiang Pengfei and Cai Zhihua (2007) employed a combination of RBF network and
genetic algorithms, which improve the performance of RBF network.
Athanasios V. Voudris (2005) used various parameters, not restricted in the demand
and supply to train BP network based on the genetic algorithms to improve the
performance.
JV Hansen* and RD Nelson (2003) showed that by applying decomposition, the
ANN can give better performance than that of the classical decomposition.

10 1 month, 3 months, 6 months, 9 months and 12 months
21
Hu Junsheng and Xiao Dongrong (2005) combined wavelet package with BP
network to forecast the economics, which shows better performance than that by pure
BP network.
Niu Dongxiao and Xing Mian(1999) gave the research of forecasting the non-linear
data based on wavelet-ANN model in order to avoid the inherent defect of BP
network.
Generally speaking, linear model is suitable for simple-relation, long-trend
forecasting, but when it comes to non-linear and high fluctuating data, it can do
nothing. Due to the special architecture of ANN, it usually has better performance
than a regression model in the non-linear data. In addition, with the help of other
technologies, it can be built, trained smarter, and gives even better results.
2.3 Data Envelopment Analysis
Table 2.5 Literature review of various DEA-based Models
Author Method Units Inputs Outputs
Angela
Stefania
Berantino and
enrico
Musso(2010)
SFA and DEA 30 terminals Dimension of quay,
number of terminals,
area of the port for
handling, handling
equipment
Variable selections
Tao
Chen(2010)
DEA-Regress
ion
140
terminals in
China
Quay length, TT
density, Operation
years, load M40
Quay efficiency
Cullinane and
Wang(2006)
DEA-CCR
and BCC
67
European
ports
Quay length, area,
equipment
Container throughput
Cullinane et
al.(2005)
DEA-CCR,B
CC and FHD
57
internationa
l ports
Quay length, quay
cranes, yard gantries,
straddle carriers
Container throughput
22
Barros and
athanassiou(20
04)
DEA-CCR,B
CC
2 Greek and
4 Portugal
ports
Labour and capital cost Freight, cargo
throughput, container
throughput, number
of ship
Tongzon(2001) DEA-CCR 16 ports Number of Crane, tug,
terminals, delay, labour
Throughput, ship
working rate
Martinez-Budri
a et al.(1999)
DEA-BCC 26 Spanish
ports
Labour expenditures,
depreciation charges,
other expenditure
Cargo moved in
docks, revenue from
port facilities.
Roll and
Hayuth(1993)
DEA-CCR Hypothetica
l numerical
example of
20 ports
Manpower, capital Cargo throughput
service level,
consumer
satisfaction, ship
calls
We can find that researchers use different parameters to measure the efficiency or
productivity. In most studies, Data Envelopment Analysis (DEA) was widely used to
quantify the relationship between the outputs and inputs and different terminals are
ranked in terms of “efficiency”. But the controversy between ship operators and port
operators concerning the target is still going on. The selection of the output depends
on the aim of the research. For example, one port may have high quay productivity
preferred by the port operator (achieved by deploying dense cranes to each quay), but
the shipping lines may be in favor of high quay crane efficiency. For this case study,
the target is to seek the best efficiency of the terminal.
23
CHAPTER 3
METHODOLOGY
3.1 Artificial Neural Network
3.1.1 Introduction of artificial neural network
Artificial neural networks are, as their name indicates, computational networks which
try to simulate, the performance of neurons in the human brain. This simulation is a
gross neuron-by-neuron or element-by-element simulation. It absorbs the principle
from the neurophysiological knowledge of biological neurons and of networks of such
biological neurons. It is different from conventional computing technology that serves
to replace, enhance or speed-up human brain computation without considering the
organization of the basic elements and of the network. It belongs to “Artificial
Intelligence” (AI), which includes all research aimed to simulate intelligent behavior.
Artificial neural networks are the major research at present, containing many different
disciplines. Methods contributing to this research consist of biology, computing,
electronics, mathematics, physics, and economics. The approaches to this target
contain a lot, but the general idea is to adopt the knowledge of the nervous system and
human brain to design intelligent artificial systems.
