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Zeszyty Naukowe 20(92) 41

Scientific Journals

Zeszyty Naukowe

Maritime University of Szczecin

Akademia Morska w Szczecinie

2010, 20(92) pp. 41–44 2010, 20(92) s. 41–44

Reliability level of safe manoeuvring area

Poziom ufności bezpiecznego akwenu manewrowego

Stanisław Gucma

Maritime University of Szczecin, Faculty of Navigation, Institute of Marine Traffic Engineering Akademia Morska w Szczecinie, Wydział Nawigacyjny, Zakład Inżynierii Ruchu Morskiego 70-500 Szczecin, ul. Wały Chrobrego 1–2, e-mail: s.gucma@am.szczecin.pl

Key words: navigation, marine traffic engineering Abstract

In the following article the methods for establishing parametres of safe manoeuvring area are presented. The methods are constructed on the basis of deterministic and probabilistic models of ships’ manoeuvring in restricted areas. The reliance level has been established for these methods in which deterministic and probabilistic model of under keel clearance has been used.

Słowa kluczowe: nawigacja, inżynieria ruchu morskiego Abstrakt

W artykule przedstawiono metody określenia parametrów bezpiecznego akwenu manewrowego. Metody te są zbudowane w oparciu o modele deterministyczne i probabilistyczne ruchu statków na akwenach ograniczo-nych. Określono poziomy ufności metod, w których zastosowano deterministyczny i probabilistyczny model rezerwy wody pod stępką.

Introduction

The vessel is able to manoeuvre safely only in area that fulfills the condition of the required depth. The vessel manoeuvring in area that meets the above condition occupies the given area that is determined by her / its next positions in this area. Such area is called a safe manoeuvring area.

There are a number of methods for the determi-nation of safe manoeuvring area parameters. These methods are built on deterministic and probabilistic models of ship movement in restricted areas and on combined models, which make use of elements modelled by various methods.

Methods of safe fairway width determination may be divided depending on how the solution is obtained: analytical (theoretical and empirical) and simulation [1, 2]. Either deterministic or probabilis-tic models have been employed in these methods.

Theoretical methods include the method of three components as developed by this author [1], in which elements of ship movement are described using deterministic models, while positioning

elements are defined with the use of the proba-bilistic model.

The following are empirical methods based only on deterministic models:

 Panama Canal method,  PIANC method,  Canadian method,  USACE method.

The empirical method based on deterministic models used for ship movement elements and on the probabilistic model utilized in relation to posi-tioning elements is the method of Marine Traffic Engineering (MTE) developed by this author [1].

Empirical methods built on deterministic models define a constant value of safe waterway width for preset conditions assuming that this is the width ensuring manoeuvring safety in specified condi-tions. This width is determined by real methods, usually expert or statistical ones, where the defini-tion of safety has various interpretadefini-tions in the as-sumptions of each method.

Stanisław Gucma

42 Scientific Journals 20(92)

The simulation method makes use of probabilis-tic models only while the three-components and MTE methods use them only in positioning ele-ments. The safe waterway width in these methods is determined at an assumed confidence level (1 – α).

Some fundamental questions asked in the processes of waterway designing and operation are as follows:

1. What confidence level should be assumed for the determination of the safe waterway width calculated by methods using probabilistic mo-dels?

2. How should the safety level be interpreted when waterway widths are calculated by methods us-ing detrministic models?

Safe manoeuvring area in probabilistic models

The probabilistic model of ship movement as-sumes that while performing a given manoeuvre the ship occupies a certain area defined by its subse-quent positions. This area, calculated at a specific confidence level, is called the safe manoeuvring area [3]. Parameters of the safe manoeuvring area, such as the width, have a stochastic character and are usually described by the normal distribution [4]. As a rule, waterway designers utilizing methods with probabilistic models assume for the safe manoeuvring area the confidence level 0.95. This problem started to be approached differently some ten years ago when more accurate methods of confidence level estimation related with safe manoeuvring area were introduced.

Researchers at the Institute of Marine Traffic Engineering, Maritime University of Szczecin, have developed a method of confidence level estimation based on the risk theory [1]. Like in most engineer-ing applications, marine traffic engineerengineer-ing defines risk R as a possibility of losses that may arise in a defined time interval and expresses risk as the product of the probabilities of accident and conse-quential losses. If there exist several factors that may cause losses, the risk is summed up [5]:



a time unit (i = 1, 2, ..., n); Si – consequences of an

i-th type accident in a time unit; n – number of

accident types.

