=Paper=
{{Paper
|id=Vol-2732/20200839
|storemode=property
|title=Choice of Ship Management Strategy Based on Wind Wave Forecasting
|pdfUrl=https://ceur-ws.org/Vol-2732/20200839.pdf
|volume=Vol-2732
|authors=Lyudmila Kravtsova,Tatyana Zaytseva,Anna Puliaieva
|dblpUrl=https://dblp.org/rec/conf/icteri/KravtsovaZP20
}}
==Choice of Ship Management Strategy Based on Wind Wave Forecasting==
https://ceur-ws.org/Vol-2732/20200839.pdf
Choice of Ship Management Strategy Based on Wind
Wave Forecasting
Lyudmila Kravtsova[0000-0002-0152-635X], Tatyana Zaytseva[0000-0001-6780-719X] and
Anna Puliaieva[0000-0003-0595-6709]
Kherson State Maritime Academy, 20 Ushakova Str., Kherson, 73000, Ukraine
limonova@ukr.net, sunny@ksu.ks.ua, leon85517@gmail.com
Abstract. The foundation of scientific research is being laid during the learning
of navigator in higher school. As in any technical institution, in Kherson State
Maritime Academy such basic disciplines as Higher Mathematics, Physics, and
Information Technologies are taught from the first year of study. Curricula based
on a competent approach to marine specialist training provides not only
mastering the one or the other discipline, but also able to use the obtained
knowledge in the professional activity. This article focuses on such an important
question as a choice of ship management strategy based on the natural
phenomena forecasting conducted on the results of statistical observations on
environment behaviour, which surrounds a ship. Since task solution of analysis
and forecasting is related with the usage of mathematical apparatus, study this
theme within of the discipline “Information Technologies”, using possibilities of
electronic tables, is supported by mathematical methods of construction of
regression equations, solution of algebraic equations systems and in more
difficult cases – solution of differential equations systems in partial derivatives.
The modern development of information technologies and the power of software
allow filling the educational material of disciplines with applied, professionally-
oriented tasks. The using of mathematical modelling apparatus allows students
to be able to solve such tasks.
Keywords: Forecasting, Natural phenomena, Wind wave, Mathematical model,
Regression equation.
1 The general problem statement and its actuality
Systematic study of researching results of water resources behaviour, weather
conditions, natural phenomena recorded in the form of statistic data contributed to the
development of the methodological basis of analysis and forecasting processes which
affect to the strategy of ships various purpose using in the all human activities. The
analysis of researching results often makes possible to conclude about cyclicity of
phenomena. It allows forecasting the climatic peculiarities of the region at one or
another time interval. It ensures the safest ship’s movement tactics.
The information about dangerous and especially dangerous phenomena that can
harm or break the terms of the voyage has a special value for the ship and its crew. The
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
largest number of studies is taking place in busy navigation and fishery. The distribution
maps of water temperature and wave height on the seas and oceans are built by received
information, and meteorological characteristics, compiled on these data.
Forecasting of natural phenomena that have different, both positive and negative
influence on the strategy of ships using is the integral part of the scientific approach to
management decision. Decision making by the chosen criterion is particularly relevant
in the extreme working conditions at the sea. Sometimes ship’s fate, health and lives of
the crew depend on that decision. The foundation of forecasting is the base of the main
features of studied phenomenon formed accordingly the analytical support of the future
mathematical model.
The current stage of development of marine forecasts is characterized by using
traditional and new methods of forecasting. Besides, modern computer technologies are
widely used in the development of forecasting methods and in making operational
marine forecasts.
In Kherson State Marine Academy (KSMA) the first year students study the
discipline “Information Technologies”. Its curriculum has several chapters “Work in
Spreadsheets”, “Conducting of calculations for navigators”, “Solving of optimization
tasks using MS Excel”, “Data analysis and forecasting”. The purpose of studying of the
course material is not mastering the amount of knowledge in subject field activity but
to form skills, abilities and competences which will provide the ability to analyze
information and predict the behavior of the system for the next period, and to find the
necessary ways to solve problems related to the performance of social and professional
functions. The applied orientation of the discipline allows qualitatively forming subject
competences connected with the using of data processing methods, calculation
methods, mathematic and information modelling, business graphics.