The biological neural network contains neurons, which include the neuron`s dendrite,
nucleus, soma, axon and axon terminal. Neural activity passes from one neuron to
another in terms of electrical triggers which transfer from one cell to the other down
the neuron`s axon, by the electrochemical process of voltage-gated ion exchange
along the axon and diffusion of neurotransmitter molecules through the membrane
over the synaptic gap. The axon can be considered as a connection wire. However, the
mechanism of signal flow is not via electrical travelling but via charge exchange that
24
is transported by diffusion of ions.
This transportation process moves
along the neuron`s cell, down the
axon and then through synaptic
junctions at the end of the axon via a
very narrow synaptic space to the
dendrites and/or soma of the next
neuron at an average rate of 3m/sec.11
Figure 3.1 Illustration of Biological Neuron
Source: Daniel Graupe, PRINCIPLES OF ARTIFICIAL NEURAL NETWORKS, 2nd edition, University
of Illinois, Chicago, USA
The basic principles of artificial neural networks were first created by McCulloch and
Pitts in 1943, who tried to understand and learn how it processes the information. It
contains 5 assumptions, setting a framework of ANNs. Later the Hebbian learning law
due to Donald Hebb(1949) was also a widely applied principle. And it can be
explained as that by repeating and persisting one action, some growth process or
metabolic change will happen in one or both of these cells such that the efficiency of
the cell will increase. In other words, the weight of one contributing neuron will
increase if it approaches the final target. Then due to doubts about the capabilities of
the early models, the research on ANNs declined after the 1960s.
But since the 1980s, the ANNs returned to people`s view, resulting from several
reasons: 1.the early simple model had been replaced by introducing the more
complicated models with newest technology. 2. Powerful computers greatly improved
the performance of the simulation of the complicated ANNs. 3. Introduction of
multiple-layer ANNs enhanced and enlarged the area of appliance, including speech
recognition, and pattern recognition. And now, more and more ANNs combine with
other different algorithms or advanced technologies12
.

11 Graupe, Daniel (2007). Principle of Artificial Neural networks, 2nd edition.
12 Graupe, Daniel (2007). Principles of Artificial Neural Networks (2nd Edition)
25
3.1.2 Definition and terminology
“An artificial neural network is an information-processing system that has certain
performance characteristics in common with biological neural networks. Artificial
neural networks have been developed as generalizations of mathematical models of
human cognition or neural biology”13
Table 3.1 Neural Network Glossary
activation /
initialization
function
Time-varying value that is the output of a neuron.
bias
The net input (or bias) is proportional to the amount that incoming neural
activations must exceed in order for a neuron to fire.
connectivity
The amount of interaction in a system, the structure of the weights in a neural
network, or the relative number of edges in a graph.
epoch One complete presentation of the training set to the network during training.
input layer Neurons whose inputs are fed from the outside world.
learning algorithms
(supervised,
unsupervised)
An adaptation process whereby synapses, weights of neural networks, classifier
strengths, or some other set of adjustable parameters is automatically modified
so that some objective is more readily achieved. The back-propagation and
bucket brigade algorithms are two types of learning procedures.
Learning rule
The algorithm used for modifying the connection strengths, or weights, in
response to training patterns while training is being carried out.
layer
A group of neurons that have a specific function and are processed as a whole.
The most common example is in a feed-forward network that has an input layer,
an output layer and one or more hidden layers.
neuron
A simple computational unit that performs a weighted sum on incoming signals,
adds a threshold or bias term to this value to yield a net input, and maps this last

13 Laurene V. Fausett (1994), Fundamentals of Neural Networks: Architectures, Algorithms, and Applications
26
value through an activation function to compute its own activation. Some
neurons, such as those found in feedback or Hopfield networks, will retain a
portion of their previous activation.
output neuron A neuron within a neural network whose outputs are the result of the network.
threshold
A quantity added to (or subtracted from) the weighted sum of inputs into a
neuron, which forms the neuron’s net input. Intuitively, the net input (or bias) is
proportional to the amount that the incoming neural activations must exceed in
order for a neuron to fire.
training set
A neural network is trained using a training set. A training set comprises
information about the problem to be solved as input stimuli. In some computing
systems the training set is called the “facts” file.
weight
In a neural network, the strength of a synapse (or connection) between two
neurons. Weights may be positive (excitatory) or negative (inhibitory). The
thresholds of a neuron are also considered weights, since they undergo
adaptation by a learning algorithm.
