International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 2
Number 1
March 2008
11
Combination of Processing Methods for
Various Simulation Data Sets
M. Gucma
Maritime University of Szczecin, Poland
ABSTRACT: Computer based simulations can be used for assessment of traffic lane perimeters, and an actual
level of risk at given area and given conditions. Navigational risk is defined as the product of probability of
failure occurrence and the consequences it can cause. Additionally, the definition of risk was supplemented by
relative frequency of performing the maneuver in given conditions and in given time t. In article method of
simulation data possessing for maneuvers of approaching and entering to port, on base of specific vessels, is
presented. Autonomous and non autonomous simulation methods are used for obtaining data sets, are
supported in presented software solution, as well as restrictions in its implementation.
1 INTRODUCTION
Article presents complex method of possessing data
from autonomous and non autonomous simulation.
Such method is important in cases where complete
navigation risk assessment must be fulfilled. This
situation has place during new terminal develop-
ment, on which non standard vessel will be handled.
2 AUTONOMOUS SIMULATION METHODS
AT OPEN AREA
Autonomous simulations are valuable source of data
where random phenomena’s such as vessels
collisions occurs. Autonomous simulations were
determined with use of traffic analysis from past
years for given area. In the next step probabilities of
vessel collisions were obtained during simulation.
2.1 Simulations of traffic stream at analyzed area
For use of autonomous model, traffic densities at
area must be gathered. Statistical data could be
obtained from Automatic Identification System
(AIS). AIS system is obligatory for any large vessel,
but also smaller vessels do have AIS receiver. Land
based monitoring stations, which works in area, can
poses data from vessels such as:
− position,
− speed,
− course over ground,
− port of destination,
− port of departure,
− current status (for example: moored, under way
etc.)
AIS gather data continuously, and its range allows
tracking particularly any vessel in area covered by
AIS. One day exemplary data from AIS are
presented at Fig. 1.
Data from AIS must be transformed into
statistical streams of perimeters:
− number of vessels following same route,
− width of route,
− route legs,
− speed and structure of ships at route (transit or
direct);
12
Fig. 1. One day AIS routes of ships
Such prepared data can be used to build model of
traffic. Sample AIS streams situation is presented at
Fig. 2.
Fig. 2. AIS originated traffic streams
Total traffic stream at given route in discrete time
lag (0, T) is presented as a random vector:
( )
,1 , ,
,..., ,...,
c c ci cm
VV V V=
(1)
Any i-th element characterizes mean traffic
stream between t
i-1
and t
i
and is a random variable
with normal distribution N (m
i
,
σ
i
2
). Thus summary
traffic stream can be expressed by generation of
random variable with normal distribution N (m
i
,
σ
i
2
)
that describes mean traffic stream V
c,i
in given lag
time, which probability density function can be
expressed by:
( )
2
,
,
2
1
( ) exp
2
2
ci i
ci
i
vm
fv
σ
σπ
−
= −
(2)
Algorithm of traffic generation can be described
by following points:
1 estimation of expected value m
i
, and variance σ
i
2
for each model of traffic;
2 generation of random variables x
1
,…x
m
so that
each value x
i
came from set described by normal
distribution as in point 1 of algorithm , i-1,…,m;
3 estimation of expected value x
i
as simulated
stream in given time lag (t
i-1
, t
i
) for i=1,…,m.
Generation of random variables was based on
such realization of
X
for random variable X of
distribution S
α
(
σ
,
β
,
µ
), with variable parameters
α
∈(0,2],
β
∈(-1,1),
µ
∈R,
σ
∈R
+
and can be
developed by performing numerical equations:
( )
1,
2,
1;
,
tg
α
α
µ βσ απ
µ
α
µ
≠
−
=
=
(3)
( )
1
2 0.5 32767;Vk
ππ
=−+ +
( )
( )
1
log 0.5 32767 ;Wk=−+
where constant: 32767 was obtained numerically and
k
1
, k
2
, values are random [Izydorczyk A., Janicki A.,
2001].
( )
,,,
/2 ;B tg
α
αβσ µ
µ βσ πα
= −
( )
( )
,
2arctg tg
C
αβ
β πα
α
=
( )
( )
( )
( )
1
,,
cos 2 ,D arctg tg
α
αβσ
σ β πα
−
=
thus for,
1
α
≠
function equals:
( )
( )
( )
( )
( )
( )
( )
1
,, ,,,
1
sin cos
cos
VC V VC
XD B
W
V
αα
αβ αβ
αβσ αβσµ
α
αα
−
+ −+
= +
,
(4)
and when,
1
α
=
function equals:
( )
( )
,,
cos
2
log ,
22
2
WV
X V tg V B
V
βσµ
π
ππ
σβ β
π
β
=+− +
+
(5)
with substituting:
( )
,,
2
log .B
βσµ
µ βσ σ
π
= +
Defined equations 4 and 5 are directly applicable
in Monte Carlo model [Izydorczyk A., Janicki A.,
13
2001]. Such defined model must be verified before
usage and this process requires implemented
computer structures.
