A Prototype Tool for Multidisciplinary Design Optimization of Ships

8/2/2019 A Prototype Tool for Multidisciplinary Design Optimization of Ships

http://slidepdf.com/reader/full/a-prototype-tool-for-multidisciplinary-design-optimization-of-ships 1/8

Ninth Congress of the International Maritime Association of the Mediterranean, April 2-6, 2000, Naples, Italy

A Prototype Tool for Multidisciplinary DesignOptimization of Ships

W.L. Neu, O. Hughes, W.H. Mason, S. Ni, Y. Chen, V. Ganesan, Z. Lin, S. TummaDepartment of Aerospace and Ocean EngineeringVirginia Polytechnic Institute and State University

Blacksburg, VA 24061

A multidisciplinary design optimization scheme for ships has been developed for use in anintegrated ship design environment. Although the system was designed with the intentionof using first principle analysis techniques, the containership design examples presented inthis paper make use of surrogate parametric analysis modules developed to examine prob-lem formulation issues prior to the availability of the higher fidelity modules. A method of hull shape control based on a barycentric blend of basis hulls is developed. It requires rela-

tively few design variables. In addition to general-purpose geometry, hydrostatic and re-sistance modules, containership-specific weight, cargo and economics modules were devel-oped. The measure of merit is taken to be the required freight rate. Optimal ship size isfound to depend largely on port loading and unloading capabilities. The required freightrate increases and the speed of the optimal ship decreases as voyage length is decreased orfuel cost is increased.

IntroductionThe work described in this paper was

conducted as part of the FIRST projectfunded under the U.S. Navy’s MARITECH

program. The goal of this project was todevelop an integrated computational designenvironment that would enable the ship de-signer to reduce the time needed to produceand analyze alternative ship designs at ahigh level of detail. It is envisioned thatdesign calculations be done at a first-principles level, including manufacturingand operational econometrics.

The idea of having hydrostatic, resis-tance, propulsion, economic, etc. analyses

enabled in a common design environmentled naturally to the desire to implement amultidisciplinary design optimization(MDO) capability. With MDO, the de-signer can break out of the traditional de-sign-spiral approach and, what has beencalled the “stove-pipe” analysis approach.

The design obtained by the design-spiral approach is a valid, balanced solutionto a given set of requirements, but it is also

a solution that is not unique. By choosing ameasure of merit, which can be calculatedfor a candidate design, the optimizationprocess will attempt to find the designwhich maximizes (or minimizes) this meas-ure. In the case of the FIRST project,which is aimed at commercial ship designand which is to include first principle eco-nomic measures, we have chosen to mini-mize the required freight rate.

This MDO process also brings to bear

the fidelity of first-principle analyses atwhat would normally be thought of as apreliminary design stage. Typically, basiccharacteristics (e.g., principal dimensions)are largely determined during the first orsecond turn around the design spiral. De-tailed analyses are not carried out until later



2

in the design process when flexibility tochange these general characteristics hasbeen greatly reduced. Decisions that de-termine these characteristics are generally

made based on a single discipline’s analy-sis. By employing the MDO process, alldesign variables are allowed to be variedbased on their effect on the measure of merit and, hopefully, converge to an opti-mum design as the process progresses.

Two generally popular classes of algo-rithms for the optimization process are gra-dient-based and genetic algorithms. In thegradient-based algorithms, sensitivities of the objective function (the measure of merit) to changes in the design variables arecalculated and the vector of design vari-ables is adjusted in the direction so indi-cated. In the genetic algorithms, an initialset of randomly chosen designs is ranked bytheir objective function values. A secondgeneration of designs is then obtained asmore or less random mutations of the betterdesigns of the previous generation. Thisprocess continues until little improvementin the objective function is seen from gen-eration to generation.

