International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 5

Number 4

December 2011

555

1 INTRODUCTION

A highly significant issue during the planning and

construction of the shore observatory stations net-

work is undoubtedly their proper location, as the

success of the entire investment depends on the right

positioning. The criterion for project evaluation may

be adopted on the basis of the extent of coverage of

the monitored area, the number of observatory sta-

tions used for this purpose and, hence, the degree of

maritime transport safety. Restrictions imposed on

such dilemma require a thorough analysis of the is-

sue long before the realisation of the project. Prob-

lem analysis ought to focus on the placement of

shore stations primarily. During the problem analy-

sis various possible locations and observatory station

types should be regarded. The results of completed

analysis should answer the question which of the

possible locations are the best for creating the suffi-

cient network of the shore observatory stations.

Above all, the choice of location ought to fulfil

marine shipping safety requirements, which are to a

great extent related to the warranty for the monitored

area coverage, as well as various technical and eco-

nomic aspects. Provided the system constructed is a

mere expansion of an already existing maritime traf-

fic monitoring system, it ought to take into account

existing observatory infrastructure.

2 FACILITY LOCATION AND LOCATION

SCIENCE

Facility location problems investigate where to

physically locate a set of facilities (resources, sta-

tions, etc.) so as to minimize the cost of satisfying

some set of demands (customers) subject to some set

of constraints. Location decisions are integral to a

particular system’s ability to satisfy its demands in

an efficient manner. In addition, because these deci-

sions can have lasting impacts, facility location deci-

sions will also affect the system’s flexibility to meet

these demands as they evolve over time.

Facility location models are used in a wide varie-

ty of applications. These include, but are not limited

to, locating warehouses within a supply chain to

minimize the average time to market, locating haz-

ardous material sites to minimize exposure to the

public, locating railroad stations to minimize the

variability of delivery schedules, locating automatic

teller machines to best serve the bank’s customers,

locating a coastal search and rescue station to mini-

mize the maximum response time to maritime acci-

dents, and locating a observatory stations to cover

monitored area. These six problems fall under the

realm of facility location research, yet they all have

different objective functions. Indeed, facility loca-

tion models can differ in their objective function, the

distance metric applied, the number and size of the

facilities to locate, and several other decision indi-

A Simulation Environment for Modelling and

Analysis of the Distribution of Shore

Observatory Stations - Preliminary Results

T. Neumann

Gdynia Maritime University, Gdynia, Poland

ABSTRACT: The paper has presented the usage of mathematical theory of evidence in evaluating of the pos-

sibility of o

bject detection by monitoring radar stations. The level of object detection allows for effortless

conversion to optimisation problem of monitored area coverage. Development of such task enables such dis-

tribution of observatory stations that maintains the detection rate higher than the assumed value. An appropri-

ate rate level is achieved by covering the analysed set of points with sufficient number of radar stations.

Combining evidence allows for calculating corresponding parameters for each set of observing equipment.

556

ces. Depending on the specific application, inclusion

and consideration of these various indices in the

problem formulation will lead to very different loca-

tion models (Hale & Moberg, 2003).

There exists two predominant objective functions

in location science: minisum and minimax. These

are also known as the median and centre problems,

respectively. The diametrics of these objective func-

tions also exist (maxisum and maximin), although

they are somewhat less studied. Other objective

functions are also studied within the location science

community, especially recently. The most notable of

these are the set covering and maximal covering ob-

jective functions. The former of these two objectives

attempts to locate the minimum number of new fa-

cilities such that a prescribed distance constraint to

existing facilities is not violated. In contrast, the lat-

ter strives to locate a given number of facilities to

best meet the (weighted) demands of the existing fa-

cilities subject to a maximum distance between new

and existing facility. It should be noted that for the

set covering formulation, because all of the demands

must be met (covered) regardless, the relative weight

of the demands generated by the existing facilities

are inconsequential, whereas in the maximal cover-

ing objective some existing facility demands may be

left unmet (uncovered).

Location problems are generally solved on one of

three basic spaces: continuous spaces (spatial), dis-

crete spaces, and network spaces. The first of these

three deals with location problems on a continuous

space (in one, two, or three dimensions) where any

location within the realm is a feasible location for a

new facility. The second looks at problems where

locations must be chosen from a pre-defined set

while the third looks at location problems that are

confined to the arcs and nodes of an underlying net-

work (Hale, Moberg, 2003).

3 MATHEMATICAL THEORY OF EVIDENCE

IN MARINE TRAFFIC ENGINEERING

3.1 The classical approach

The mathematical theory of evidence, one of various

tools employed in the application, will be used for

evaluating the possibility of objects detection by,

e.g., radio stations monitoring specified area. Ap-

proximate reasoning, the other significant element

used in the application, provides extrapolation and

interpolation of the incomplete knowledge of moni-

toring stations characteristics. The solution to the

problem of detection, namely assessing the possibil-

ity of detection by each station, allows for moving

on to the optimisation problem of supervised area

coverage. Such task can be solved by locating ob-

servatory stations in a manner enabling detection

level indicators to be higher than the assumed value.

