Maritime University of Szczecin
Akademia Morska w Szczecinie
2010, 21(93) pp. 5–11 2010, 21(93) s. 5–11
Application of artificial intelligence methods for improving
ship transport efficiency
Zastosowanie metod sztucznej inteligencji do poprawy
sprawności transportowej statku
Tomasz Abramowski
West Pomeranian University of Technology, Faculty of Maritime Technology Zachodniopomorski Uniwersytet Technologiczny, Wydział Techniki Morskiej 71-065 Szczecin, al. Piastów 41, e-mail: tomasz.abramowski@zut.edu.pl
Key words: ship design for performance, optimization, design parameters Abstract
The paper presents some selected results of research on applications of artificial intelligence to the optimization of main ship design parameters and hull shape coefficients with the ship transport efficiency as an objective function. Basics of ship transport formulation are concisely discussed, together with examples for different approaches to optimization. An example of neural network use for the determination of ship transport efficiency is given with an assessment of its ability for data generalization. Moreover, two optimization procedures are presented: one using genetic algorithms and the other with simulated annealing approach. Both procedures lead to the improvement of ship transport efficiency.
Słowa kluczowe: projektowanie statków pod kątem maksymalizacji osiągów, optymalizacja, parametry
projektowe
Abstrakt
W artykule zaprezentowano wybrane wyniki badań nad zastosowaniem metod sztucznej inteligencji do optymalizacji parametrów projektowych statku oraz współczynników kształtu kadłuba. Jako funkcję celu proponuje się zastosowanie wskaźnika sprawności transportowej. Podstawowe zależności i sformułowanie tego wskaźnika zostały zwięźle przedstawione, z egzemplifikacjami różnego podejścia do optymalizacji. Zaprezentowano przykład zastosowania sieci neuronowej do wyznaczania sprawności transportowej oraz ocenę zdolności sieci do uogólnienia wyników. Ponadto przedstawiono dwie procedury optymalizacyjne prowadzące do zwiększenia wskaźnika sprawności transportowej statku: jedną z zastosowaniem algorytmów genetycznych, a drugą z użyciem metod symulowanego wyżarzania.
Introduction
Due to increasing prices of oil every user of a transport vehicle is interested in saving fuel and this objective can be achieved with different approaches. It is obvious that fuel consumption is lower when the ship’s resistance decreases and this can be done by forming the hull shape more slender. Parallel to this, however, the ship’s cargo capacity decreases. A sensible compromise is needed. A measure for designing a ship which is economical from the fuel costs point of view and has sufficient cargo capacity at the same time can
be formulated as transport factor or transport efficiency. The factor can be written as:
B P P V W TE (1)
where: V denotes ship’s speed, PB is total installed
propulsion power and WP represents design
pay-load.
Design payload may be considered different for various types of cargo ships. For example, for container ships design payload can be defined as the TEU (the number of twenty-foot containers:
Tomasz Abramowski
TEU – twenty-foot equivalent unit) number and
then the transport factor can be written as:
B P
V TEU
TE (2)
while for ro-ro ships a loading lane length given in meters will be applied. So that the formula will be:
B P
V
TELanemeters (3)
All variables in the above formulae depend on main ship dimensions and ratios such as: ship length L, breadth B, draft T, height H, block coeffi-cient CB, midship coefficient CM, waterplane area
coefficient CW and many others. Usually, when
a traditional design approach is considered the fol-lowing problem is given:
find a vector of independent variables (main ship dimensions and ratios):
) ... , , (x1 x2 x3 xm x x (4)
which minimize or maximize the objective or fitness function, the subject of equality constraints:
, 0 ) ( x fi i1...j (5) or inequality constraints: , 0 ) ( x fi i j1...k (6)
Constraints determine the space of design solu-tion variasolu-tion. In the ship design problem, an opti-mization task may be formulated as: for given deadweight DWT, speed v, and / or range R; find a set of ship dimensions L, B, T, H, CB for which
the product: D C T B L B (7)
reaches a minimum, when the following constraints are fulfilled: min ) , , , , (L BH T C GM f GM B (8) R S L B P P P C T H B L f DWT ( , , , , ) (9)
where: PL is cargo weight, PS is the weight of stores
and PR is the reserve weight. GM is the metacentric
height.