Source: Earth online, http://envisat.esa.int/handbooks/meris/CNTR4-2-5.htm
3.1.3 The neural structure and activation function
 The structure of a Neuron
Due to imitation of human neural network, each process in the neuron will contain
receiving the input, transforming the data, and output.
Figure 3.2 Constitution of a neuron
The input function of the neuron
y = (∑ ∗ + )
Where wji is the weight of each connection,
27
xj is the input,
b is the threshold.
 Activation function
The activation function of a node defines the output of that node given an input or set
of inputs. Normally, these functions can take many forms, but they are usually found
as one of three functions:
 Gaussian:
 Multiquadratics:
 Inverse multiquadratics:
Besides, in RBF (radial basis functions) network, they use the special activation
functions which have extreme efficiency as universal function approximators.
3.1.4 Memorization and generalization ability and learning rules
For a successful model, the ability of memorizing and generalizing is very important.
 Memorization
Memorization means “to learn what happened in the past”. In practice, it consists of
identifying, memorizing, and simply classifying the data into the “slot”
 Generalization
Generalization means “forecast the unknown data in terms of the principle studied
from the known data”. In the ANNs, people usually adopt testing the model to check
the generalization because there is no uniform standard to measure it. To some degree,
we can compare the ANNs to the black-box model, which people only can check the
output to verify the generalization instead of analyzing the structure inside.
 Learning
Leaning contains supervised and unsupervised learning. In our case, the learning is
supervised, which means both the information of the input and the reaction of the
system are given. In other words, it is like teacher who knows all the answers teaching
the students. In ANNs, the supervised learning is a process of memorizing data pairs.
Both the input data and desired target are known. Although the target has been
28
provided, the time to terminate the learning process is hard to decide. The main reason
is that when the overall error is satisfied, the actual
performance may be under-trained/over-fitted. If the
model is trained too many times, the model will remember
everything in the input data, including the error. But if the
model is trained too few times, the model cannot identify
the whole input pattern. In both situations, the
performance of generalization will be damaged.
Figure 3.3 Illustration of gradient descent
Source: gradient descent, Wikipedia, http://en.wikipedia.org/wiki/Gradient_descent
Most learning rules are applied by changing the weight, which will decrease the error
between the output and desired target. The typical method is Gradient descend.
The step gradient descent will repeat until the goal is achieved or stop condition is
met.
3.1.5 Single layer and multiple-layer neural network
 The single-layer network
A single layer network contains several neurons each having several inputs. This kind
of network is commonly used for simple questions. But when it comes to complicated
problems, the multiple-layer neural network will be more useful and practical.
 The multiple-layer network
The multiple-layer introduces the hidden layer/layers, whose neurons provide the
additional transforming. The hidden layer can be 1 layer or
multiple layers. The higher the number of hidden layers, the
easier the input can be. In other words, if the input data is
insufficient, the complicated/multiple-layer network will be
suitable by increasing the number of neurons and hidden
layers.
29
Figure 3.4 Illustration of Multiple-layer neural network
3.1.6 The Back-propagation Network
Before introducing the RBF (radial basis functions) network, it is necessary to proide
a brief introduction to the BP network, which is the most commonly used network and
which will be adopted in Chapter 3.
1. Initiate the weight and bias by assigning random values between (-1, 1)
Figure 3.5 The procedure of BP network training
Source: Graupe Daniel (2007). PRINCIPLES OF ARTIFICIAL NEURAL NETWORKS (2nd Edition).
The stop condition is usually defined as:
The error ≤ goal of error set before or time of epoch reached
The initial selection of weight will determine the beginning place for the error. Too
large a value will cause the error changing nearly to 0, and too small value will also
make the value approaching too slowly.
3.1.7 The Radial basis function(RBF) network
 The introduction of RBF network
A radial basis function network uses radial basis functions as activation functions. It is
a linear combination of radial basis functions, which have three layers: an input layer,
2. Pick up one pair
(input, target) as the
training pattern, and
mark it as used
3. Calculate forward, we
can get the output of
hidden layer, then input
the summation of the
output from hidden layer
into output layer.