An adequate level of indicator values is achieved by

covering a set of analyzed points with the relevant

number of suitably located stations. Detection levels

are estimated for a specific discrete search area with

regard to records consisting of observing equipment

data. Submission of records allows for calculating

appropriate parameters for each point of the ana-

lyzed area. Solving this problem is possible through

the mathematical theory of evidence.

The characteristics of each observatory station are

the starting point in the computational process. Suf-

ficient technical parameters provided by the equip-

ment manufacturers are incomplete values, calculat-

ed for a certain meteorological conditions at sea

(e.g., calm sea) and for typical naval units. Approx-

imate inference mechanisms as well as additional

knowledge of experts are needed, the latter being a

major source of output data due to the subjective ex-

pert assessment, affected by a degree of uncertainty.

This subjectivism requires the use of appropriate

mathematical apparatus. The mathema-tical theory

of evidence in its flexibility allows the use of fuzzy

and approximate figures. Calculation of masses of

the particular framework of discourse hypotheses

with use of membership function creates a structure

of beliefs enabling extensive use of the mathematical

theory of evidence.

Water areas monitoring is conducted with the use

of radar (among others), characterized, as any other

technical equipment, by certain limited level of

functioning and of reliability in the sense of realisa-

tion of basic tasks. The possibility of detecting ob-

ject is vital parameter of any device of this kind.

Modern monitoring stations are able to detect float-

ing objects in considerable distances. One may ven-

ture to say that their range is horizontal in fine hy-

drometeorological conditions. Obviously, the ability

to detect depends on the so-called Radar Cross Sec-

tion (RCS), a feature which is associated primarily

with the size of a given unit. Another significant pa-

rameter is a draft of a vessel, which in turn reduces

the above-water body, affecting directly the size of

the reflecting surface. Detection of smaller units at

rough sea may pose problems. Whether a specific

type unit will be detected in particular conditions

depends on the distance to the observatory station,

the sea state and the observing equipment character-

istics. In some areas the heavy maritime traffic calls

for an appropriate location of observatory stations

ensuring sufficiently high level of unit detection.

The Dempster–Shafer theory (DST) is a mathe-

matical theory of evidence. In Dempster-Shafer (DS)

theory, there is a fixed set of n mutually exclusive

and exhaustive elements, called the frame of dis-

cernment, which is symbolized by:

557

{ }

AAA ,...,,

=Ω

(1)

The representation scheme Ω describes the work-

ing space for the desired application since it consists

of all propositions for which the information sources

can provide evidence. Information sources can dis-

tribute mass values on subsets of the frame of dis-

cernment,

Ω

∈ 2

. An information source assign

mass values only to those hypotheses, for which it

has direct evidence.

( )

10 ≤≤

(2)

Basic Probability Assignment (BPA) has to fulfil

the conditions as follows:

( )

(3)

( )

∑

Ω

∈

(4)

If an information source cannot distinguish be-

tween two propositions,

and

, it assigns a mass

value to their union

( )

AA ∪

. Mass distribution

from different information sources, are combined

with Dempster’s rule of combination (5). The result

is a new distribution, which incorporates the joint in-

formation provided by the sources.

( )

AAAA

−













∑

∏

=∩∩∩

≤≤

...

(5)

( )

∑

∏

=∩∩∩

≤≤













AAA

AmK

...

(6)

A factor K is often interpreted as a measure of

conflict between the different sources (6) and is in-

troduced as a normalization factor (5). The larger K

is when the more the sources are conflicting and the

less sense has their combination.

If factor K = 0, this shows a consensus of opin-

ions, and if 0 < K < 1, it shows partial compatibility.

Finally, the Dempster’s rule of combination does

not exist when K = 1. In this case, the sources are to-

tally contradictory, and it is no longer possible to

combine them. In the cases of sources highly con-

flicting, the normalisation used in the Dempster’s

combination rule can be mistaking.

From a mass distribution, numerical values can

be calculated that characterize the uncertainty and

the support of certain hypotheses. Belief (7)

measures the minimum or necessary support where-

as plausibility (8) reflects the maximum or potential

support for that hypothesis.

( )

∑

⊆

AmABel

(7)

( )

∑

≠∩

AmAPl

(8)

3.2 Mathematical theory of evidence and fuzzy

values

When the assessment of the situation undergoes

solely a subjective expert rating, the results are only

to be obtained in form of linguistic variables. Theo-

ries presented show (Zadeh, 1975) possibility of

transforming such values into figures with use of the

fuzzy sets theory, a concept created by L.A. Zadeh

in the sixties of the 20th century and developed ever

since (mainly by its author), which increasingly in-

tercedes in various economic issues. According to

Zadeh, the aforementioned theory has not been suf-

ficiently employed for the purpose of detection anal-

ysis of marine units. A more extensive use of possi-

bilities offered by the fuzzy sets theory appears as a

necessity for rational construction of new maritime

traffic monitoring systems.