This article focuses on the one of discipline chapter “Data analysis and forecasting”
on the example of mathematical modelling of the phenomena forecasting connected
with professional marine activity based on results of statistical observations of the water
environment behaviour.
2 Analysis of recent research and publications, which launched
the solution to this problem
Vasilii V. Shuleikin [25] has been greatly contributed to the tropical storms, ice, and
wind wave researches. His works are in fact the theoretical basis of methods for
predicting water temperature and have received the further development in modern
researches of the features and regularities of the water environment. The study [2] is
concentrated on analysis and methods of solving operational oceanographic service
tasks. It covers such areas as hydrologic prediction (heat and water balance, ocean-
atmosphere interaction), windswell forecasts, sea current and level forecasts, and ice
prediction. The automated calculation system of optimal navigation course is built
based on short- and long-term forecasts.
The works of Igor V. Lavrenov [14], Evgenii S. Nesterov [19], Leonid I. Piterbarg
[21] are dedicated to mathematical modelling of wind swell in the spatially and non-
homogeneous ocean. Aleksandr P. Khain [10] paid much attention to mathematical
modelling of tropical cyclones. The manual “Marine Forecasting” [3] focuses directly
on the methodological, statistical, mathematical fundamentals of the forecasting and
reliability assessment, where detailed information on the gathering methods and
analysis of data on the state of the sea and the oceans is offered, physicomathematical
models of the short-term, long-term and over long-term forecasts of the main elements
of the marine regime are considered. For example, the wind swell forecast provides
practical advice on how to navigate the ocean.
Foreign researchers have also made a great contribution to analysis and forecasting
of processes that affect to safe navigation (K. D. Pfeiffer [20], John Andrew Ewing [7]
and others).
Fundamentals of numerical methods for solving problems are published in scientific
and educational publications by Liudmyla I. Bilousova [4], Steven C. Chapra [5], Joe
D. Hoffman [9], Illia O. Teplytskyi [23], Serhiy O. Semerikov [24]. Modern
applications of numerical methods are associated with the use of information
technology, so many scientists consider the MS Excel spreadsheet as a computer
environment for modeling, such as Mohamed A. El-Gebeily [6] and Leonid O.
Flehantov [8].
Problems of introduction of computer modelling in the study of informatics
disciplines paid attention to Hennadiy M. Kravtsov [11], Lyudmila M. Kravtsova [27],
Maiia V. Marienko [16], Oksana M. Markova [15], Yevhenii O. Modlo [18], Pavlo P.
Nechypurenko [17], Yaroslava B. Samchynska [22], Mariya P. Shyshkina [26],
Tatyana V. Zaytseva [27].
Modern operative oceanography develops by integration of many countries’ efforts.
International projects involving Germany, Italy, Portugal and the Netherlands are being
successfully implemented. Understanding of importance direction in the study of World
Ocean allows developing research effort that an improvement ship coordination and
disaster prevention systems to ensure safe navigation are resulting.
3 Solving basic problems
Hydro-meteorological stations are the main source of statistical data. Their information
is data about the past, present and future state of the seas and oceans, based on
observations and appropriate methods of analysis and forecasting of oceanographic
characteristics. Increasing of incoming information from all of its sources requires the
introduction of new methods for the collection, transmission, processing and storage of
hydro meteorological information. The use of modern computer technologies makes it
possible to automate the process. It is clear, research work which is being done in this
direction and its application are needed.
Unnatural hydro-meteorological conditions are particularly dangerous and scientific
interested. Hydro-meteorological processes that, in terms of time, intensity, duration
and area of occurrence, can cause significant damage or natural disasters relate to
hydrologic extremes. There are dangerous and especially dangerous hydrological
phenomena [13] on the seas and oceans, such as:
1. Irregular sea level variations (above or below critical points) in which populated
places and coastal installations are flooded, ships and other household objects are
damaged, and navigation is stopped.
2. Tsunamis that cause a sea level rise of 2 m or more.
3. Wave height is 8 m or more in the oceans; and wave height in the sea that are
dangerous for navigation, fishing and coastal installations.
4. Tropical storms and typhoons when wind speed is 35 m/s and more.
5. The appearance of the ice cover at an unusually early date; is repeated no more than
once every 10 years.
