optimization of an air cushion vehicle bag and finger skirt using genetic algorithms

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Aerospace Science and Technology 8 (2004) 219–229www.elsevier.com/locate/aesc

Optimization of an air cushion vehicle bag and finger skirtusing genetic algorithms

Joon Chung∗, Tae-Cheol Jung

Department of Aerospace Engineering, Ryerson University, Toronto, Ontario M5B 2K3, Canada

Received 16 May 2003; received in revised form 4 November 2003; accepted 6 November 2003

Abstract

The air cushion vehicle (ACV) is the advanced marine vehicle that provides not only excellent performance on rough surfacethe high speed that other conventional marine vehicles could not achieve. Hence, a large number of ACVs have been utilized fpurposes and missions. At the present the flexible skirt system, the bag and finger skirt, is recognized as the most updated and adsystem. In this paper, the ACV’s bag and finger skirt system geometry is optimized to modify an undesirable heave response forride quality by using the Genetic Algorithm (GA). The pure heave motion of a two dimensional section of the bag and finger skirt sinvestigated using a mathematical model. Two configurations representative of a 37 ton vehicle used by Canadian Coast Guard150 ton vehicle used by US Navy show a resonance associated with the skirt mass at frequencies at which humans are most seskirt geometry obtained by GA considerably ameliorates this effect, and the ride comfort of the optimized ACV can be greatly icompare to the original configuration within the given constraints such as the required vehicle’s hard structure dimensions and we 2003 Elsevier SAS. All rights reserved.

Keywords: Air cushion vehicle; Bag and finger skirt; Linearization; Genetic algorithm; Optimization

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1. Introduction

1.1. Background of air cushion vehicle

The early concept about Air Cushion Vehicle (ACwas started from Sir Christopher Cockerell’s experimin England, 1955 [1]. Then many forms of design aconstruction for ACVs have continuously been develofor better performance and real world application. SinACV is a transport vehicle that relies on a novel formsupport by the air cushion, many applications have bdeveloped. For example in North America, US Nav150 ton Landing Crafts Air Cushion (LCAC) are nowservice where other vehicles are difficult to operate sas on-water operations and amphibious assault warCanadian Coast Guard (CCG) also utilized ACVs for seaand-rescue missions and ice-breaking service. The prework extends a previous analysis by Chung et al. [3]the numerical investigation of the linear dynamics osimplified bag and finger skirt configurations representa

* Corresponding author.E-mail address: [email protected] (J. Chung).

1270-9638/$ – see front matter 2003 Elsevier SAS. All rights reserved.doi:10.1016/j.ast.2003.11.002

.

t

of 150 ton LCAC craft and 37 ton CCG craft to finoptimized bag and finger skirt system for the better rquality by using the Genetic Algorithm (GA). It is intendethat this work will lead to proposals for improved skdesigns.

1.2. Bag and finger skirt

The air flow paths and pressures in a typical bagfinger skirt system are described as follows. The aircushion lift is provided by centrifugal or mixed-flow fanThe lift fan system thus provides the required pressto support the vehicle, and accommodates changes incushion volume as the vehicle passes over various terrThe fans deliver air directly into a plenum chamber of whthe bag volume forms a part. Then air passes througnumber of orifices located on the bottom portion of the bas depicted in Fig. 1 to the main cushion. Once in the custhe air pressure should be sufficient to support the craftthe equilibrium pressurepce is determined primarily by theplanform dimension and weight of the craft. From the finthe flow finally exits to the atmosphere through the hovgap.

220 J. Chung, T.-C. Jung / Aerospace Science and Technology 8 (2004) 219–229

Fig. 1. Basic concept of the bag and finger skirt.

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The bag and finger skirt, as the most widely used on laACVs, provides good performance such as a significanduction in power requirement, reasonable maintenanchover gap, better maneuverability, and stability [19]. Nertheless its behavior is still not completely understoodit is not free of problems. One such problem is its tendeto produce a rough ride [1] and another is its susceptity to an instability known asskirt bounce. The skirt bounceis a self-excited limit cycle oscillation involving predomnantly vertical motion of the entire skirt [6,11]. Fig. 1 showthe principal elements of the bag and finger skirt. Theacts as a filter for long-wavelength disturbances by chaing its shape in response to changes in both bag and cupressures induced by vehicle motion. The fingers providecontinuous surface seal by keeping the effective hoverto a minimum in the presence of short wavelength disbances. The typical finger element is also shown in Figand this can be easily replaceable due to wear with use.

