Scenario-based Hydrodynamic Design Optimization ...

Scenario-based Hydrodynamic Design Optimization of High Speed Planing Craft for Coastal Surveillance Ahmad F. Mohamad Ayob

Tapabrata Ray

Warren F. Smith

School of Engineering and I.T University of New South Wales Australian Defence Force Academy ACT 2600, Canberra, Australia Telephone: +61 2 626 88479 Email: [email protected]

School of Engineering and I.T University of New South Wales Australian Defence Force Academy ACT 2600, Canberra, Australia Telephone: +61 2 626 88581 Email: [email protected]

School of Engineering and I.T University of New South Wales Australian Defence Force Academy ACT 2600, Canberra, Australia Telephone: +61 2 626 88262 Email: [email protected]

Abstract—In this paper, an optimization framework for the design of hard chine planing craft is presented. The proposed framework consists of a surface information retrieval module, a geometry manipulation module and an optimization module backed by standard naval architectural performance estimation tools. Total resistance comprising calm water resistance and added resistance in waves is minimized subject to constraints on displacement and stability requirements. Infeasibility Driven Evolutionary Algorithm (IDEA) is incorporated in the optimization module. A scenario-based hydrodynamic optimization problem using an example of United States Coast Guard (USCG) WPB-110ft vessel is presented in this work. The concepts presented in this paper is an extension of the works of [15] [16] where instead of only performing total resistance minimization of high speed planing craft at a single operational speed, a set of collective speed spanning over a predefined lifetime is illustrated. The proposed framework is capable of generating the optimum hull form while at the same time enabling a provision for ship designers to evaluate the candidate designs’ performance over various operating scenarios.

I. I NTRODUCTION Constant increase in fuel cost drives ship designers to produce more efficient designs thus minimizing the operational cost in long run. Assuming the changes of other cost to be equal throughout years 1990 to 2010, the world witnessed a 200% increase of diesel price [28] thus forcing ship operators to shift the burden to the users. Agreeing to this long-standing interest, numerous literatures have been dedicated to solve such problems, for example optimization of displacement crafts such as containerships [19] [9] [18], surface combatants [27] [17], transport ferries [5] and fishing vessels [12] [8]. Design of high speed planing crafts have been attempted by [1]. Case studies on United States Coast Guard (USCG) WPB-110ft patrol craft design are also available from the works of [10] and more recently on its hull form design optimization by [16]. The optimization algorithms used in the aforementioned studies and others include gradient-based method [27], simulated annealing [19], genetic algorithm [3] [5] and particle swarm optimization [18].

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While most of optimization studies or even design attempts aim to identify the best hull form for a particular operating speed, in reality most of such crafts operate over a range of speeds during its lifetime. This paper presents an approach and a framework that allows for the identification of an optimum hull form that performs well over a range of speeds. Outlined in [2], a United States Coast Guard (USCG) patrol craft is expected to conduct its operations in six basic speed modes; idle, tow, patrol, low transit, high transit, and intercept. Hence, extending the works of [15] [16], a scenario-based resistance optimization based on a set of collective speed experienced over predefined lifetime is presented using the proposed framework to identify the performance of optimized candidate craft in preliminary design stage. The paper is organized as follows. The optimization framework that is capable to handle high speed planing craft hydrodynamic design optimization problem is presented in the next section. In Section III, the problem definition is addressed followed by the results in Section IV. Section V concludes the paper. II. O PTIMIZATION F RAMEWORK C OMPONENTS The optimization framework presented in this paper consists of three applications namely Matlab, Microsoft Excel and Maxsurf. Maxsurf Automation Library built upon Microsoft COM interface is used as a medium of communication (inter-process) between applications. Shown in Fig. 1 is a generic sequence diagram to illustrate the work flow of the current optimization framework. The interprocess communication is initialized with the selection of principal dimensions length, beam and draft (L, B, T ) by the optimizer module in Matlab. Parametric transformation is invoked to generate a candidate hull followed by evaluation of the hydrostatics and calm water resistance of the candidate hull in Maxsurf using the methods of [21]. Finally the seakeeping performance is evaluated using the Savitsky and Koelbel [22] method. This completes one work flow loop. The detailed

flowchart of the optimization framework is presented in Fig. 2 with further discussion of this provided in subsequent sections.

maintained when the hull sections are moved forward and aft, the displacement value of the hull is changed in the process. In this study the parametric transformation module of Maxsurf is considered as it offers the capability to produce new candidate hull forms while maintaining the displacement and coefficient values of the parent hull [14]. Control points defining the non-uniform rational B-splines surface (NURBS) of the ship are moved in a smooth fashion producing an acceptable fair surface of the resulting hull. An elaborate discussion on the development of Maxsurf parametric transformation can be found in [13]. B. Resistance Estimation Tools

Fig. 1.