6. The pressure drift of floating ice that threatens oil rigs, flyovers and other facilities.
7. Ship icing when rate of ice growth is 0.7 cm/h or more.
8. Strong riptide in the port waters.
Danger warning of port services, port-side territories, ships in the waters, maritime
industries and population are faced by and caused by adverse hydrologic events is an
important practical task. The initial materials for the warning are:
1. Forecast of an expected hydrologic hazard and the time of its occurrence.
2. Hydrologic hazard criteria.
Forecasting Methodological Bases. Hydro-meteorological condition forecasting
provides for a scientific evidence system, development of different hypotheses and
using methods that characterized by mathematical formalization [9]. The variability of
oceanological processes depends on a rangier of factors, so marine forecasts tend to
have a probabilistic nature. The long-term prediction of any characteristics of the seas
and oceans regime can only be made approximately because all influencing factors to
this process are unknown. Next, the forecasting methods as usually are based on the
using discrete values of characteristics which also brings a certain error in the study
results of this process.
Applying of cyclicity that discovered on a long series observations of forecasted
characteristic is useful in a long-range marine prediction techniques besides physical
patterns. Some methods of over long term forecasts take into account the influence of
space and global geophysical factors (solar activity, long tides, fluctuations in the
Earth’s rotation axis, etc.).
Usage of the linearized system of hydrodynamic equations and simultaneously a
non-linear model development is the methodological basis for the work on numerous
long-term forecasts. Applying of statistical characteristics to solve the
hydrothermodynamics equations is quite possibly. Space-time correlation relations
between phenomena are established with the help of statistical methods. The advantage
of using this approach to the forecasting problem is that own correlation matrix
functions a priori contain useful information about the structure of some or other hydro-
meteorological fields.
Methods of probability theory, mathematical statistics, factor and spectral analysis,
differential equations describing physical processes whose characteristics form the
basis of research are most commonly used as the mathematical apparatus in marine
hydrologic prediction.
So, two main directions are considered in the development of marine forecasting
techniques: physicostatistical and hydrodynamic. Using of the physical hypothesis that
reveals the interrelations between predictors (factor feature or prediction parameters)
and predictant (the resultant factor, or value that at the some point in time is determined
using predictors) underlies physicostatistical direction. The physical hypothesis
facilitates the task of applying statistical methods in forecasting.
Statistical methods for forecasting are provided an opportunity to evaluate the
development of hydro-meteorological processes in the future based on the results of
past observations using knowledge of probability characteristics of these processes. An
observation series of the predicted characteristic and factors that it depends on is
composed to establish a link between investigated quantities. Methodology
development suitable for making operational forecasts is a complex scientific study that
can be broken into several stages.
At the first stage of study a general patterns between phenomena are identified and
main factors are determined. As forecasting experience has shown, many predictors
that are used in the methods do not improve forecast quality. The optimal number of
predictors is three or four as a rule. The optimal number of predictors is three or four
as a rule. The optimal number of predictors understands a set of predictors when further
increase their number does not lead to an increase of the correlation coefficient and
improving forecasting results. The right decision when choosing the number of
predictors is greatly facilitated development of forecast method and ensures the
increased reliability of operational forecasts.
In the second phase of forecast methodology development, a general physical
regularity that was previously identified applies to specific physical and geographical
sea conditions. For this purpose, observational data that needed to develop of the
method are carefully analysed for representativeness and comparability of observations
in different years. Methods of operative forecast are usually local because World Ocean
basins are very different on physico-geographical and ocean conditions. Attempts of
researchers to create a common forecasting methods that would be suitable for large
areas of the seas and oceans have not yet led to positive results, because of global
differences in the basic characteristics of these objects.
A third stage is start of receiving predictive quantitative dependencies. Graphical
comparison of predicted element with predictors should be considerate as a visual way
to find connections. This technique gives possible not only to establish the existence of
a statistical relationship, but also to determine the type of its dependency. A detailed
analysis of the deviations should be made, and determine the reasons that led to a
disturbance in the general regularity. The wider points’ variation on the link’s graph,
the more influence degree of random factors.