4. Backward calculate
the gradient descent,
which gives the
stepper.
5. Renew the
weights according
to the stepper in
order to make the
output approach
the target
6. repeat from
step 2 until all
the pairs are
marked as used.
7. reset all pairs
“unused”, and
repeat from step 2
until the stop
condition is
satisfied.
30
a hidden layer with a non-linear RBF activation function and a linear output layer. Or
we call it as: forward, radial basis function as the activation function in the hidden
layer, neural network.
Figure 3.6 Illustration of Radial basis function neural network
The output can be expressed by:

( ) = ∑ ∅ ( − )

=1
Where j=1, 2, 3….J
J is the number of neurons in the hidden layer
wjk is the weight between the j neuron in the hidden layer and the k neuron in the
output layer
cj is the j center vector
x is the input vector
And ∅ ( − ) = exp [−
( −
)
( − )
2
2
]
Where: σj
is the parameter of the width of the function, and T is transposition. This
function is Gaussian Kernel function, most commonly used in RBF. And it means
changing one parameter of one neuron will have
little effect on the input, which is far away from
the center of that neuron. In other words, the
further away from the center, the smaller the
effect it will make, which shows that only special
31
inputs can affect the RBF
. Figure 3.7 Illustration of Radial Basis Function
Source: RBF neural network, decision trees, https://monkessays.com/write-my-essay/dtreg.com/rbf.htm
 The procedure of RBF network
The general idea of RBF network is similar to BP network, which tries to adjust the
weight to approach the stop condition by using Least Mean Square (LMS).
The difference is that in RBF, we need to decide the position of the center vector.
Normally we adopt K-means clustering method. It will update the central clustering
vector (CCV) after input of data. Then we compare the current one with the last one,
if the center clustering vector did not change, we can continue to calculate the weight
by LMS, if the center clustering vector changes, then we repeat input of the data and
compare them again until we find the unchanged center vector.
After adjusting the weight, the error meets the stop condition, the whole system
terminates.
RBF network as a forward neural network, can approximate any kind of function, and
can locate the universal optimal point, which avoids the local minimum in the BP
network. Besides, researchers have proved that RBF network with enough hidden
neurons can approximate any continuous function with arbitrary precision.
The best advantage of RBF network
is the high efficiency of training and
good generalization. It does not
need too much input/output. When
training the network, the RBF can
automatically decide the number of
neurons by comparing the
performance instead of it being
nominated by people, which saves a
lot of time and energy.
32
Figure 3.8 The procedure of RBF neural network training
Source: modified from RBF Neural Networks, https://monkessays.com/write-my-essay/dtreg.com/rbf.htm, And Radial basis
function network, http://en.wikipedia.org/wiki/Radial_basis_function_network
3.2 Data envelopment analysis(DEA)
In fierce competition, it is very important to measure how resources are used, whether
they are optimally distributed. The more efficiently the resource is utilized, the higher
profit the company can achieve.
Data envelopment analysis (DEA) is a non-parametric method in operations research
and economics for the estimation of production frontiers. It is used to empirically
measure productive efficiency of decision making units (or DMUs). In 1978, Charnes,
Cooper & Rhodes (CCR for short) applied the linear programming to estimate an
empirical production technology frontier for the first time. Since then, people have
used DEA to solve various problems. There are two basic types of DEA: CCR-DEA,
BCC-DEA.
 The CCR-DEA is the first DEA model obtained by Charine in 1978, and it is
mainly used in the analysis of technical efficiency. It assumes constant returns to
scale so that all observed production combinations could be scaled up or down
proportionally.
 The BCC-DEA is raised by Banker, Charnes and Cooper in 1984, and this model
is applicable for estimation of pure technical efficiency and scale efficiency. It
allows for variable returns to scale and is represented by a piecewise linear
convex frontier.