Since genetic algorithms do not requiredifferentiation of the objective functionwith respect to the design variables, theyhandle cases of discrete design variables(such as choice of power plant) more easilythan gradient-based algorithms. On theother hand, they usually require a muchlarger number of objective function evalua-tions than is necessary for the gradient-based algorithms. Thus, genetic algorithmsare practically restricted to parametricanalysis methods by the computational timerequired. Since it is our intention to employfirst-principle analysis codes, we have cho-sen to use gradient-based algorithms in thiswork. Frank, et al (1) present a further dis-cussion of optimization methods.

Keane, et al (2) present another exam-ple of gradient based methods applied toships. An application of a genetic algo-rithm to minimizing hull resistance is given

by Day and Doctors (3). Sen (4) and Rayand Sha (5) present approaches to the mul-ticriteria optimization problem.

System OverviewThe computational code consists of a

number of analysis modules, an optimizerand a user interface. The code is writtenwith a target platform of Microsoft Win-dows NT and uses Microsoft’s ComponentObject Model (COM) framework. This was

done so that the MDO system will be com-patible with the larger FIRST project designtool into which it will be integrated. In theworld of COM, each module acts as an in-dependent server exposing its services toother independent client modules throughone or more interfaces. Thus, as long as theinterfaces are the same, the modules sup-plying analysis services may be replaced byanother module providing the same servicewith negligible impact on the rest of thecode.

This feature was important in that boththe MDO system and the larger FIRST toolof which it is to be a part, were being de-veloped simultaneously. The higher fidel-ity analysis tools, which will ultimately beused in this system, were not yet availableand thus surrogate analysis modules werewritten. In order to explore problem for-mulation issues, these surrogate modulesneeded to perform in the same generalmanner as the high fidelity modules andthus simple parametric representations of the analyses were used.

The Design Optimization Tools (DOT)package from Vanderplaats Research andDevelopment, Inc. was chosen as the opti-mizer. DOT includes the choice of threegradient-based optimization methods, a



3

modified method of feasible directions, se-quential linear programming, and sequentialquadratic programming. We have created aDOT COM object by writing a C++ wrap-

per around the DOT FORTRAN sourcecode. Tests have shown that the quickestand most consistently reliable results areobtained using sequential linear program-ming. It is used for the examples presentedbelow.

Besides the optimization module, thesystem has modules which perform thefollowing functions: calculate a NURBS(Non-Uniform Rational B-Spline) hull ge-ometry surface, calculate a mesh of offsetson the surface described by the NURBSnet, integrate the surface and calculate hy-drostatic properties, calculate ship resis-tance, calculate propulsive efficiency, pow-ering requirements and fuel rate, calculatelightship weight and CG, calculate payloadweight and CG, calculate roll period, mini-mum GM and freeboard, and calculate eco-nomic characteristics. Each of these is dis-cussed briefly below.

Immediately obvious is that the weightand economics modules depend on the shiptype. A containership design problem waschosen for the construction this prototypeMDO system.

The design variables, i.e., those vari-ables that the optimizer manipulates, arechosen to be: the overall length, beam anddepth of the hull, the draft, the cruisingspeed, and a (set of) parameter(s) that con-trols the hull shape. The hull shape ma-nipulation is discussed in the next section.

Hull GeometryAs a means of controlling the hull

shape, the hull is represented as a barycen-tric blend of basis hulls. This can be repre-sented as

∑C n BasisHulln = Resultant Ship Hull

where,

∑C n = 1and,

0 ≤ C n ≤ 1,

n = 1, 2, …, N.Thus, the hull resulting from this blendingprocess is restricted to being a member of the hull shape space bounded by the basishulls. Figure 1 illustrates the blending con-cept for the midship section in a case of only two basis hulls.

Figure 1. Illustration of geometry blendingtechnique.

The blending coefficients, C n, are thedesign variables that adjust the hull shape.