Inter-process communication flow between applications

Calm water resistance estimation of planing craft is bounded by certain validation criteria. The details of the range of validation is discussed in the work of [21] and [23] and in this study will be employed as constraints to the optimization problem. The details of the planing craft studied in this paper are presented in Table I. As discussed in [23], a craft is in full planing mode for speed coefficient cv ≥ 1.5. In this regime, the resulting dynamic forces cause a significant rise of the center of gravity, positive trim, emergence of the bow and the separation of the flow from the hard chines. C. Seakeeping Estimation Technique

Fig. 2.

Detailed flowchart of the optimization framework

The method described in Section II-B is suitable for calm water resistance. However, an additional formulation is required in order to calculate the total resistance, RT of the planing craft operating in a seaway. Fridsma’s [7] experimental tank test data on planing craft operating in rough water has been reworked by Savitsky and Ward Brown [23] in a form of equations suitable for computer programming. The estimation modules discussed serve as mathematical model in order to search for the optimum design inside the framework. Total resistance over irregular waves having energy spectrum of Pierson-Moskovitz is used in this study.

A. Geometry Tools The geometry tools consist of a surface information retrieval module and a geometry manipulation module. Shown in Fig. 2, the surface information retrieval module is employed to generate B-spline representation of the hull while the geometry manipulation module changes the shape of the hull based on principal dimensions given by the optimizer. The formulation of surface information module is based on the inverse B-spline method [20]. A set of known surface (offset) data is used to determine the defining polygon net for a B-spline surface that best interpolates the data. This method is further expanded to yield a representation of a hard chine form that normally represents a planing craft [15]. Three Bspline surfaces defined by their own respective polygon nets station-wise with the exclusion of the bow are connected to produce hard chines of the planing craft as shown in Fig. 3. Since the work of [11], the parametric transformation method has been used widely by naval architects to modify the form parameters of an existing parent hull form. While LCB and Cp values of the resulting hull can be

D. Maxsurf Automation Maxsurf Automation is an interface that provides extensive possibilities of integration between different naval architectural tools, whether developed in-house or commercially [14]. The automation library is built upon the c COM framework, thus allowing automation of Microsoft calls between compatible applications. E. Optimization Algorithms Solutions to real-life constrained optimization problems often lie on constraint boundaries. It is reasonable for a designer to be interested in solutions that might be marginally infeasible. Nondominated Sorting Genetic Algorithm-II (NSGA-II) [4] and most other optimization algorithms intrinsically prefer a feasible solution over an infeasible solution during its search process. However, some recent works suggest that preservation of marginally infeasible solutions during the course of a search can expedite the rate of convergence. The Infeasibility Driven Evolutionary

Algorithm (IDEA) introduced by [26] [25] is used in this study and further elaborated in this section. A multi-objective optimization problem can be formulated as shown in (1). Minimize f1 (x), . . . , fk (x) Subject to gi (x) ≥ 0, i = 1, . . . , m

(1)

where x = (x1 , . . . , xn ) is the design variable vector bounded by lower and upper bounds x ∈ S ⊂ IRn . A singleobjective optimization problem follows the same formulation with k = 1. To effectively explore the search space (including the feasible and the infeasible regions), the original k objective constrained optimization problem is reformulated as a k + 1 objective unconstrained optimization problem as given in (2) Minimize

f1′ (x) = f1 (x), . . . , fk′ (x) = fk (x) ′ (x) = Violation measure. fk+1

Algorithm 1 Infeasibility Driven Evolutionary Algorithm (IDEA) Require: N ; {Population size} Require: NG ≤ 1; {Number of generations} Require: 0 ≤ α ≤ 1; {Proportion of infeasible solutions} 1: Ninf = α × N ; 2: Nf = N − Ninf ; 3: pop1 = Initialize() 4: Evaluate (pop1 ); 5: for i = 2 to NG do 6: childpopi−1 = Evolve(Pi−1 ); 7: Evaluate childpopi−1 ; 8: (Sf , Si nf ) = Split(popi−1 + childpopi−1 ) 9: Rank (Sf ); 10: Rank (Sinf ); 11: popi = Sinf (1 : Ninf + Sf (1 : Nf )) 12: end for