The mathematical theory of evidence deals with

function combining information contained in two

sets of assignments, subjective expert ratings. This

process may be interpreted as a knowledge update.

Combining sets results in forming of new subsets of

possible hypotheses with new values characterising

probability of specific options occurrence. The

aforementioned process may continue as long as

provided with new propositions. This function is

known as Dempster’s rule of combination.

A fuzzy nature can be attributed to events which

may be interpreted in fuzzy manner, for instance, in-

accurate evaluations of precisely specified distances

to any point. Subjective evaluations in categories:

near, far, very far may be expressed with fuzzy sets

defined by expert opinions. Such understanding of

fuzzy events is natural and common. Introduction of

events described by fuzzy sets moderates the manner

in which the results of processing are used, expands

the versatility of such approach, as well as changes

the mode of perceiving the overall combining proce-

dure. Deduction of specific events involved in the

process of combining pales into insignificance, as

obtaining information on related hypotheses is of

greater interest. Combining evidence of fuzzy values

brings new quality into knowledge acquisition due to

the usage of combination results as a data base capa-

ble of answering various questions. After combing

many fuzzy distances, the results allow to set the

support level for the veracity of statement claiming a

distance between a vessel and a barrier is very close,

safe or yet another. Other possibilities of the mathe-

558

matical theory of evidence in problems of navigation

can be found in Filipowicz, 2010.

As to the problem of monitored area coverage,

phrases used for assessing the distance of units will

be linguistically interpreted. The determination of

distance at which an object is located is possible

with use of linguistic values: very close, close, far,

very far. Particular linguistic expressions and corre-

sponding exemplary range of values are presented in

the Figure 1. More on this subject can be found in

Neumann, 2009.

very close

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

close medium far very far

Figure 1. Diagram of linguistic relations

3.3 The optimisation problem of observatory

stations distribution

Optimisation is determining the finest solution,

therefore finding the extremum of given function in

terms of specified criterion (e.g., cost, time, distance,

efficiency).

The optimisation of observatory stations distribu-

tion is achieved by such location of stations that

makes the tracking surface of the monitored area

nearest to the overall surface of study area. Obtain-

ing equality in two aforementioned surfaces marks

an ideal state of no occurrence of shaded area. The

usage of a given sort of observatory stations affects

the type and size of shaded areas resulting from en-

vironmental impact. In case of conventional radar

stations tracking surface depends on:

− blind spots caused by port infrastructure, topog-

raphy of the area,

− range and bearing discrimination.

Arrangement of shore stations seeks to maximise

the tracking surface while minimising the number of

newly built radar stations. Object-caused bind spots

may be eliminated by installing higher number of

observatory stations in various locations in a manner

enabling their range to cover the entire tracking sur-

face. This goal may be achieved by using a number

of additional observatory stations. However, one of

the regarded optimisation criteria are economic con-

ditions, additionally: the characteristics of the terrain

where stations are to be built, technical possibilities

of connecting stations to the network. The presented

approach has been implemented in the computer ap-

plication allowing for analysing maritime areas, pro-

posing a distribution of observatory stations, as well

as for comparative assessment of existing area moni-

toring schemes.

4 THE FEATURES OF APPLICATION

The application was created for MS Windows oper-

ating system (Neumann, 2010). This software pro-

vides an uncomplicated system for management of

stored shoreline patterns along with the suggested

locations of shore stations. This very construction

scheme for the aforementioned application was cho-

sen due to its ability to design, analyze and assess

practically all substantial parameters to be evaluated.

Its functions include: creating new projects, brows-

ing the list of existing projects, browsing the infor-

mation on given project and editing information on

given project. Transparent, clear and flexible appli-

cation architecture makes expanding the system and

implementing changes easier. This allows to avoid

many mistakes that could have a significant impact

on the quality of performed calculation.

The application was designed according to the

design pattern Model-View-Controller, with the

main purpose of separating the part of application

responsible for realisation of data processing from

the representative part displaying data. Such parti-

tion has numerous advantages, e.g., greater flexibil-

ity of the application, more readable code and in-

creased degree of code reuse.

In such constructed architecture three main layers

may be distinguished:

− the presentation layer – responsible for output da-

ta formatting and displaying the final result,

− the business logic layer - mechanisms employing

the basic logic of the application with implement-

ed methods of mathematical theory of evidence.

Contain the entire application engine.

− the data layer – the database and the data stored

in the system.

The main purpose of this application is such dis-

tribution of shore observatory stations that provides

coverage of the entire desired area. Therefore, prin-

cipal objectives of the observatory stations location

test may be specified as follows:

− to ensure the greatest possible coverage of the

monitored area, using the smallest possible num-

ber of observatory stations.

− to ensure the highest possible probability of float-

ing unit detection in the medium weather condi-

tions.

The greatest possible coverage is one of the input

parameters of the application. While using the visual

interface of the application, the user determines the

maritime area of his or her interest, whose monitor-

ing is to be ensured by the shore stations. The user