Other constraints may be applied if necessary. Frequently, relationships for GM or DWT are em-pirical and come from statistics of the newly-built ships. The neural networks can be applied for better performance of algorithms and this will be shown further in the paper. The presented approach can be easily upgraded to multicriteria optimization.
Considering the relations (1) – (3) the propul-sion power PB can be written as:
T E B P P (10)
where: PE is the ship effective power, the product
of ship’s total resistance and speed; PE = RT V and
T is the total efficiency, defined as: S R H
T
0 (11)
where: H is the hull efficiency, 0 is the open
wa-ter efficiency, R is the relative turning efficiency
and S is the shaft efficiency.
The process of optimization of ship transport factor TE may be thus formulated in many ways depending on global constraints and assumptions from the ship owner. The examples are:
• direct optimization of TE (maximization) – the transport factor becomes the objective function itself. Then the objective function is formulated on the basis of empirical formulae or neural network approximation. The results of such optimization are both the speed and the payload and the set of considered ship dimensions and ratios;
• optimization of PB (minimization) only for the
constant payload – objective function is formu-lated as PB = PB(L, B, T, H, CB, ...). The payload
becomes an equality constraint. The results are ship dimensions and ratios giving a lower value of PB for assumed speed or speed range.
Application of artificial neural networks For the purpose of transport efficiency maximi-zation it is necessary to identify an objective func-tion such that the TE will have this form:
) ... , , (x1 x2 x3 xn TE TE (12)
where a vector of variables (x1, x2, x3 ... xn) will
form a particular solution containing chosen ship particulars and dimensions. Usually, regression analysis can be applied and an example is given in figure 1, where the transport efficiency is plotted versus the TEU number.
Obviously, as it is presented in figure 1, the transport efficiency generally increases together with TEU number, but such regression does not allow for any application during design. There are more ship parameters affecting its efficiency. For the purpose of better approximation a neural net-work has been constructed.
The network has five inputs and forms the de-sign vector of: ship speed v, length L, breadth B, draft T and TEU number. Thus the network represents the following function:
) , , , , (v L B T TEU TE TE (13)
The network has been constructed with the help of the Matlab software, using Levenberg-Marquard learning algorithm. The total of 1783 cases of con-tainer ships were in the whole data set and the cases were divided between training (70% of cases), vali-dation (15%) and testing (15%) sets. The structure of the network is presented in figure 2. The network has one input layer, one hidden layer with 9 neu-rons and output layer producing the result.
Fig. 2. The constructed network for TE Rys. 2. Opracowana sieć neuronowa dla TE
The network performance has been studied for the testing, training and validation data sets. The results, presented in figure 3, have sufficient accuracy for implementation during the design. The network produces results with correlation coefficient not less than 0.9. The network can be used for comparing the design vectors improving the quality of the design process.
Log-sigmoid transfer function was selected for all neurons:
x e x 1 1 sig log (14)where: x is the input signal. The function generates outputs between 0 and 1 and requires inputs to be normalized to the given range.
Application of heuristics optimization algorithms
The heuristic optimization techniques are in-creasingly applied in engineering applications. The goal of combinatorial optimization is to find a dis-crete mathematical object that maximizes (or mi-nimizes) an arbitrary function specified by the user of the metaheuristic. These objects are generically called states, and the set of all candidate states is the search space. The nature of the states and the search space are usually problem-specific.
In the paper the optimization examples of ship shape parameters with the application of genetic and simulated annealing algorithms are presented. As shown in section 1, transport efficiency is
Fig. 1. Transport efficiency as the function of TEU number Rys. 1. Sprawność transportowa w funkcji liczby TEU
TEU TE TE = f (TEU) 0.0 2000.0 4000.0 6000.0 8000.0 10 000.0 12 000.0 4.50 4.00 3.50 3.00 2.50 2.00 1.50 1.00
Tomasz Abramowski
inversely proportional to ship propulsion power PB
or ship effective power PE. Both of them depend on
ship hull resistance, for example PE is equal: V
R
PE (15)
where: R is the resistance. Hence, the task of opti-mization of transport efficiency may consist in re-ducing ship resistance or ship effective power.