(2)

The additional objective represents a measure of constraint violation, which is referred to as “violation measure” in this study. It is based on the amount of relative constraint violation among the population members. Each solution in the population is assigned m ranks, corresponding to m constraints. The ranks are calculated as follow. To get the ranks corresponding to ith constraint, all the solutions are sorted based on the constraint violation value of the ith constraint. Solutions that do not violate the constraint are assigned rank of 0. The solution with the least constraint violation value gets rank 1, and the rest of the solutions are assigned increasing ranks in the ascending order of the constraint violation value. The process is repeated for all the constraints and as a result each solution in the population gets assigned m ranks. The violation measure is the sum of these m ranks corresponding to m constraints. The main steps of IDEA are outlined in Algorithm 1. IDEA uses simulated binary crossover (SBX) and polynomial mutation operators [4] to generate offspring from a pair of parents selected using binary tournament as in NSGA-II. Individual solutions in the population are evaluated using the original problem definition (1) and infeasible solutions are identified. The solutions in the parent and offspring population are divided into a feasible set (Sf ) and infeasible set (Sinf ). The solutions in the feasible set and the infeasible set are both ranked separately using the non-dominated sorting and crowding distance sorting [4] based on k + 1 objectives as per the modified problem definition (2). The solutions for the next generation are selected from the sets to maintain feasible solutions in the population. In addition, the infeasible solutions are ranked higher than the feasible solutions (described below) to provide a selection pressure to create better infeasible solutions resulting in an active search through the infeasible search space. A user-defined parameter α is used to maintain a set of infeasible solutions as a fraction of the size of the population. The numbers Nf and Ninf denote the number of feasible

and infeasible solutions as determined by parameter α. If the infeasible set Sinf has more than Ninf solutions, then first Ninf solutions are selected based on their rank, else all the solutions from Sinf are selected. The rest of the solutions are selected from the feasible set Sf , provided there are at least Nf number of feasible solutions. If Sf has fewer solutions, all the feasible solutions are selected and the rest are filled with infeasible solutions from Sinf . The solutions are ranked from 1 to N in the order they are selected. Hence, the infeasible solutions selected first will be ranked higher than the feasible solution selected later. III. E XPERIMENTAL S ETUP A. Basis Hull The base hull form used in the study is a United States Coast Guard (USCG) patrol boat, referred to as USCG WPB-110ft. Comprehensive performance estimates of this vessel appears in the works of [30]. In this study, multiple surfaces of the hard chine planing craft are approximated by the surface information retrieval method [15]. Shown in Figure 3(a) is the body plan of the hull, and the derived approximations of the hull surfaces are shown in Figure 3(b). The published principal characteristics [30] called the actual craft are compared against those of the derived mathematical model in terms of the percentage error of differences and tabulated in Table I to establish the validity of the mathematical model. The vertical center of gravity, V CG of the basis ship is set equal to the actual ship. Although the block coefficient, cb and volumetric displacement, ∇ are not reported in [30], they are calculated and included in Table I. It can be observed that between the measured hull and the mathematical model, the geometric values (length, beam and draft) are matched within 1.3% and displacement value within 2.2% of error. A small error of the speed coefficient, cv and the calm water resistance, RC which is less than 5% of error served as a good fit thus allowing the modelled craft to be the basis ship in this study. Following the basis ship approach method, the

optimized candidate designs are compared with the modelled craft referred as basis ship hereafter.

16 knots, 25 knots and 30 knots denoted as RT16 , RT25 and RT30 respectively, can be written as RL =

(a) Ship lines [30] Fig. 3.

(b) B-splines surfaces

Body plan of the USCG WPB-110ft (actual and basis ship)

TABLE I C HARACTERISTICS OF USCG WPB-110 FT ( ACTUAL AND BASIS SHIP ) Description Displacement, ∆(kg) Length, L(m) Beam, B(m) Draft, T (m) V CG (m) Speed, Vk (knots) Cv Rc (kN) Cb ∇ (m3 )