Because of the constraint, ∑C n = 1, thenumber of design variables the optimizermust adjust is N - 1. The blending is ap-plied to the NURBS net points of the basishulls (which have standard dimensions) andthe resulting hull is then scaled to the nec-

essary length, beam and depth.

HydrostaticsFrom the NURBS net obtained by the

blending and scaling discussed above, a setof unequally spaced points located on thehull surface represented by the NURBS netis calculated. Hull volumes and areas arecalculated from this mesh of surface pointsand the displacement, the hydrostatic coef-ficients, and the metacentric height are cal-

culated by the hydrostatics module.

Resistance and PropulsionThe ship’s resistance at the current

cruising speed is calculated using the Hol-trop/Mennen regression formula (6). Addi-tional resistance due to appendages is ig-

+ =



4

nored; however, the effect of a bulbous bowis retained. The propulsion module, at pre-sent, simply assumes an overall propulsiveefficiency of 0.65. From this a shaft horse-

power is obtained and, from a specific fuelconsumption that is input as a parameter, afuel rate is calculated.

WeightsParametric relationships for lightship

weights and centers of gravity were ob-tained from Benford (7), Taggert (8) andSchneekluth (9). Lightship was broken intothree categories: hull steel, outfit and pro-pulsion machinery, each with its own para-

metric equations for weight and center of gravity. Because the coefficients used inthe parametric equations obtained from theabove references did not reflect modern de-sign and construction practices, the weightequation coefficients were recomputedbased on seven modern containershipsranging in length from 186 to 263 m. Athree percent margin was added to the cal-culated lightship weight and a 0.3 m marginwas added to the vertical center of gravity.

Fuel weight was based on the specifiedship range, its speed and the calculated fuelrate. A ten percent reserve was added tothe fuel weight. Relations for miscellane-ous weights, including, crew and provi-sions, fresh water and lube oil, were ob-tained from Erichsen (10).

CargoIt is necessary to calculate the con-

tainer carrying capacity as the ship’s di-mensions vary. Two relations were devel-oped, one for containers, in terms of TEU’s(Twenty foot Equivalent Unit, 6.1 m x 2.44m x 2.44 m), below deck and one for TEU’son deck.

For TEU’s below deck, the integernumber of containers that will fit alongeach of the length, beam and depth direc-tions is found, allowing for wing tank and

double bottom spaces. These integer valuesare multiplied together to form a block ca-pacity, which is then multiplied by a stow-age factor that is a function of block coeffi-cient. The stowage factor was determinedfrom the known capacities of twelve exist-ing ships.

The relation for number of containersabove deck is similar to that below deck,except that the number of tiers of containerson deck (not required to be an integer) issubstituted for the number that would fitdepthwise and a different stowage factor isused.

Cargo weight is simply the total num-ber of containers multiplied by an averagecontainer weight. The center of gravity of the containers above deck is calculated con-sidering them to be of uniform density andraised off the deck by a hatch coamingheight. The CG of the containers belowdeck is raised from the mid height of theavailable depth by a factor that depends onblock coefficient.

With this scheme, the container capac-ity, cargo weight, etc., is a discontinuousfunction of the ship’s dimensions (Figure2). This results in a discontinuous, saw-tooth like objective function (the requiredfreight rate) with many local minima thatthe optimizer can fall into. Also, the valuesof the numerically calculated gradients canbe significantly in error in the vicinity of the discontinuities, which is a problem forgradient-based methods. To remedy thissituation, we have chosen to fit a linear re-sponse surface to the discontinuous con-tainer capacity function as is illustrated intwo dimensions in Figure 2.



5

Figure 2. 2-D illustration of container ca-pacity function and linear re-sponse surface.

EconomicsTo calculate the required freight rate,

the economics module must find building

costs and annual operating costs. These areobtained using the relations of Benford (7)and Erichsen (10).