Development of forecasting method of the oceanological phenomena, such as: wind-
wave, marine currents, fluctuations, water temperature, etc., usually begins from with
analysing and generalizing ideas about the general physical regularity of predicted
phenomena, searching for factors that affect its changes in time and area, and identify
among them the most informative in the prognostic sense. Other words, a researcher
accepts the general provisions (hypothesis) based on the examination of priory
information about these phenomena that characterize relation, which must be found
between the predicted phenomenon (predictive) and factors that cause it (predictors).
The next stage is the choice of the most adequate mathematical apparatus, which
would allow the best approach to the problem, that is, the creation of a reliable forecast
method.
Then, hydrodynamic methods of the forecast are based on solving of hydro- and
thermodynamics equations. As of today, with some simplifications, numerical analysis
for short-term forecasts of storm surges, water temperatures of the upper quasi-
homogeneous ocean layer and its thickness, ice formation period, ice thickness
increasing and melting of snow and ice cover have developed. For example, when
ocean physical processes are described for Southern Hemisphere, such equations of
thermodynamics of turbulent liquid can be accepted:
for moving:
du 1 p u
fv k
d p x z z (1)
du 1 p v
fu k (2)
d p y z z
p
g (3)
z
for continuity:
divhu 0 (4)
z
for heat distribution:
t t t
u grad ht kt Q (5)
z z z
for salt distribution:
S S S (6)
u grad h S kS
z z z
for state of sea water:
(t , S , P ) (7)
where all parameters of the relation represent some characteristics of sea water
condition.
This example illustrates, how complex the mathematical model of the phenomenon
studied can be. The solution of hydrodynamic equations without professional
mathematical training is practically impossible.
Students of Kherson State Maritime Academy learn discipline Information
Technologies in the first year. It is clear that the first-year student hasn’t sufficient
mathematical knowledge to comprehend the essence of such equations. However,
understanding of the importance of the data analysis and prediction, the main methods
for their solving, possibility using in the professional navigational workload – quite an
achievable task. Weak students’ knowledge in the field of mathematics is a one of the
problems that first-year students face from one side and teachers, which work with them
from the other side. Therefore, the task before teacher is to systematize them
knowledge, increase level of understanding mathematical formulas, recognizing them
not as just “picture”, but as an instruction for action that result is strategy to ship and
crew management. And thanks to the applied aspect of mathematical models, student
interest to natural-science disciplines can be increased.
Most simple way to objectively realization of information that’s based on statistical
observations for forecast of ocean phenomena is constructing a regression equation.
Application of the mathematical statistics apparatus provides availability of long
enough series of observations for predicant and predictors. These temporary series can
be considered as system of random correlated variables. The normalized correlation
matrix is a good feature of relations in such systems.
Functional dependence is a most studied kind of link between quantities, in term of
implementation, when each value of one quantity (factor sign) X corresponds to quiet
defined value (result sign) Y. But in practice, as a rule, have not dealt with functional
dependencies, but of statistical ones. In this case, for each value of one quantity
corresponds many possible values of another. Dispersing of possible values explains
by the influence of many additional factors, which usually neglected when relations
between quantities are studied. A dimensionless correlation coefficient characterizes
the measure of linear dependence between variables, that in absolute value no more
than one: abs(r) ≤ 1.
Correlation coefficient equals zero for independence quantities X and Y. Equality of
the correlation coefficient to zero means that linear dependence is absent (but does not
eliminate nonlinear dependence). Another correlation methods are used in nonlinear
relationship. The closer the absolute value of correlation coefficient is to one, the closer
the linear dependence between quantities. Equality of correlation coefficient to one
means that functional dependence is present between X and Y. Correlation coefficients
don’t change when starting point and measurement scale of quantities of X and Y are
changed. It makes possible for significantly simplify the calculation by selecting a
convenient starting point (X0, Y0) and corresponding units of scale. The correlation
coefficient and regression equation for both variables can be found approximately from
the correlation chart, and more accurately – by method of least squares.
First-year students, at the time of studying the topic “Data Analysis and Forecasting.