Course and position variance of a vessel at given
route is mainly contributed by changes in planning
and keeping control over route by navigator and
changes in keeping vessel at course due to hydro -
meteorological conditions [Gucma L. 2005].
2.2 Algorithm for assessment of vessels collision
probability
Probabilistic methods of analysis and estimation of
risk was used to develop algorithm of collision
assessment. Fault tree and collision assessment tree
was applied.
Fault tree consist of analysis consequences during
accident. This allows for building model inside
which several factors were implemented. Some of
these factors can be presented as: equipment fault,
human factor (human error), environment influence
and other. Reliability elements were applied as well,
in order to build more detailed model, and its
interactions between human and machine [Pietrzy-
kowski Z. 2004].
Model of rendezvous for two vessels, which take
into computation decision model of navigator, is
presented at Fig. 5. One of major factor influencing
work of this model is human behavior indetermina-
tion. One of possible decision making model of
human behavior model is presented at Fig. 3 and
Fig. 4.
Navigational
Situation
AREA
HYDRO METEO
CONDITIONS
OWN VESSEL
OTHER
OBJECTS
RULES AND
REGULATIONS
Type Of Area
Wave
,
Wind
,
Visibility
,
Current
,
Tide
Dimensions
–
Length
,
Breadeth
,
Draft
,
Dimensions
–
Length
,
Breadeth
,
Draft
,
COLREGs
,
Local
Authorities
parameters
of area
parameters of
conditions
motion vector
parameters
motion vector
parameters
detailed rules
Fig. 3. Rendezvous model of two vessels [Pietrzykowski Z.
2004]
Possessing of
data
Analysis and
assessment of
situation
Decision making
Performing of
action
Fig. 4. Decision making process in human behavior model
[Pietrzykowski Z. 2004]
Using such defined model, description and
implementation of detailed fault tree for normal and
failure states is possible. Then basing on literature
and gathered experimental data, density distributions
were determined. Such defined algorithm was tested
using statistical data of accidents from past years at
analyzed area.
3 AUTONOMOUS METHODS OF
SIMULATION ON APPROACHES TO PORTS
On approaches to ports, from anchorages to entrance
heads of particular ports, mainly straight line traffic
occurs – changes of courses are not significant.
Maneuvering on such area is quite simply and do not
need to apply direct control by human navigator.
Thus fast time autonomous simulation could be used
in order to assess probability of grounding at such
area.
Main advantages of fast time autonomous
simulations in comparison to non autonomous
models are[Gucma S., 2001]:
− much shorter period of time used to perform
simulations,
− lower costs of researches due to lack of hiring
experts to perform its,
− possibility of testing model in different con-
ditions.
In this type of simulations, modeling of decision
making process on base of human behavior is crucial
element. When maneuver must be done, decision
making process is very flexible and its parameteriza-
tion is difficult. Also individual preferences are very
important when human navigates.
Predictive models are used in order to build fast
time autonomous models. These systems are
constructed using mathematical model of vessel
movement. Simulation autonomous model with
respect to dependence function vessel – area –
navigator is presented at Fig. 5.
Mathematical
model of area
and navigational
marks
Hydro - meteo
conditions model
Navigators
decision process
model
Vessel
mathematical
model and
prediction block
Planned maneuver
M
o
d
e
l
c
o
n
t
r
o
l
Performed maneuver
Fig. 5. Autonomous simulation model of movement vessel at
restricted area [Gucma S. 2001]
14
4 NON AUTONOMOUS SIMULATIONS
During entering the port, turning and mooring
operations maneuvering the vessel is extremely
complex process, thus in order to estimate collision
probability vessel with hydro constructions, real
rime non autonomous simulations are deployed.
Complete description of method can be found in
large literature of MTE filed for example: [Gucma L.
2005], [Gucma M. 2006] and other.
Real time human – computer interaction is used
for development of this type of simulators. Human
is usually an expert that has proper experience
in maneuvering at given area. Computer has
specialized subsystems for visualization and
controlling vessel mathematical model. Such model
is presented at Fig. 6.
Mathematical
model of area
and navigational
marks
Hydro - meteo
conditions model
Human -
Navigator
Vessel
mathematical
model
Planned maneuver
M
o
d
e
l
c
o
n
t
r
o
l
Performed maneuver
Model of
visualization
Fig. 6. Non autonomous simulation model of vessel movement at
restricted areas [Gucma S. 2001]
This method is much more accurate than fast time
autonomous simulations, but its application is more
expensive and time consuming than the latter.