A problem of resistance reduction was studied with the help of Matlab Genetic Algorithm and Direct Search Tool. As an objective function the
Holtrop-Mennen algorithm has been adopted and
implemented in Matlab – programming language. The optimized parameters were:
waterline length – LW,
breadth – B, draft – T,
block coefficient – CB,
buoyancy center location – xB,
prismatic coefficient – CP, waterplane area coefficient, area of bulb section at FP – ABT,
center of bulb section area from BL – hB. The constraints were so formulated that the optimized ship should keep constant deadweight, according to the buoyancy equation. The rest of particulars may be changed in the range of values
Fig. 3. The performance assessment of constructed network for TE Rys. 3. Ocena działania opracowanej sieci neuronowej dla TE
Training: R = 0.922 Output = 0.85Target + 0.36 Validation: R = 0.929 Output = 0.83Target + 0.39
Application of artificial intelligence methods for improving ship transport efficiency
typical for bulk cargo ships. The Matlab function file has been defined with the constraints:
function [c, ceq] = confun3(x) % Nonlinear inequality constraints DWT=10000; c = [x(1)*x(2)*x(3)*x(4)*1.005*1.025–(DWT/0.74); %DWT/DISP<=0.74 –(x(1)*x(2)*x(3)*x(4)*1.005*1.025)+(DWT/0.8); %DWT/DISP>=0.8 –(x(1)/x(2))+5.5; %L/B>=5.5 (x(1)/x(2))–7.6 %L/B<=7.6 –(x(2)/x(3))+2; %B/T>=2 (x(2)/x(3))-2.9; %B/T<=2.9 (x(8)/(x(2)*x(3)))-0.16; %ABT/BT<=0.16 –(x(8)/(x(2)*x(3)))+0.07; %ABT/BT>=0.07 (x(9)/x(3))-0.6; %hB/T<=0.6 –(x(9)/x(3))+0.3]; %hB/T>=0.3 % Nonlinear equality constraints ceq = [];
The vector of x(i) in the above listing forms a design solution of variables, x(i) = (LW, B, T, CB, XB, ABT, hB), for which constraints were adopted. Other values were assumed constant or are the function of variables in the vector. The calculations were carried out for several deadweights. The table 1 shows some selected results with computed parameters of ship dimensions and the assumed dimension ranges.
The computed mean value of resistance is
R = 278 kN. For the considered ship speed of
14.5 kts, according to the formula (14), the result-ing value of effective power: PE = 2179 kW. Even
if we assume total efficiency as low as 60%, 15% of sea margin and 10% of engine margin this gives the ship engine power PB = 4594 kW. According to
the information presented in [1] it is 376 kW less than a typical bulker of the considered deadweight class features.
Another application of heuristic algorithms for the purpose of improving ship transport efficiency has been presented in [2]. Instead of genetic algo-rithm, the simulated annealing method has been studied. Similar to genetic algorithms simulated annealing models a natural process, which is the
recrystallization of liquid metal during annealing. In the annealing process a metal is heated up to a temperature when atomic structure becomes dis-ordered and the particles are capable of moving around in the melt. Then it is slowly cooled down and atoms reach the minimum energy state (global minimum). Three major parts define the simulated annealing algorithm:
annealing schedule: the main control parameter of the annealing process is the temperature. This is an artificial parameter for programming pur-poses. The annealing schedule determines how the temperature is lowered during iterations. generating probability density function: new free
variables are created by random disturbance of the current best point. The generating probabili-ty densiprobabili-ty function defines the probabiliprobabili-ty for a certain disturbance. At high temperatures large disturbances have also a high probability. Large jumps in the design space are possible. During cooling the variance of generating density func-tion is getting smaller.