Linear and quadratic regressions” have fully mastered the basic techniques of MS Excel
spreadsheets, have skills (in accordance with a course syllabus) to solve systems of
linear equations using the Cramer method and matrix method, calculating the inverse
matrix and matrix multiplication operations using built-in functions. In terms of
obtaining parameters of the linear and quadratic dependences in accordance to the
method of least squares for building of an optimal analytical function, that’s enough, if
student’s understanding of the problem formulation, its solving methods and analysis
of the obtained results. Appropriate theoretical material and stepwise solution of the
classical task of the task of finding dependency parameters of linear and quadratic
regression for students are posted on the discipline “Information technologies”
webpage of the E-learning system KSMA (based on the Moodle).
Our objective is to show student, the future navigator, how important to have the
analysis skills of real situation based on observations, to forecast, to apply their
knowledge in practice, to make the right management decision. For this purpose, real
application tasks are proposed to the student after the techniques of solving the classical
task of linear and quadratic dependence equations constructing founded by the table
data (results of observation) he has mastered.
Consider a typical task of wave height forecasting depending on wind speed and the
duration of its effects (forecasts of wind waves).
As a result of the enhancement of sea economic activity, the knowledge of its
condition and forecast changes is of great practical importance [9]. Accordingly, the
role of the wind swell forecast significantly increases.
Using of information about actual and expected conditions of wave swell helps to
successfully navigate the most profitable routes, water landing, offshore drilling,
effective and safe fishing, sea loading, sporting regattas, etc.
Characteristics of the maximum waves are most important characteristic of sea
swell, because these waves are the most dangerous for ships and hydrotechnical
structures. Therefore, the efficiency of the swell forecast depends largely on how well
predict characteristics of the maximum wave. Note that, the term “forecast” for wind
swell is used conventionally to difference retrospective calculations from the daily
operational calculations of the meteorological predictions of the wind field.
The main elements of wind waves are: height H, period Т, length X, phase speed C,
steepness E ridge length L.
In case sea depth is more than half the wavelength, wave elements are independent
of the depth. If sea depth is less than half the wavelength, then wave elements are
change influenced by seabed. The concept of “deep water” has a relative meaning and
is defined by the ratio of depth H and wave length X.
Table 1 data are the basis material of parameters for analysis and making forecast.
Table 1. Wave height depending on wind time
Wind duration (in hours)
Wind speed
5 10 15 20 30 40 50
10 knots 2.0 2.0 2.0 2.0 2.0 2.0 2.0
15 knots 3.5 4.0 4.5 5.0 5.0 5.0 5.0
20 knots 5.0 7.0 8.0 8.0 8.5 9.0 9.0
30 knots 9.0 13.5 15.5 17.0 18.0 18.5 19.0
40 knots 13.5 21.0 25.0 27.5 31.0 32.0 33.0
50 knots 18.0 29.0 36.0 40.0 46.0 48.0 50.0
60 knots 23.0 37.0 46.0 43.0 61.0 66.0 70.0
The task is to determine the type and dependence parameters of the wave height on
the wind duration. Based on the table data where row number corresponds to the column
of wind duration that is measured in hours, the charts are drawn (see Fig. 1).
Fig. 1. Dependence of wave height on wind speed and duration
The created scatter chart allows making conclusion that in the wind duration from 5 to
15 hours the dependence can be approximated by linear function; in the wind duration
from 20 to 50 hours the dependence will be probably quadratic.
Let us find the dependence parameters which are relevant and evaluate average
squared deviation for each of obtained analytic relationships.
Three ways are offered to student for finding the parameters of linear dependency
that are determined by the solution of the equations’ system (8).
a n x 2 a n x n x y
0
i 1
i 1 i
i 1
i i
i 1 (8)
n n
a0 xi a1 n yi
i1 i 1
1. Using Cramer’s formulas.
n n n
n xi yi yi xi
i1 i1 i1 (9)
a0 n n n
n xi2 xi xi
i1 i1 i1
n n n n
xi2 yi xi xi yi (10)
i 1 i 1 i 1 i 1
a1 n n n
n xi2 xi xi
i 1 i 1 i 1
2. Using Excel’s built-in functions SLOPE (parameter а0) and INTERCEPT (parameter
а1).
3. Using Excel’s Solver add-in “Trendline. Linear”.
4. The objective of such approach is that student has to, firstly, understand analytic
formula, action order, can be possible to calculate by formula; secondly, to use built-
in functions and thirdly, to use add-ins.