The results of nonlinear simulations for the 150 tUS Navy’s Air Cushion Landing Craft (LCAC) and 3ton Canadian Coast Guard (CCG) configurations shcharacteristically nonlinear dynamic phenomena suchperiod doubling and chaos during the normal operaof ACVs equipped with the bag and finger skirt [4]. Ban important feature, revealed also by linear analysisthe presence of resonance associated with skirt massfrequency close to the range at which humans are msensitive and this may significantly affect ride comfort. Twork described here is continuation of linear analysis witview to find the optimal properties of the bag and finger ssystem for better ride comfort and stability of ACVs.

The ride quality can be defined from the amplitudethe craft heave frequency response. Typical heave amplresponse to small ground input as a function of frequeshows a characteristic double-peak with the lower frequepeak being associated with the craft mass and the hi

n

a

r

frequency peak associated with the skirt mass [4]. Tsecond peak is very large due to the large motion ofskirt interacting with the nonlinear characteristics of floescape between the bottom of the fingers and the groThis large resonance peak is undesirable since its frequis very close to the range of 25 rad s−1 to 50 rad s−1 wheremost of people feel the maximum sensitivity for the vertivibration [7,12]. Thus for better ride quality, the second pof frequency response curve should be out of this frequerange and its magnitude must also be reduced as mucpossible. This condition will improve ride comfort.

For the stability of ACVs, it can be analyzed frostudying the eigenvalues of the system matrix forlinearized equations of motion. Instability of ACVsalso coming from the skirt bounce that is the dynaminstability of the skirt-cushion system under the interactof cushion flow process and skirt deformation. It becoma particular problem when the skirt oscillation frequenexcites the natural frequency in heave of the craft. Ofparameters, which affect the dynamic stability, the bagcushion pressure ratio is the dominant one apart fromgeometry. In order to reduce the skirt bounce, the higpressure ratio is necessary but it will also increase thepower requirement for the system. Thus Mantle suggthe proper pressure ratio ranging from 1.0 to 1.6 in orto minimize the instability caused by skirt bounce [13].

1.3. Proposals of paper

Genetic Algorithm (GA) is an optimization tool thahas shown the strength to various optimization probleIn this paper, GA will find the best skirt system, whiincludes the skirt geometry and pressure ratio, by examithe frequency response curve, system matrix and propeof a vehicle at equilibrium or craft operating conditionThis optimized bag and finger skirt system will shift t

J. Chung, T.-C. Jung / Aerospace Science and Technology 8 (2004) 219–229 221

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second resonance peak away from the range of senfrequency and reduce the magnitude of heave ampliresponse. Two existing ACVs, the CCG’s Waban-Aki aUS Navy’s LCAC, will be optimized with GA and then thcharacteristics of original models will be compared withoptimized ones.

2. Genetic algorithms

2.1. Genetic process

Genetic Algorithm (GA) is the search technique basedthe mechanics of natural selection and natural geneticfind the best solution for specific environment or problconditions [8,14]. GA starts with generating random initpopulation consisted of potential solution points (or inviduals). The value obtained for each individual from tevaluation procedure with objective function is called thefit-ness. The decision is made whether the individual is goor bad for the given problem, based on the magnitude oness value. Once fitness value is evaluated and assigneach individual, then initial population meets the first gnetic operator, selection process. The purpose of this oator is to give more chances of survival for the strong inviduals and to die off the weakest ones according to tfitness values. Next, crossover operator is performed onlected individuals to build the new individuals by combinithe existing ones. This process can be compared to theural evolution process generating new children from theents. Finally, mutation operator follows the crossover pcedure. The main role of mutation process is to providediversity in the population. Without the mutation, it is hato reach the solution point that is located far from the currdirection of search. It insures that the probability of reachany point in the search space never go to zero [10]. Thiserator also prevents the premature convergence of GA toof the local optimal solutions. Once all three main operaare performed on the initial population, the new populatiodeveloped. This new population is genetically superior toprevious one and has better chance to survive for the gproblem condition. Then this whole procedure is continuntil the satisfaction is met or it reaches the maximum nuber of generations which is pre-set by users.