Building cost is broken into labor andmaterials costs for each of: hull steel, outfit,hull engineering and propulsion machinery,miscellaneous costs, accommodation costs,overhead costs, yard’s profit and owner’sexpenses. Each of these costs has its ownparametric relation that is ultimately basedon one or more components of lightshipweight, installed horsepower, or number of crew. The building cost is converted to anannual cost by specifying a life of the shipand an interest rate.

To calculate annual operating costs,the number of round trips made annually bythe ship must be known. This depends onthe cruising speed, to find time spent at sea,and on time spent in port. The port timeincludes waiting time and time spent load-ing and unloading the ship. The load-ing/unloading time depends on the numberof cranes being used. The number of cranescan be specified or can be calculated basedon length. The annual operating cost isthen formed as the sum of individual rela-tions for wages, stores and supplies, insur-ance, maintenance and repair, port ex-penses, and fuel cost.

The required freight rate is then ex-pressed as total average annual cost per tonof cargo carried per mile. Important pa-rameters used by the system but not men-

tioned above include, labor cost, materialcosts for hull, outfit and engineering, num-ber of containers handled per day per crane,voyage distance and fuel price. No percontainer cargo handling charges are in-cluded since they vary widely from port toport and they do not affect the point in thedesign space at which the minimum occursbut serve only to boost the value of the re-quired freight rate for all designs.

ConstraintsThe condition that weight equal dis-placement is enforced as a constraint. Wetreat draft as an independent design variablerather than enforce the weight-displacementbalance through an internal loop at eachdesign iteration. This has been called anoptimization based decomposition ap-proach. Tests have shown that this quick-ens the calculation over an approach wherethe design is balanced at each iteration.

The U.S. Coast Guard wind heel crite-rion for minimum initial stability and theU.S. Coast Guard minimum freeboard re-quirement are also imposed as constraints.

The user may select constraints onminimum rolling period, maximum dis-placement, maximum shaft horsepower,and both upper and lower bounds on con-tainer capacity. A structural constraint andconstraints on the dimension ratios will beimplemented in the future.

Two modifications of the constraintswere needed to ensure convergence from aninfeasible starting point with a negativeGM . First, since the natural roll period isundefined for GM < 0, it was artificiallyextended into this region as an even func-tion of GM . Second, the initial stabilityconstraint is formulated as

Ship dimensions, L, B, D

C

o n t a i n e r c a p a c i t y

Response surfaceapproximation

Discontinuous

capacity function



6

.01min

≤−=GM

GM g

For GM << 0, the derivative of g with re-

spect to beam, B

g∂

∂, can become positive

(due to the dependence of GM min on beam)indicating that the beam should be de-creased rather than increased and the opti-mizer fails to find a feasible solution. Toovercome this, we hold GM min equal to itsinitial value while GM < 0.

Example ApplicationsSeveral applications are presented be-

low. In each case, the hull shape is adjustedby blending two basis hulls. Only oneshape design variable is needed, C 1. Basishull 1 is finer than basis hull 2. The im-portant parameter values for each case are:ship life = 20 yrs, interest rate = 8%, weightper TEU = 12 mt, and specific fuel con-sumption = 120 g/BHP/hr. Except in Ex-ample 4, the number of cranes loading andunloading is calculated based on one craneevery 135 feet over 75% of the ship length.For the 300 m designs that result below,this means 6 cranes. Except in Example 5,

voyage distance = 7000 nmi. Except forExample 6, the fuel price used was $80 permt. In light of the return of fuel prices toconsiderably higher values in recent months(December 1999), the final example is arepeat of the first with a fuel cost of $120per mt.

Table 1 gives the initial values of thedesign variables used for Example 1 alongwith their upper and lower limits. The up-per limits on length, beam, and draft were

chosen to roughly coincide with a recentlybuilt, large containership. The initial valuesof the design variables result in an infeasi-ble design with an initial GM of –7.4 m, aweight of 42,000 mt, and a displacement of 33,700 mt. The results for each exampleare presented in Table 2. Convergence is

quick; these examples each converge in 7 –15 iterations.