Performing the calculations show that the results obtained by three different methods
match and confirm the hypothesis about linearity of dependences, because the
regression coefficients, that are corresponding, R2 (approximation reliability) are close
to 1 (the type of dependence is chosen correctly):
first row (wind duration 5 hours):
y 0,423x 3,004; R 2 0,995 (11)
second row (wind duration 10 hours):
y 0,71x 6,62; R 2 0,9946 (12)
third row (wind duration 15 hours):
y 0,893x 9,132; R 2 0,9909 (13)
Parameters of quadratic dependence y a0 x 2 a1 x a2 are determined by system
decisions:
a n x 4 a n x 3 a n x 2 n x 2 y
0 i 1
i 1 i
i 1
2 i
i 1
i i
i 1
n n n n (14)
3 2
a0 x i a1 xi a2 xi xi yi
i1 i 1 i 1 i 1
n 2 n n
a0
i 1
xi a1 xi a2 n yi
i 1 i 1
and are found by matrix method using built-in mathematical functions.
We will remind that system can be presented in matrix form = , where is the
coefficient matrix, is the unknown vector column, is the right part. If is the
inverse matrix, then solution of the system has a view = ⋅ . In our case the
parameters of quadratic dependence a0, a1, a2 will be system solution (built-in functions
MINVERSE and MMULT are used). Accordantly,
fourth row (wind duration 20 hours:
y 0,0115x 2 0,2714x 1,7868; R 2 0,9998 (15)
fifth row (wind duration 30 hours):
y 0,0115 x 2 0,3945 x 3,5319 ; R 2 0,9992 (16)
sixth row (wind duration 40 hours):
y 0,0144x 2 0,2763x 2,3435; R 2 0,9999 (17)
seventh row (wind duration 50 hours):
y 0,0166 x 2 0,2013 x 1,7246; R 2 1 (18)
Applying the obtained equations (analytical dependencies), it is possible to make a
wave height forecast for any wind duration and actually any wind speed.
An expert review of the proposed material was conducted to support expedience of
teaching “Data analysis and forecasting” of the course “Information Technologies” on
example of math modelling of wave height forecasting in depended on some nature
factors and also of the adequacy of the built model to the real conditions. For it, the
Method of Expert Estimations (or Delphi method) has been used. This method is the
following: expert group was requested to review the work, evaluate its professional
direction, reply to the questionnaire and draw conclusions about actuality of the
proposed study and the practical application of the obtained results.
The method is used for obtaining quantitative assessment of quality characteristics,
parameters and features. Analysis of expert estimations involves each expert
completing an appropriate questionnaire, which will help to obtain an objective analysis
of the problem and to develop possible solutions [12].
A group involved to work was consisted of marine industry specialists, chief officers
and sea captains who works at the academy or undergoes retraining and has extensive
experience on the ships. The twelve persons were invited for expert evaluation in a
total. The authors took into account such factors as competence, constructive thinking,
attitude to work as an expert when form expert group.
The purpose of expert estimation is an establishing of efficiency index (quality)
compliance of the proposed method of authenticity solving the real situation.
To confirm or contradict the research conclusions, we used the following forms of
conducting and processing expert evaluations:
1. Determining experts’ competence and forming of expert commission composition.
2. Construction of the quality weighting coefficients ranking.
3. Parameterization of quality indicators.
4. Conducting expert quality assessment.
Study of the adequacy of obtained examination results.
Expertise of computer modelling method efficiency when analysing natural
phenomena should take into account cognitive, software and technological,
psychological and pedagogical features.
The expert questionnaire consisted of 16 questions, 12 experts took part in the
survey. A quality indicator is number parameter which determines evaluation of the
method according to its qualitative characteristics, 5-Point Likert Scale [1] was used
for this.
For example, there is a table 2, which contains several questions.
Table 2. (Questionnaire fragment) Quality parameters and their weighting coefficients
Qualitative Weighting
No Name of quality
parameters coefficient
Full 5
Compliance with the STCW Convention, IMO Model
1 Lack of full 3
Courses, requirements of the Shipping Register of Ukraine
No 1
Full 5
Lack of full 4
Completeness of the proposed method for solving the
2 Average 3
problem
Below average 2
Low 1
Full 5
Lack of full 4
Feasibility of using mathematical modelling methods in
3 Average 3
teaching IT discipline
Below average 2
Low 1
High 5
Feasibility of using methods of mathematical modelling of
4 Average 3
wave height forecasting depending on certain natural factors
Low 1
Yes 5
5 Adequacy of built model to the real process Partly 3
No 0
Quality 5
Above average 4
Efficiency of computer-assisted processing of observation
6 Average 3
results
Below average 2
Low-quality 1
The expert evaluation of method efficiency will only be reliable if expert responses are
agreed, and concordance method will be used for this purpose.