If we put the frontier of BCC and CCR into one graph, the efficiency point of
CCR-DEA is the “absolute efficiency”. But the frontier of BCC-DEA can be generally
divided into 3 parts, including “BCC-DEA efficiency>CCR-DEA efficiency” (means
scale efficiency increase at the beginning stage), “BCC-DEA efficiency=CCR-DEA
efficiency” and “BCC-DEA efficiency

28 It means 31 working days, from Monday to Friday.
82
New Algorithms can contribute a more efficient and better model. For example, in
theory, the genetic algorithm can improve the performance of BP network by
optimizing the weight. But in practice, performance is influenced by a lot of factors.
New algorithm also may foul the network. So in further study, let the facts speak.
 Standard access
In this study, all the calculations and transformations are based on Excel and
MATLAB, but the operation of commands was done manually, with lack of access
between each component. So in the future, based on this method, a new integrated
system can be developed to process the data automatically without human
intervention.
6.2 Optimization of the number of container cranes
 Conclusion
Firstly, in the development of global containerization, the challenges to ports
increased gradually, including the contrast between shipping lines` expectations and
congestion in ports, and fiercer competition against neighboring ports. So expansion
of new terminals is a good idea. Investment in new terminals is completely different
from expansion of an existing terminal because the known terminal can provide all
the data required by simulation programs. The simulation program will figure out the
“gooseneck” of the current system, and the expansion can be guided in terms of
balancing each component. In contrast, new terminal planning has to go forward in
the dark.
Secondly, because investment in new terminals contains high uncertainty, a practical
and efficient tool is needed to measure the performance of ports based on the known
data. So DEA, as an efficient tool to measure relative efficiency, is combined with
Artificial Neural Network, which provides effective ability of simulation. By training
BP network with 46 groups of data, the throughput for each different number of
cranes was estimated. Then another BP network was created to simulate the
input/throughput-efficiency pattern. After full training of the 2
nd BP network, the
input/estimated throughput was input into the model so as to get estimated efficiency.
83
After discussion of the result, the practical optimal option was chosen to achieve the
best throughput and efficiency.
This combination method can give better performance, compared to a pure linear
program DEA model, especially in a large population.
 Recommendations
 Classification of ports
As mentioned before, the main business of the port will affect the structure of
terminals. In further studies, it is better to classify the ports into several categories
based on the main cargo: regional hub ports, feeder ports, and mix of the two previous
ports. And 3 individual networks should be clearly trained by 3 different kinds of
ports, focusing on different cargo.
 Multiple goals
Because the networks in this case study are all single output, in fact, the ANN can also
solve multiple-goal problems. So in further studies, this model can be applied to
complicated situations, which contain multiple goals.
84
REFERENCE LIST
Akdemir, B., Bilgili, E., Ziarati, M., Stockton, D. (2008). Supply and demand in
shipping market using intelligent neural networks. Internation Maritime
Lecturers Association 16th Conference on MET, Izmir, Turkey.
Devcic, J. Weighted Moving Averages: The Basics. Retrieved July 20, 2012 from
https://monkessays.com/write-my-essay/investopedia.com/articles/technical/060401.asp#axzz25dIkTM00
Moon, S.H. (2011). SPM 232: Port Management unpublished handout. World
Maritime University, Malmö, Sweden.
Barros,C, Haralambides, H. Hussain, M & Peypoch, N. (2011). Seaport efficiency
and productivity growth. International Handbook of Maritime Economics
(2011). (pp 363-382). Edward Elgar, Celtrnham, UK.
Beenstock, M. & Vergottis, A. (1993). Econometric modeling of world shipping.
London: Chapman & Hall
Bergantino, A.S. & Musso, E. (2011). A multiple-step approach to model the relative
efficiency of European ports: the role of regulation and other non-discretionary
factors. International Handbook of Maritime Economics (2011). (pp 383-404).
Edward Elgar, Celtrnham, UK.
Bibby Ship Management & Dehutech, Guideline for lay-up of ships. Retrieved July
20, 2012 from
https://monkessays.com/write-my-essay/gac.com/upload/GAC2010/Brochures/Solutions/Ship%20Lay%20U
p%20Guidelines%20Mar10.pdf
85
Buhmann, M. D. (2003). Radial Basis Functions : Theory and Implementations. (pp
209-230) Cambridge University Press, West Nyack, NY, USA.