Lowerlimit

Initialvalue

Upperlimit

LOA 130.0 200.0 300.0Beam 15.0 28.0 43.0Depth 10.0 20.0 30.0Draft 4.0 10.0 13.5Speed 4.00 19.0 35.00C1 0.00 0.5 1.00

Table 1. Design variable bounds andinitial values for Example 1.

Example 1 is a minimally constrainedcase. The only constraints applied, otherthan the side bounds on the design vari-

ables, are weight equals displacement, thestability criterion and the minimum free-board. The optimizer goes to the maximumlength and beam and chooses the fullestpossible ship that could result from theblending. The value of C 1 is essentiallyzero, or the optimum ship is all basis hull 2.It is interesting to note that the requiredfreight rate is relatively insensitive to thevalue of the blending coefficient. The op-timum ship has a B/D = 3.1 and a L/D =

21.6, both very high. This is the result of the absence of a structural constraint. Con-straints on these ratios would serve to artifi-cially impose a structural requirement.

Example 2 is the same as Example 1except that the lower bound on the speedhas now been raised to 25 knots. Ratherthan going for the fullest hull, the optimizernow chooses the finest possible hull; theoptimum is all hull 1, C 1 = 1. The ship car-ries fewer containers but has a larger dis-

placement. This is due, in large part, to theincreased engine weight, which also causesa drop in GM and subsequent raise in natu-ral roll period. The required freight rate jumps about 20% with the high speed.Both Examples 1 and 2 have the minimumrequired freeboard.



7

Example 3 is the same as Example 1except with the additional constraint of a 25second natural roll period. By using severalstarting points, the optimizer found two

solutions to this problem that give ap-proximately the same required freight rate.These are shown as 3a and 3b in Table 2.Solution 3a uses a smaller beam, smallerdepth, and less freeboard than does solution3b. It consequently carries fewer containersbut requires less SHP for about the samespeed and so the required freight rates aresimilar. This illustrates that the optimizerfinds local rather than global optima. Thelarger roll period costs about 5% in requiredfreight rate.

The fourth example illustrates the ef-fect of port time on the optimum design.This example is, again, the same as Exam-ple 1 but with only one crane being used toload and unload the ship. The increase intime spent in port reduces the benefit of in-vestment in a larger, faster ship. The resultis a much smaller, slower ship than wasobtained in Example 1. The requiredfreight rate has increased 41%.

For the fifth example, the voyage dis-tance was halved to 3500 nmi but other-wise, the conditions were the same as forExample 1. It was thought that changes in

the optimum ship in the same direction aswas seen in Example 4 would be obtainedsince the time in port relative to that at seawas again increased; however, what wasfound was a very similar, only slightlyslower ship with a 20% higher requiredfreight rate shown as Example 5a. Thevoyage distance was then cut to 1000 nmi.The result, shown as Example 5b, wasagain, a very similar, but slower ship. Itappears that if the cranes are available, it isworth building a large ship, assuming of course that the market exists for the largecapacity.

Example 6 looks at the effect of raisingthe fuel cost from $80/mt to $120/mt. Ex-cept for this change, the input is the same asfor Example 1. The optimum ship is nearlyidentical to the one in Example 1 with theexception of a slower speed and the conse-quent smaller SHP and displacement. Thefuel cost was also raised in Example 2,where a 25 kn speed is required; a nearly

Table 2. Design variable values and various ship characteristics at the optimumpoint for each example.