When measuring the ordinal scale by the ranking method, the purpose of processing
the individual expert assessments is construction of generalized objects’ order based on
the averaging their assessments.
Using questionnaire data the summary rank matrix has been compiled (Table 3).
Table 3. Types of criteria
Types of criteria
Expert
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 3 8 13 4 7 2 6 9 5 12 10 11 16 14 15 1
2 4 10 11 6 8 2 3 5 7 12 9 13 14 15 16 1
3 3 10 12 7 8 2 6 4 5 11 9 13 14 15 16 1
4 4 7 10 6 8 2 5 3 9 12 11 14 13 15 16 1
5 2 10 14 9 8 3 12 4 5 6 7 11 13 15 16 1
Types of criteria
Expert
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
6 3 9 10 8 7 2 6 4 5 11 12 14 15 13 16 1
7 2 12 11 8 10 5 4 3 7 13 6 9 14 15 16 1
8 2 11 14 7 9 4 5 3 6 12 8 10 13 15 16 1
9 2 11 14 4 8 9 10 5 6 16 3 7 12 13 15 1
10 2 5 13 8 7 3 6 4 10 11 9 12 16 14 15 1
11 2 11 12 6 10 5 4 3 8 13 7 9 14 15 16 1
12 2 9 11 7 8 3 4 5 6 10 12 13 14 15 16 1
Δi -71 11 43 -22 -4 -60 -31 -50 -23 37 1 34 66 72 87 -90
Si 5041 121 1849 484 16 3600 961 2500 529 1369 1 1156 4356 5184 7569 8100
Let us calculate the concordance coefficient by formula:
12S
W (19)
m ( n 3 n)
2
Computed by the formula (19) coefficient W = 0,875 is closer to one (concordance
coefficient can vary from 0 to 1), so we can consider that the experts’ answers are
agreed.
Let us calculate the Pearson matching criterion to evaluate the significance of
concordance coefficient:
12S
W2 157,49 (20)
m n (n 1)
Calculated criterion χ2 is comparable to the table value for number of degrees of
freedom K = n – 1 = 16 – 1 = 15 and at the specified significance level α = 0,05.
Conclusions of expert commission. Since χ2 calculated is 157,49 that is greater than
or equal to critical (24,99579), so W = 0,875 is non-random value, therefore the experts’
conclusions confirm the practical significance of the results obtained in the article and
practicability of their use for further research.
4 Conclusions and directions for further research
A professional navigator, a specialist with advanced training, who claims an officer’s
position on a ship, has to know not only all the details of navigation and sailing
directions, ship’s construction, has skills to work with crew and so on. The navigator is
responsible for safety of navigation, safety of the ship, crew and cargo. So, he has to
follow the instructions of the coastguard controlling the ship’s movement, but to
analyze the current situation and forecast the consequences of his decisions.
The aim of the discipline “Information Technologies” is studying of the
mathematical (computer) modelling method, its application in various subject areas, as
well as ability to predict and analyse the results of obtained decisions. In other words,
the discipline lays one more necessary brick in the formation of competencies set of a
marine industry specialist.
The learning material of discipline provides that students solve problems formulated
in their subject area and related to formalization and further use of computer
technologies. Such tasks require considerable time for solving, system approach to
development.
In the using of information technologies, students practice skills of development of
information models, solution algorithms, evaluating of obtained results. They feel a
qualitatively new socially significant level of competence; develop professional
qualities of a person.
Significant number of navigational, engineering tasks is reduced to the solving of
the equations (inequations), the system of equations (system inequations), differential
equations or systems, calculating the integrals described objects or phenomena. Using
of mathematical (information) modelling methods, forecasting of decision-making
results in various activities demand specialists to mastery of the appropriate
mathematical apparatus.
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