Actual ship 120,909 33 7.62 1.58 2.70 30 1.785 130 -

Basis ship 118,217 32.93 7.52 1.60 2.70 30 1.797 135.93 0.291 115.4

% Error 2.23 0.21 1.33 1.27 0 0 0.67 4.56 -

X

(RT16 × 60% + RT25 × 20% + RT30 × 20%) × t (3)

where t can be set as constant (t = 1) in comparing between competing optimized candidate designs over RL values. In this paper, the WPB-110ft patrol craft is required to spend 60%, 20% and 20% of the time operating at 16 knots, 25 knots and 30 knots respectively as defined in Equation (3). Determined from the towing tank experiments at various speed of the model ship, effective power, PE is the power required to move the ship hull at a given speed in the absence of propeller action. In preliminary design stage where the knowledge on the propeller efficiency is absent, it can be assumed that PE is approximately equal to the thrust power, PT (Equation (4)). (4) PE ≈ PT m where PE = RT [kN] × v s . The fuel consumption, F C of a hull is proportional to the product of RT and the speed experienced by the hull. Given the value of specific fuel consumption, sf c of the engine, F C of a candidate ship can be written as: F C = RT [kN] × v

B. Definition of the Operability Condition Fuel cost depend on required engine output and operating time of a vessel [24]. The required power of a vessel in preliminary stage can be estimated through resistance estimation tools given the principal parameters and the required operating speed of the vessel. In this perspective, speed can be decisive for the economic efficiency of a ship thus influences the main dimensions in turn. The service speed of a WPB-110ft planing craft is incorporated based on a set of guidelines prepared by U.S. Department of Homeland Security [2]. Shown in Table II is a set of generic speed guideline for U.S. Coast Guard patrol vessels. In this work, the speed variation assumptions are incorporated where loitering (16 knots), transit (25 knots) and intercept (30 knots) are chosen. TABLE II NATIONAL S ECURITY PATROL C RAFT O PERATIONAL S PEEDS Mode Idle Tow Patrol Low Transit High Transit Intercept

Operations Stopped (e.g. boarding) Short distance transit/towing/training Economical patrol speed Transit to patrol area – rougher seas Transit to patrol area – calmer seas Top mission speed

Speed (knots) 0 5 15 18 21 ≥ 28

In any predetermined operational tempo, t the total resistance experienced over lifetime, RL with total resistance at

hmi

× sf c

h grams i

(5) s kW.s hence the lifetime fuel consumption between competing candidate designs can be compared. In real life where detail information are available for ship designers, the high speed planing craft optimization can be executed to minimize the fuel consumption, F C. However given the limited information in concept/preliminary stage, the optimization problem is defined as minimization of total resistance, RT and total resistance over a predefined lifetime, RL which are elaborated in the next section. C. Optimization Problem Formulation The single-objective optimization problem executed is described as the identification of a planing craft hull form with minimum total resistance, RT subject to the constraints on volumetric displacement, ∇ and stability (transverse metacentric height, GM ). Seaway operational scenario with one sea-state conforming to Pierson-Moskovitz energy spectrum represented by significant wave height H1/3 = 1.34m (seastate 1) is conducted. The objective functions and constraints are listed in Equation (6) where the subscripts ‘B’, ‘I’, ‘A’ and ‘C’ denote basis ship, candidate ship, added resistance and calm water resistance respectively. The procedure for estimating RT of the candidate design is bounded by validation ranges as suggested by [23] [14] such as half angle of entrance at bow (Ie ), length-cubic root of volumetric displacement ratio (L/∇1/3 ), length-beam ratio (L/B) and beam-draft ratio (B/T ) thus included in the formulation.

Minimize:

f (LI , BI , TI ) = RT where

Constraints:

are represented in ‘bold’ with respect to the speed it was intended to be optimized at.

RT = R C + R A

TABLE III S TATISTICAL SUMMARY OF THE OBJECTIVE FUNCTIONS VALUES OBTAINED USING IDEA

3

g1 = ∇I ≥ ∇B (∇B = 115.4m ) g2 = GMI ≥ GMB (GMB = 1.64m) 1/3

g3 = 3.07 ≤ LI /∇I ≤ 12.4 g4 = 3.7o ≤ IeI ≤ 28.6o g5 = 2.52 ≤ LI /BI ≤ 18.28 g6 = 1.7 ≤ BI /TI ≤ 9.8 Variables: 29.93m ≤ LI ≤ 35.93m (LB = 32.93m) 6.51m ≤ BI ≤ 8.51m (BB = 7.52m) 1.50m ≤ TI ≤ 1.70m (TB = 1.60m) (6)

Opt. Run 16 knots 25 knots 30 knots Lifetime

(7)

where the constraints and variables are similar to (6).