Table 1. Computed ship dimension for deadweight DWT = 20 000 t, ship speed v = 14.5 knots Tabela 1. Obliczone wymiary kadłuba statku o nośności DWT = 20 000 t i prędkości 14,5 węzła
Lw [m] B [m] T [m] CB [–] xB [%] CP CW ABT [m2] hB C stern
166.14 22.00 8.03 0.82 0.73 0.83 0.82 28.28 4.82 –9
L / B B / T CB xB CP
min max min max min max min max min max
5.5 7.6 2 2.9 0.75 0.87 –2 2 0.76 0.879
value value value value value
7.549 2.740 0.826 0.735 0.835
CW DWT / DISP CB / CP ABT / BT hB / T
min max min max min max min max min max
0.82 0.88 0.74 0.8 0.98 0.99 0.07 0.16 0.3 0.6
value value value value value
0.820 0.800 0.990 0.160 0.600
Fig. 4. Value of the fitness function during optimization process
Rys. 4. Wartości funkcji celu w trakcie optymalizacji
Generation Fi tn ess va lu e Best: 256.06 kN Mean: 278.76 kN Generation Fi te ss v al ue
Tomasz Abramowski
acceptance probability density function: if for a newly generated design f (xk+1) > f (xk) then xk+1 replaces the previous design xk. If f (xk+1) < f (xk) a random number u [0, 1]
is created and the following test is performed:
if u T x f x f EXP obj k k ( 1) ( )
the new design xk+1 is set,
if u T x f x f EXP obj k k ( 1) ( )
then the new design xk+1 is rejected.
The temperature of the objective function Tobj
is initially adopted to the magnitude of the objec-tive function and then reduced by the annealing schedule. At high temperatures the probability of designs which are much worse than the current one is high. This probability decreases with the tempe-rature and the acceptable increases of f will become smaller and smaller.
As before, for the purpose of optimization giv-ing reasonable results constraints must be adopted. Unconstrained optimization usually yields results which are unacceptable for various reasons which must be taken into account during the design. These reasons in ship design can be, for example, a mini-mum cargo load required by an owner or safety issues. In the presented research the adopted con-straints are ship displacement (Eq. 7) and the meta-centric height of a ship, a measure of safety from stability point of view. The metacentric height GM is the distance from the gravity centre of a ship to its metacentre. The GM is used to calculate the stability of a ship and must be positive for the right-ing arm to exist when the ship is heelright-ing. The GM changes for different load condition but in the design process it is assumed that ship is fully loaded. The constraint on GM is: GM > x, where x is an adopted criterion, usually not less than 0.2 m. The location of gravity centre must be known for the determination of GM. At the initial design process it can be estimated only using empirical formulae relating dimensions of the hull (mostly height of a ship H and draft T). One such formula, given in [3], has been applied.
The developed optimization technique has been tested for a virtual ship for which the design task was assumed. The task was to determine the main dimensions and block coefficient of the ship hull giving the lowest effective power PE. The
con-straints were:
displacement of a ship should satisfy:
D (16 100, 16 500) [T],
speed of a ship should satisfy:
v (12.5, 13) [kts],
metacentric height: GM > 1.2 [m].
The constraints were also specified for the de-termination of upper and lower bounds of design solution vector, X = [L, B, T, CB, v]. It was assumed
that the ship length will vary during the optimiza-tion process from 125 m to 135 m and other vector components will be bounded to ratios: L / B = 68,
B / T = 2.43.6. Block coefficient CB will vary from
0.7 to 0.8. The process of optimization – values of objective function during iterations – is given in figure 5. The penalty function was set to the algo-rithm such that if a solution does not fulfill the criteria, the objective function receives very high value. The optimization process has been stopped after about 850 iterations. The minimum objective function value was 1486 kW, and the vector of design solution is: [127.3, 22.5, 7.1, 0.79, 12.5]. It is obvious that the selected value for the ship speed (12.5 knots) is at the lowest bound of the assumed vector. This is because the relation be-tween speed and propulsion power of a ship (or any other vehicle) is in third order power, so that it is the strongest relation in the objective function. When considering the design problem of minimiza-tion of ship effective power, the upper and lower bounds on the speed should be set very close.