Performance of these maneuvers can be done at 2D
limited task simulator as well as 3D full mission
simulator. Marine Traffic Engineering Institute has
developed variety of limited task simulators for
different navigational situations – example of these
is presented at Fig. 7. Full mission simulators from
third parties are used as well when reality is
indispensable for researches – Fig. 8.
Fig. 7. Limited task simulator used for marine traffic
engineering researches
Fig. 8. Real time full mission simulator used for marine traffic
engineering researches
The vessel performing a given manoeuvre in an
accessible navigational area occupies a certain area
determined by her successive locations in the area.
The parameters of this area are random and depend
on various factors. This area, calculated on a
definite reliability level is called safe manoeuvring
area. A safe manoeuvring area so defined can be
presented in the form of area d
ijk
(set of points) and
the basic navigational safety condition can be written
down as follows [Gucma S. 2001]:
( )
( , ) ()
(, ,) (, ,) (, ,)
ijk
pxy t
t
h yt T xyt xyt
∈
⊂
≥ +∆
D
dD
where:
D(t)
–
accessible navigational area (meeting
the condition of acce
s
sible depth at
moment
t),
d
ijk
–
accessible manoeuvring area (traffic
lane) of the
i-
th vessel, performing the
j
-th manoeuvre in k-th naviga
tional
conditions,
h(x, y, t)
–
the depth of the area at point with
coordinates
(x, y) at moment t,
T(x, y, t)
–
the draft of the vessel at area point
with coord
inates (x, y) at moment t,
∆(x, y, t)
–
underkeel clearance at area point with
coord
inates (x, y) at moment t.
5 RESULTS COMBINATION OF DIFFERENT
METHODS
Important application of Monte Carlo models are the
methods used for the determination of probability of
damage of underwater pipelines by the ship after
emergency dropped anchor [Gucma L. 2005]. Such
models need long time of simulation because
modelled events are very rare. The example algo-
rithm of second category of MC based models is
presented on Fig. 9.
(6)
)(),(
tyxp
D∈
15
Fig. 11. Distribution of times between consecutive gas pipeline
damages [Baltic Master Report, 2006]
The example result as distribution of anchor – pipe
accidents are presented on Fig. 10. The interesting
analysis can be made by the investigation of times
between accidents (Fig. 11). Usually due to stochastic
nature of simulated process, the distribution of times
between accidents is exponential (Fig. 11).
Fig. 9. General procedure of MC researches based on
generalized simulation data
Fig. 10. Localizations of simulated anchor accidents during
whole simulation time and examples of technical engine break
out as the main causes of such accidents during 100 years of
simulation [Baltic Master Report, 2006]
Other result type consists of non autonomous
simulations performed at confined port areas. The
probabilistic concept of safety manoeuvring area
obtained from these type of simulations. is presented
on Fig. 12. The distributions are strongly dependant
of waterway area arrangement and could be
evaluated in simulations and validated in real
experimentations.
Fig. 12. Probabilistic concept of safe maneuvering area
determination on the waterway [Baltic Master Report, 2006]
6 CONCLUSIONS
Both non autonomous simulations and autonomous
ones, requires thoroughly processing and deep
knowledge of process itself, for correct analysis.
Presented combination of marine traffic engineer-
ing tools allows to develop complete method of risk
assessment at particularly any area. Method has been
recently used for LNG carrier maneuvering at
Southern Baltic and prospected terminal at Polish
coast at work: [Gucma S., Gucma M., 2007].
REFERENCES
Gucma M., Risk assessment for LNG carrier maneuvers in a
restricted sea area, 4th International Probabilistic
Symposium, Berlin 2006, Proceedings of IPS, Berlin 2006
Gucma L., Modelowanie czynników ryzyka zderzenia jednostek
pływających z konstrukcjami portowymi i pełnomorskimi,
Studia nr 44 MU of Szczecin, Szczecin 2005 - in Polish.
Gucma S., Gucma M., Simulation method of navigational risk
assessment in optimization of LNG terminal parameters,
Proceedings ESREL 2007, A.A, Balkema, Stavanger 2007
Gucma S., Marine Traffic Engineering, Shipbuilding and
Shipping, Gdańsk 2001, - in Polish.
Izydorczyk A., Janicki A., Komputerowe metody w modelo-
waniu stochastycznym, WNT Warszawa, 2001 - in Polish.
Pietrzykowski Z., Modelowanie procesów decyzyjnych w
sterowaniu ruchem staków morskich, Studia 44, MU of
Szczecin, Szczecin 2004 - in Polish.
Baltic Master report MII part ¾ general assumptions for the
integrated model of navigational safety on the Baltic Sea,
Team leader: Lucjan Gucma, Marine Traffic Engineering,
Szczecin 2006.