Std. Dev. (kN) 1.00 0.29 1.30 1.35

47

IV. E XPERIMENTAL R ESULTS The experimental results are divided into two sections, namely; minimization of total resistance, and observation of savings in fuel cost between basis ship and the optimized candidate ship. The former is focused on the amount of resistance that can be reduced through the optimization while the latter discussed the amount of fuel cost saved between the competing candidate designs.

Worst (kN) 45.21 136.70 166.28 87.84

48

Total resistance (kN)

f (LI , BI , TI ) = RL

Median (kN) 42.26 135.8 162.96 85.35

49

Minimization of total resistance over a set of collective speed (Equation (3)) is also included and defined as Minimize:

Best (kN) 41.87 135.46 161.95 84.31

46 45 44 43 42 41

0

Fig. 4.

5

10 15 20 Number of function evaluations

25

30

Progress plot of best design for optimization at 16 knots

A. Minimization of Total Resistance 146

144

Total resistance (kN)

Thirty independent runs of IDEA were performed. A population size of 40, crossover probability of 1, mutation probability of 0.1, crossover distribution index of 10 and a mutation distribution index of 20 has been used by the algorithm. The number of function evaluations of the algorithm was restricted to 1200. The best, median, worst and standard deviation of the objective functions obtained from optimization across 30 runs are reported in Table III. On a HP z400 workstation (with Intel(R) Xeon(R) 3.33 GHz processor and 6 GB RAM), the CPU time taken to complete 1200 function evaluations is 150 mins. The RT values corresponding to the best run of IDEA for each speed definitions are plotted against function evaluations in Fig 4, 5, 6 and 7 respectively. The algorithm is able to derive savings in RT as compared to the basis hull while satisfying the constraints on displacement and stability. The best designs are tabulated and compared against their corresponding basis designs operated at 16 knots (D16 ), 25 knots (D25 ), 30 knots (D30 ) and different percentage of speed spent lifetime (DL ) in Table IV. Other principal particulars such as block coefficient (cb ), prismatic coefficient (cp ), waterplane coefficient (cwp ), deadrise angle (δ) and wetted surface area (W SA) are also included in the table. The values

142

140

138

136

134

0

Fig. 5.

5

10 15 20 Number of function evaluations

25

30

Progress plot of best design for optimization at 25 knots

Shown in Table IV, the value of RT of the basis ship and its optimized candidate design operating at 16 knots (D16 ) is 47.23 kN and 41.87 respectively, accounting for 11.34% of reduction. For the candidate design at 25 knots (D25 ), 10.87% of reduction is achieved with the RT of the basis and optimized candidate design are 151.97 kN and 135.46 kN

TABLE IV M INIMIZATION OF RT FOR THREE DIFFERENT SPEEDS OF 16, 25 AND 30 KNOTS

176 174

Basis

D16

D25

D30

DL

L(m) B(m) T (m) GM (m) cb cp cw p δ(o ) W SA(m2 )

115.4 32.93 7.52 1.6 1.64 0.291 0.680 0.614 32.09 193.82

115.4 35.92 7.16 1.52 1.64 0.295 0.686 0.623 31.31 192.75

116.54 35.91 7.29 1.51 1.80 0.295 0.686 0.623 30.68 194.71

115.4 35.92 7.16 1.52 1.65 0.295 0.686 0.623 31.29 192.77

115.5 35.93 7.17 1.52 1.65 0.295 0.686 0.623 31.29 192.91

16 (kN) RC 16 (kN) RA 16 (kN) RT

39.54 7.69 47.23

34.33 7.54 41.87

35.53 7.69 43.22

34.34 7.54 41.89

34.4 7.55 41.94

11.34

8.49

11.31

11.20

98.39 35.11 133.49

99.35 36.11 135.46

98.36 35.14 133.5

98.46 35.16 133.62

12.16

10.87

12.15

12.07

121.93 40.00 161.94

123.01 41.29 164.30

121.9 40.05 161.95

112.02 40.08 162.10

8.33

6.99

8.32

8.32

84.21

85.88

84.22

84.31

10.47

8.69

10.45

10.37

Total resistance (kN)

172

∇(m3 )

170 168 166 164 162 160

0

Fig. 6.

5

10 15 20 Number of function evaluations

25

30

Progress plot of best design for optimization at 30 knots

% savings 25 (kN) RC 25 (kN) RA 25 (kN) RT

91

90

113.08 38.89 151.97

% savings Total resistance (kN)

89

30 (kN) RC 30 (kN) RA 30 (kN) RT

88

135.93 40.72 176.65

% savings

87

RL (kN) 86

94.06

% savings

85

84

Fig. 7.