Cariou, P. and Notteboom, T. (2011). Bunker costs in container liner shipping: are
slow steaming practices reflected in maritime fuel surcharges? Current Issues in
Shipping, Ports and Logisitics. (pp 69-82). Uitgeverji UPA University press
Antwrep, Belgium
Certin, C,K. & Cerit, G. (2010). Organisational effectiveness in seaports: a system
approach. International Handbook of Maritime Business (2010). (pp 174-197).
Edward Elgar, Celtrnham, UK.
Chau, Foo-tim Gao, Junbin Liang, Yi-zeng (2004). Chemical Analysis, Volume 164 :
Chemometrics : From Basics to Wavelet Transform. (pp 1-22, 99-147).
Wiley-Interscience, Hoboken, NJ, USA.
Cooper, W. W. Seiford, L. M. Zhu, J. (2004). Handbook on Data Envelopment
Analysis. (pp 1-22, 41-49). Kluwer Academic Publishers, Hingham, MA, USA.
Cullinane, K.P.B. & Wang, T.F. (2006). The efficiency of European container ports:
A cross-sectional data envelopment analysis, International Journal of Logistics
Research and Applications: A Leading Journal of Supply Chain Management,
9:1, 19-31″
de Koster, M.B.M.,Balk, B.M., van Nus, W. (2008). The applicability of data
envelopment analysis to benchmarking of container terminals. Retrieved July
20, 2012 from
https://monkessays.com/write-my-essay/google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&cad=
rja&ved=0CDwQFjAD&url=http%3A%2F%2Fwww.mhia.org%2Fdownloads
86
%2Findustrygroups%2Fcicmhe%2Fcolloquium%2F2008%2Fde%2520Koster.p
df&ei=gnxGUML6E8Hh4QSptoC4Bg&usg=AFQjCNEBgB8G8WgtUaXGVi
MDHBHxi442RA
Drewry Shipping Consultant (1999-2012). The Drewry Monthly. Drewry Shipping
Consultants Limited, London, UK.
DTREG. RBF Neural Network. Retrieved July 20, 2012 from
https://monkessays.com/write-my-essay/dtreg.com/rbf.htm
Duc, T.L. (2005). Forecasting dry bulk freight market. World Maritime University,
Malmö, Sweden.
EEO. The shipping market in the first half year: Index below 1000 point, competition
of loss (Chinese Version). Retrieved July 20, 2012 from
https://monkessays.com/write-my-essay/eeo.com.cn/2012/0710/229663.shtml
Erdem, S. & Kocakoc, I.D. (2010). A new ANN training approach for efficiency
Assessment, Hacettepe Journal of Mathematics and Statistics, Volume 39(3)
(2010), 439-447.
ESA. Neural Network Glossary. Earth Home 4.2.5. European Space Agency.
Retrieved July 20, 2012 from
http://envisat.esa.int/handbooks/meris/CNTR4-2-5.htm
Fayyad, U.,Piatetsky-Shapiro, G., & Symyth,P. (1996). From Data Mining to
Knowledge Discovery in Databases. Retrieved July 20, 2012 from
https://monkessays.com/write-my-essay/kdnuggets.com/gpspubs/aimag-kdd-overview-1996-Fayyad.pdf
87
Fine, T. L. Lauritzen, S. L., Lawless, J. (1999). Feedforward Neural Network. (pp
144-161). Methodology. Springer, Secaucus, NJ, USA.
Global Security. Container ship types. Retrieved July 20, 2012 from
https://monkessays.com/write-my-essay/globalsecurity.org/military/systems/ship/container-types.htm
Graupe, D. (2007). Principles of Artificial Neural Networks (2nd Edition). World
Scientific, River Edge, NJ, USA.
Hansen, J.V.* andNelson, R.D. (2003). Forecasting and recombining time-series
components by using neural networks. Journal of the Operational Research
Society (2003) 54, 307-317
Hu J.S., Xiao D.R., & Xia J.M. (2005). Analysis of forecasting economy based on
the wavelet neural network. Nanjing University of Information Science and
Technology, Nanjing, China.
Internation Maritime Organization, The development of the Hong Kong Convention.
Retrieved July 20, 2012 from
https://monkessays.com/write-my-essay/imo.org/ourwork/environment/shiprecycling/pages/Default.aspx
ISL, Shipping Statistics Yearbook (from 1997 to 2012). Institute of Shipping
Economics and Logistics, Bremen, Germany.