Ex. 1 Ex. 2 Ex. 3a Ex. 3b Ex. 4 Ex. 5a Ex. 5b Ex. 6

Loa (m) 300.0 300.0 300.0 300.0 209.0 300.0 299.8 300.0Beam (m) 43.0 43.0 36.1 39.2 43.0 43.0 43.0 43.0Depth (m) 13.9 16.6 14.7 16.6 11.7 13.8 13.7 13.9Draft (m) 9.14 11.9 9.44 10.1 8.29 9.06 8.96 9.10Speed (kn) 17.1 25.0 17.5 17.8 15.1 16.8 15.3 15.9C1 0.0 1.00 0.003 .012 0.008 0.008 0.013 0.0Displ.(mt) 85,030 88,370 73,320 83,780 54,400 83,960 82,900 84,520# TEU’s 5203 5049 4427 4996 3393 5183 5165 5195SHP 22,040 72,650 20,700 23,050 11,970 20,790 15,110 17,260Roll per. (s) 11.2 17.8 25.0 25.0 9.32 11.2 11.2 11.2Cb 0.714 0.568 0.710 0.703 0.722 0.712 0.712 .713RFR ($/t/nmi) .00106 .00126 .00111 .00111 .00149 .00124 .00212 .00115



8

identical ship was obtained but its requiredfreight rate went up by 18% to 0.00149$/t/nmi.

ConclusionsA prototype MDO tool for ship designhas been developed based on Microsoft’sCOM framework. With this design, theanalysis modules can be replaced with aminimum of programming effort. Surro-gate parametric analysis modules have beendeveloped for the purpose of exploringproblem formulation issues while higherfidelity analysis modules are being devel-oped. A geometric shape manipulation

scheme was developed in which the hullwas formed by blending a set of basis hulls.The MDO system was exercised on a

set of containership design problems withthe objective being to minimize the re-quired freight rate. It was found that with-out being otherwise constrained, the opti-mizer sought the largest allowed length andbeam. In the absence of a structural con-straint, the optimizer seeks a design with ahigh B/D ratio.

The MDO system generally behaves asexpected. Test exercises have shown that if the loading/unloading time is constrained,investment in larger, faster ships is notbeneficial. Required freight rate decreaseswith increasing voyage distance but vesselsize is determined by how fast it can beturned around in port. The limited studyperformed indicates that fuel cost affectsthe required freight rate and optimum speedbut not the principal dimensions of the ship.

References

1. Frank, P. D., A. J. Booker, T. P. Caudel,and M. J. Healy. A comparison of optimi-zation and search methods for multidisci-plinary design. AIAA-92-4827, 4th Sympo-sium on Multidisciplinary Analysis and

Optimization, Sept. 21-23, 1992, Cleveland,OH.2. Keane, A. J., W. G. Price and R. D.Schachter. Optimization techniques in ship

concept design. Trans. RINA, Part A, Vol.133, 1991, pp. 123-139.3. Day, A. H. and L. J. Doctors. Resis-tance optimization of displacement vesselson the basis of principal parameters. J.Ship Res., Vol. 41, No. 4, Dec. 1997, pp.249-259.4. Sen, P. Marine design: the multiple cri-teria approach. Trans. RINA, Part B, Vol.134, 1992, pp. 261-272.5. Ray, T. and O. P. Sha. Multicriteria op-timization model for a containership design.Marine Tech., Vol. 31, No. 4, Oct. 1994,pp. 258-268.6. Holtrop, J. and G. G. J. Mennen. A sta-tistical re-analysis of resistance and propul-sion data. Inter. Shipbldg. Progress, Vol.31, Nov. 1984.7. Benford, H. The practical application of economics of merchant ship design, MarineTech., Jan. 1967.8. Taggart, R. Ship Design and Construc-tion, The Society of Naval Architects andMarine Engineers, 1980.9. Schneekluth, H. Ship design for effi-ciency and economy. Aachen University of Technology, 1987.10. Erichsen, S. Optimum capacity of shipsand port terminals. Doctoral dissertation,Univ. of Mich., Ann Arbor, April 1971.

A Prototype Tool for Multidisciplinary Design Optimization of Ships

Documents

Transcript of A Prototype Tool for Multidisciplinary Design Optimization of Ships