Navigational risk is expressed as the product of accident probability and the consequences caused by that accident. Additionally, the definition of risk

has been supplemented with the concept of relative frequency of performing the examined manoeuvre. Assuming that an accident and its consequences are independent events, we can define navigational risk as the product [1]:

R = IR PA S (2)

where: IR – average yearly frequency of performing

a given manoeuvre; PA – probability that a specific

accident will occur; S – consequences such accident will cause.

It should be noted that the product IRPA is the

probable number of specific accident occurrences in a year.

Based on the definition of navigational risk, the condition of safe navigation has been determined:

Rakc  R (3)

After transformation:

Rakc ≥ IR PA S (4)

where Rakc – acceptable risk of making a specific

manoeuvre.

Dutch criteria of navigational safety on fairways (restricted waters) allow for one major accident in 237 years at the maximum, which is equivalent to not more than 0.004 major accident (grounding) per year. English criteria, on the other hand, allow for maximum 0.001 major accident (grounding) in a year.

Designed waterways are expected to be operated for 50 to 100 years, while life expectancy for ships is 15 years. However, the following facts should be taken into consideration:

 in a period of 50100 years a waterway is modernized a few times, which results from the implementation of improvements in shipboard navigational systems, manoeuvring methods and vessels as such;

 each new generation of vessels (after approx. 15 years) is increasingly more perfect in terms of manoeuvrability, navigational systems, technical reliability etc.

With these facts taken into account, it has been concluded that safety requirements should not be risen if it is not reasonably justified; therefore, the following navigational safety criteria were adopted:  tidal areas: maximum 0.004 major accident per

year or the maximum of 0.04 of all accidents (major and minor);

 non-tidal areas: maximum 0.007 major accident per year or the maximum of 0.07 of all accidents (major and minor).

Reliability level of safe manoeuvring area

Zeszyty Naukowe 20(92) 43

The probability that an accident occurs during a given manoeuvre can be determined by either of the two methods:

 method based on the deterministic model of under keel clearance,

 method based on the probabilistic model of un-der keel clearance.

Probability of a navigational accident – the method based on a deterministic model of under keel clearance

It has been assumed in the deterministic model of under keel clearance that the ship can safely ma-noeuvre only in an area which at each of its points at any moment (t) satisfies the following condition:



 

 



h , ,  , ,  , , (5) where: h(x, y, t) – area depth at a point with coordi-nates x,y at a moment t; T(x, y, t) – ship’s draught at a point with coordinates x,y at a moment t; (x, y, t) – under keel clearance at a point with coordinates

x,y at a moment t.

The probability of an accident during a specific manoeuvre (fairway passage) can be presented in this form:

PA = 1 – Pn Pt (6)

where: Pn – probability that a ship of specific

para-meters steered by a navigator with specific qualifi-cations will not have an accident while performing a given manoeuvre in defined navigational and hydrometeorological conditions; Pt – probability of

reliable operation of ship systems and equipment that are critical for failure-free performance of a given manoeuvre.

The probability that a specified type ship ma-noeuvres smoothly in specific navigational and hydrometeorological conditions, steered by a navi-gator with specific qualifications, at a specific time and place:

Pn = P(Xj  dj) (7)

and the probability expressed by the standardized normal distribution has this form [1]:

   _           1 j j j j j j n x d x X P P (8)

where: Xj – maximum distance of the ship’s

ex-treme point on port or starboard side from the fair-way axis at a j-th section of the area (random varia-ble), x_j,_j – mean value and standard deviation of the maximum extreme points of the ship on the port or starboard side from the fairway axis at a j-th

section of the area, dj – minimum distance from

a danger at a j-th section of the area,  – signifi-cance level.

Used for the determination of the ship’s swept path width, the distribution parameters x_j,_j are calculated from field or simulation studies of a given manoeuvre.

Technical reliability has been identified with as smooth performance of a given manoeuvre. This reliability depends on failure-free work of the main engine, auxiliary engines and generators, steering gear / rudder, tugs, and radars  in case of bad visi-bility.