Jiang, P.F., Cai, Z.H. (2006). Combined algorithms for training RBF neural
networks based on genetic algorithms and gradient decent. Journal of Computer
Applications 2007, 27(2) 366-368
Lloyd`s List (1993-2012). Lloyd`s Shipping Economist Monthly. Lloyd`s List,
London, UK
88
Lyrids,D.V., Zacharioudakis, P., Mitrou, P., & Mylonas, A. (2004). Forecasting
Tanker market using Artificial neural networks. National Technical University
of Athens, Athens, Greece.
Ma, S. (2011). Maritime Economics. Unpublished lecture handout, World Maritime
University, Malmö, Sweden.
MATLAB,Wavelet Families, Matlab Product Documentation. Retrieved July 20,
2012 from https://monkessays.com/write-my-essay/mathworks.se/help/toolbox/wavelet/ug/f8-24282.html
NIST. Box-Jenkins models. Engineering Statistics Handbook 6.4.4.5. Retrieved July
20, 2012 from
https://monkessays.com/write-my-essay/itl.nist.gov/div898/handbook/pmc/section4/pmc445.htm
NIST. Introduction to Time Series Analysis. Engineering Statistics Handbook. 6.4.
Retrieved July 20, 2012 from
https://monkessays.com/write-my-essay/itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm
Niu D.X., and Xing M. (1999), A Study on Wavelet Neural Network Prediction
Model of Time Series, Systems Engineering-theory & Practice, (1999) 5
Notteboom T. (2006). The time factor in liner shipping service. Maritime economics
& logisitics, 8:1, (pp 19-39)
Panayides, P. & Lambertides, N. (2011). Fundamental analysis and relative
efficiency of maritime firms: dry bulk vs tanker firms. International Handbook
of Maritime Economics (2011). (pp 85-106). Edward Elgar, Celtrnham, UK.
89
Shipping Information, The price of new building ship fell to lowest in the past 8
years, experts say in the next three years, 50% of the ship enterprises will go
bankruptcy (Chinese Version). Retrieved July 20, 2012 from l
http://ship.csi.com.cn/face/hyzxNews/20120702092706.html
Steenken, D., Vob, S., Stahlbock, R. (2005). Container terminal operation and
operations research – a classification and literature review. Container
Terminals and Automated Transport Systems. (pp 3-50). Springer, Berlin,
Germany.
Stopford, M. (2009). Maritime Economics, 3rd edition. London: Routledge.
Tao C. (2011). Quay efficiency of container terminals: Comparison between ports in
China and its neighboring ports. Current Issues in shipping, ports and logistics.
(pp 299-314). Uitgeverji UPA University press Antwerp, Belgium
The Baltic Exchange, Baltic Dry Index. Retrieved July 20, 2012 from
https://monkessays.com/write-my-essay/balticexchange.com/
United Sates Census Bureau. Monthly & Annual Retail Trade. Retrieved July 20,
2012 from https://monkessays.com/write-my-essay/census.gov/retail/
Veenstra, A.W. (1999). Quantitative Analysis of Shipping Markets. Delft: Delft
University Press.
Visvikis, I. (2011). SPM 230: Quantitative Methods and Market Analysis
unpublished handout. World Maritime University, Malmö, Sweden.
Voudris, A.V. (2006). Analysis and forecast of the capesize bulk carriers shipping
90
market using artificial neural networks. Massachusetts Institute of Technology,
USA.
Wang, D. (2009). Analysis of volume of vessel traffic based on BP neural network.