0

5

10 15 20 Number of function evaluations

25

30

Progress plot of best design for optimization at lifetime operation

respectively. The value of RT of the basis ship and optimized candidate design operating at 30 knots (D30 ) is 176.65 kN and 161.95 kN respectively, giving a reduction of 8.32%. It can be observed that the RT16 , RT25 and RT30 for DL are 41.94 kN, 133.62 kN and 162.10 kN respectively, accounting for highest savings when operated at 25 knots (12.07%) followed by 16 knots (11.20%) and 30 knots (8.23%). The RL for basis and DL is 94.06 kN and 84.31 kN respectively, resulting a total of 10.37% of savings across collective speed over lifetime. Highlighted in Section III-B, a USCG patrol craft is required to undergo different speed while completing several tasks namely loitering, transit and intercept. Shown in Table IV, each candidate designs D16 , D25 and D30 are further evaluated in different speed to observe the total reduction of RT and compared against the basis ship. The resistance experienced over the percentage lifetime, RL is calculated, resulting 84.21 kN for D16 , accounting for 10.47% of RL reduction. D25 is able to reduce up to 8.69% with RL of 85.88 kN, and D30 with RL of 84.22 kN accounting for

reduction of 10.45% respectively. B. Savings in Fuel Cost The total resistance for each candidate designs can be used to measure the fuel consumption given the operational definition. The expected operational tempo, t at sea for USCG WBP-110ft is 3000 hours per year [29] [10], thus the fuel consumption, F C for each candidate designs with RT16 , RT25 and RT30 given the value of specific fuel cost, sf c can be calculated using the expression below: F C =(RT16 × v16 × 0.6 + RT25 × v25 × 0.2+

(8) RT30 × v30 × 0.2) × sf c × t   where v is in ms and it is assumed that the sf c = grams 0.06 kW.s [6]. Shown in Table V are the fuel consumptions of the optimized candidate designs compared against basis ship. The estimated reduction in annual fuel consumption for D16 is 10.21%. For D25 and D30 , the reduction in annual fuel consumption are 8.58% and 10.20% respectively. DL is able to reduce the annual fuel consumption up to 10.11%. One can observe that there is a similarity among candidate designs D16 , D30 and DL in terms performance and principal particulars. It can be implied that the three candidates

TABLE V F UEL CONSUMPTION COMPARISONS BETWEEN CANDIDATE AND BASIS DESIGN (t=3000 HOURS / YEAR )

Basis ship D16 D25 D30 DL

F C[kg/hr] 175.39 157.48 160.33 157.50 157.66

fuel saving (%) 10.21 8.58 10.20 10.11

are effectively the same design, while D25 is in overall a different design. Although in this exercise, no advantage can be observed in terms of defining a set of collective speed over predefined lifetime, the proposed framework is capable of generating the optimum hull form while at the same time enabling a provision for ship designers to evaluate the candidate designs in terms of performance over various operating scenarios. V. S UMMARY AND C ONCLUSIONS In this paper an optimization and analysis of high speed planing craft named USCG WPB-110ft is presented. Rather than focusing on single speed optimization, a scenariobased optimization is demonstrated through the application of operational tempo that is required for a USCG WPB110ft patrol craft by U.S. Department of Homeland Security. Optimized candidate designs identified from minimization of total resistance at 16 knots, 25 knots, 30 knots and collective speeds over predefined lifetime are further evaluated in different operating conditions and its respective corresponding performance is compared. The study demonstrated that around 10.21% reduction in fuel consumption can be achieved over the performance of the basis design through the use of hydrodynamic design optimization framework proposed in this paper. One can observe that there is a similarity among candidate designs D16 , D30 and DL in terms performance and principal particulars thus implying that those are effectively the same design, while D25 is in overall a different design. Although no advantage can be observed in terms of defining a set of collective speed over predefined lifetime in this exercise, the proposed framework demonstrates the principles governing its use for scenario based optimization problems. ACKNOWLEDGMENT This material is based on work supported by the University of New South Wales at Australian Defence Force Academy (UNSW@ADFA), Australia and University Malaysia Terengganu (UMT), Malaysia. Any opinions, findings and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the UNSW@ADFA and UMT. R EFERENCES [1] J. M. Almeter. Resistance Prediction and Optimization of Low deadrise, Hard Chine, Stepless Planing Hulls. In SNAME Ship Technology and Research Symposium (STAR), 1995.

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