If we assume that failure of any of the above mentioned machines may in certain circumstances lead to a ship’s accident, the probability of reliable operation of all the units is a product of the proba-bilities of reliable work of each unit:

Pt = P1 P2 P3 P4 P5 (9)

which approximated to the second order of magni-tude may be written in this form:





1 t t t t t

P_t        (10) where: t1 – time interval during a manoeuvre in

which a main engine failure will cause a risk of an accident; t2 – time interval during a manoeuvre in

which an auxiliary engine / generator unit failure will cause a risk of an accident; t3 – time interval

during a manoeuvre in which a steering gear/rudder failure will cause a risk of an accident; t4 – time

interval during a manoeuvre in which a tug failure will cause a risk of an accident; t5 – time interval

during a manoeuvre in which a radar failure will cause a risk of an accident; 1 ÷ 5 – respective

intensities of failures of each unit or system.

Probability of a navigational accident – method based on the probabilistic model of under keel clearance

It has been assumed in the probabilistic model of under keel clearance that the water depth under the ship’s keel is a random variable, and the proba-bility of hull contact with the bottom can be written as (Fig. 1):





_

 

where f() – distribution density of under keel clearance.

Under keel clearance has been determined by building a probabilistic Monte Carlo model [4]:



 

 





Stanisław Gucma

44 Scientific Journals 20(92)

where: δh – uncertainties connected with water

depth and its determination, δT – uncertainties

con-nected with draught and its determination, δw –

uncertainties connected with water level and its determination, δN – water navigational margin

(con-stant),  – under keel clearance, h – depth of the examined area (map reading), T – vessel’s draught (maximium draught reading), W – water level in the proportion of map zero (used).

Fig. 1. Distribution of under keel clearance Rys. 1. Rozkład zapasu wody pod stępką

If we take into account the independence of na-vigational and technical reliability and that of under keel clearance, the probability of an accident during a specific manoeuvre incorporating the model above will have this form:





P_A 1 _{n t}  (13)

Summary – confidence levels of safe manoeuvring areas

The following conclusions can be drawn from an analysis of the two methods of navigational accident probability estimation:

1. The method built on the deterministic model of under keel clearance can have applications in defining dimensions of water areas restricted by vertical banks (Fig. 2a), or by ships (lying or proceeding). In these cases, the width of safe manoeuvring area is confined by the confidence level determined after substitutions and trans-formation of the inequality (6):

t akc P S I R    1 1  (14)

2. The method using the probabilistic model of under keel clearance may be applied for defining the dimensions of areas restricted by slope banks (Fig. 2b). In such cases the width of safe

ma-noeuvring area wil be limited by the confidence level obtained from this inequality:





These remarks refer to the confidence level for waterways calculated by methods built on probabil-istic models.

a) b)

Fig. 2. Types of banks restricting a manoeuvring area: a) vertical bank, b) slope

Rys. 2. Rodzaje brzegu: a) skarpa, b) brzeg toru wodnego

Methods using deterministic models enable calculating the constant value of safe waterway width for strictly specified navigational conditions. The conditions are specified seperately for each method. Reliability of the probabilistic methods depends on the conditions of their employment and they are as follows:

 type of area and type of vessel’s manoeuvre,  existing hydrometeorological conditions,  used positioning methods.

Deterministic methods can be applied as appro-ximated methods in the process of designing waterways parametres, however even then it is advisable to obey the range of their employment.

References

1. GUCMA S.: Inżynieria ruchu morskiego. Okrętownictwo i Żegluga, Gdańsk 2001.

2. GUCMA S.,GUCMA L.,ZALEWSKI P.: Symulacyjne metody badań w inżynierii ruchu morskiego. Pod redakcją S. Gucmy. Wydawnictwo Naukowe Akademii Morskiej w Szczecinie, Szczecin 2008.

3. GUCMA S.: Nawigacja pilotażowa. Fundacja Promocji Przemysłu Okrętowego i Gospodarki Morskiej, Gdańsk 2004.

4. GUCMA L.: Modelowanie czynników ryzyka zderzenia jed-nostek pływających z konstrukcjami portowymi i pełno-morskimi. Studia nr 44, AM, Szczecin 2005.

5. FULLWOOD R.R.: Risk as consequence expectation value from linear superposition. Nuclear Safety, 1977, Vol. 18.

T(x,y,t) draught

water level

h(x,y,t) depth

ijk (x,y,t)

Probability of hull-bottom contact

 f()