Wuhan University of Technology, Wuhan, China
Wei, H. (2006). The application of economic cybernetics to forecast in dry bulk
market. Dalian Maritime University, Dalian, China
Wikipedia. Artificial Neural Network. Retrieved July 20, 2012 from
http://en.wikipedia.org/wiki/Artificial_neural_network
Wikipedia. Fourier Transformation. Retrieved July 20, 2012 from
http://en.wikipedia.org/wiki/Fourier_transform
Wikipedia. Gradient descent. Retrieved July 20, 2012 from
http://en.wikipedia.org/wiki/Gradient_descent
Wikipedia. Haar Wavelet. Retrieved July 20, 2012 from
http://en.wikipedia.org/wiki/Haar_wavelet
Wikipedia. Maersk Triple-E Class. Retrieved July 20, 2012 from
http://en.wikipedia.org/wiki/Maersk_Triple_E_class
Wikipedia. Radial basis function network. Retrieved July 20, 2012 from
http://en.wikipedia.org/wiki/Radial_basis_function_network
Wikipedia. Regression Analysis. Retrieved July 20, 2012 from
http://en.wikipedia.org/wiki/Regression_analysis
91
Wikipedia. Wavelet Transformation. Retrieved July 20, 2012 from
http://en.wikipedia.org/wiki/Wavelet_transform
92
APPENDEX: A
The common used wavelet functions
As we mentioned before, the wavelet function is flexible, people can create their
wavelet function according to their goal as long as these function follows the
characteristic of wavelet.
 Haar
The Haar wavelet is also the simplest possible wavelet, proposed in 1909 by Alfréd
Haar. The problem is that it is not continuous and therefore not differentiable because
the function contains several quantum transitions.
The Haar wavelet’s mother wavelet function can be described as
The father wavelet:
Figure Illustration of Haar wavelet
 Daubechies wavelet
Named after Ingrid Daubechies, the Daubechies wavelets are a family of orthogonal
wavelets defining a discrete wavelet transform and characterized by a maximal
number of vanishing moments for some given support.
Except db1(it`s actually haar), other dbN have no clear expression.
93
It has several characters:
If P(y) = ∑
−1 −1
=0

, then
| 0( )|
2 = ( 2

2
)
∙ (sin2

2
)
Where 0
( ) =
1
√2
∑ ℎ
2 −1 −
=0
Effective supporting length of the wavelet function and scaling function is 2N-1, and
the wavelet function vanishing moments is N.
Most of dbN don`t have symmetry, but they are all orthogonal.
The regularity will increase due to the rise of series Number N.
 Symlets wavelet
The symN wavelets are also known as Daubechies’ least-asymmetric wavelets. The
symlets are more symmetric than the extremal phase wavelets. In symN, N is the
number of vanishing moments. These filters are also referred to in the literature by the
number of filter taps, which is 2N.
Figure Illustration of Sym wavelet
Source: Matlab Product Documentation,
https://monkessays.com/write-my-essay/mathworks.se/help/toolbox/wavelet/ug/f8-24282.html
 Coiflet wavelet
Coiflets are discrete wavelets designed by Ingrid Daubechies, at the request of Ronald
Coifman, to have scaling functions with vanishing moments. The wavelet is near
symmetric; their wavelet functions have vanishing moments and scaling
94
functions , and has been used in many applications
using Calderón-Zygmund Operators.
Figure Illustration of Coiflet wavelet
Source: DaBler, Coiflet, Wikipedia, http://en.wikipedia.org/wiki/Coiflet
 Biorthogonal Wavelet Pairs
The Haar wavelet is the only orthogonal wavelet with linear phase. You can design
biorthogonal wavelets with linear phase. Biorthogonal wavelets feature a pair of
scaling functions and associated scaling filters — one for analysis and one for
synthesis. There is also a pair of wavelets and associated wavelet filters — one for
analysis and one for synthesis.
 Mexican Hat Wavelet
This wavelet is proportional to the second derivative function of the Gaussian
probability density function. The wavelet is a special case of a larger family of
derivative of Gaussian (DOG) wavelets.
The mother wavelet:
ψ(x) =
2
√3
π
−
1
4(1 − x
2
)e
−
x
2
2
It is the second derivative of Gaussian function.
There is no scaling function associated with this wavelet.
The analysis and synthesis wavelets can have different numbers of vanishing
moments and regularity properties. You can use the wavelet with the greater number
of vanishing moments for analysis resulting in a sparse representation, while you use
the smoother wavelet for reconstruction.
We can find 7 wavelets in MATLAB software, and we will test the performance one
by one, finally get the most suitable one.

Order | Check Discount

Tags: AI Plagiarism free essay writing tool, Australian best tutors, best trans tutors, buy essay uk, cheap dissertation writer