Fig. 5. Optimization process for the virtual ship
Rys. 5. Proces optymalizacyjny dla jednostki teoretycznej
The method has been also applied for optimiza-tion of dimensions of real ship – a tanker built in Szczecin Shipyard. The ship has displacement of 46542 m3 and this value was selected as the
minimum criterion. The ship has the following dimensions; L = 176 m, B = 32.2 m, T = 10.5 m,
CB = 0.8. The hull of a ship model was tested in
a towing tank and for the speed of 15 knots the effective power is 4818 kW. It was decided that the speed of ship equal to 15 knots should be kept at the same level due to the strong relation with
effec-Current Function Value:1486.6975
Iteration Ef fe ct iv e po w er PE [ kW ]
tive power. Since the ship has a breadth B = 32.2 m, a Panamax vessel size, and the upper bound for this value should not exceed 32.2 m. The results of op-timization are given in figure 6. The opop-timization process has been stopped after 300 iterations.
Fig. 6. Optimization process for a tanker Rys. 6. Proces optymalizacyjny dla tankowca
The solution vector of best value function is: [177.8, 30.08, 12.08, 0.72, 15]. Now the ship is longer but the breadth and block coefficient are decreased and the draft is bigger. The optimized ship has exactly the displacement of 46542 m3 so
that the optimized ship should be capable of carry-ing the same amount of cargo as before optimiza-tion and the resulting effective power is 4192 kW. This seems to be very promising because power reduction was 626 kW. Nevertheless, as the objec-tive function is the simplified form of empirical method, more tests should be carried out for the proper verification of the presented approach.
In the above research a neural network was developed for the effective power PE, instead of
calculating ship resistance as it was used in the method with genetic algorithms.
Final remarks
Some results of research into the application of artificial intelligence to improving ship transport efficiency have been presented. Two approaches of the optimization of main ship dimensions have been briefly discussed. Both the neural network and em-pirical algorithm can be used for the formulation of fitness or objective function. It was shown that optimization problem of transport efficiency may
be formulated in many ways but the results are encouraging. The reduction of effective power of the tanker being the subject of investigation is sig-nificant and if achievable in the design must yield substantial reduction of fuel consumption. At the same time emissions of harmful exhaust gases would be lower with the favorable impact on the environment.
Design criteria can be applied and their use does not disturb the optimization process and the results are feasible. If there are any constraints concerning the ship service or navigational matters (such as size limitations for channels or locks), they can be introduced to the algorithm. Subsequent research will be devoted to the development of methods taking into account more dimensions and hull shape coefficients and models will be compared systemat-ically with existing ships.
References
1. MAN B&W Diesel A/S: Propulsion trends for bulk car-riers. 2005.
2. ABRAMOWSKI T.,ZMUDA A.: Combining Artificial Neural Networks and Simulated Annealing Algorithm for Reduc-ing Ship Effective Power. P.J. Environmental Studies, 2008, 17, 4C, 67–71.
3. SCHNEEKLUTH H.,BERTRAM V.: Ship design for efficiency and economy. Butterworth-Heinemann, 1998.
Others
4. CHĄDZYŃSKI W.: Elementy współczesnej metodyki projek-towania obiektów pływających. Prace Naukowe Politech-niki Szczecińskiej. Szczecin 2001.
5. ABRAMOWSKI T.,ZMUDA A.: Generalization of Container Ship Design Parameters by Means of Neural Networks. P.J. Environmental Studies, 2008, 17, 4C, 111–115.
6. Matlab User Guide, Genetic algorithm and direct search toolbox, Neural network toolbox. The MathWorks, 2008. 7. MESBAHI E.,ATLAR M.: Artificial neural networks:
applica-tions in marine design and modeling. 1st Int. Conf.
Com-puter Applications and Information Technology in the Maritime Industries. Potsdam 2000.
Recenzent: dr hab. Zenon Zwierzewicz, prof. AM Akademia Morska w Szczecinie Current Function Value:4192.3934
Iteration Ef fe ct iv e po w er PE [ kW ]