2.2. Genetic components

The first component is the coding of each individuin order to represent its characteristics and to makeasy for the computation of genetic process. Two commcoding methods are binary representation and real numrepresentation [18,21]. The main advantage of binary cois that it can save a great deal of time consumpduring the genetic process. The next component is penfunction to apply the condition of constraints. Several forof penalty function have been proposed and studied

o

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-

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GA literatures [5,15]. Penalty function checks whetherindividual satisfies the given constraints and how muchthe individual is located from the boundaries of constraif it is not met the condition of those constraints. Insteady state GA, it is important to decide how to makspace for the new individuals when the population is fThe common replacement method isElitist replacement [8].In Elitist replacement, it selects a random individualcondition that the best elite fraction is not replaced. Tstrategy provides the fast convergence in the solutionalso keeps the good structures of individuals for futreference in the next generation process.

3. Optimization of the ACV bag and finger skirt system

3.1. A dynamical model of the bag and finger skirt

One of the problems in investigating the bag and finskirt system is that its dynamics are quite complex. Tinvolve consideration of the dynamic behavior of the sstructure, the fluid mechanical processes in the cusand air supply system, and the vehicle dynamics combwith the interaction of all three. The skirt material effeccan play a role in skirt dynamics and the geometry oftypical cushion can be complex, and the skirt geomcan undergoe large changes during vehicle motion [2Furthermore, to adequately describe the cushion air esprocess, the model must account for intermittent sksurface contact around the craft periphery arising frcraft motion and from wave action; this can have maeffects on the dynamics. It follows that the developmentractable analyses from first principles requires considersimplification. In this regard the first published analyses uempirical data on skirt deflection [16,17].

Several assumptions were made based on the phymodels which were the basis of the experiments to althe appropriate mathematical simplifications. The geomof skirt design was determined by considering the sas a two dimensional section of an inflated membranstatic equilibrium of forces. The simplest dynamics occwhen the vehicle moves at a constant speed over sudisturbances having wave lengths which are much grethan the given vehicle length or width. In this casesurface disturbance or ground motion is equivalent to ahorizontal surface moving in pure heave under the cushand the resultant craft motion in the vertical plane can abe assumed to be pure heave. Very little lateral curvaexists in the skirt except for the skirt corners, thus justifythe two dimensional approach used in treating the smodeling problem for pure heave dynamics.

Fig. 2 shows the main elements of the bag and finger ssystem being studied in this paper and it shows the bmotion variables required to describe pure heave dynamThe vehicle or hard structure dynamics is described byheight hc(t) of the vehicle base above a datum, and


Fig. 2. Two dimensional section of the bag and finger skirt.

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surface input is described by a specified ground heighthg(t).The bag ABCDE is a loop of elastomer-fabric materattached to the periphery of the craft base at A and E.fingers CDF are folded from triangular pieces of mateand attached to the bag at C and in such a way that horizsections through them are approximately U-shaped.flows from the vehicle’s lift fans into the bag and thenthrough orifices above the fingers into the cushion. Tcollapsible structure is inflated and stabilized by the gapressurepc of the cushion air and by the pressurepb in thebag, which is typically 1.2pc.

Considering now the fluid mechanics, the air flowQbfrom the vehicle lift fan into the bag is modeled asquasisteady response to the fluctuatingpb(t) by specifyinga function of the formpb = fb(Qb) representative of asteady fan characteristic. The volume fluxQc from bagto cushion through the orifices in the inner bag and frcushion to atmosphereQa through the hovergaphe shownin Fig. 2 are assumed to be quasisteady and describeBernoulli’s law together with suitable discharge coefficienWith he defined as the distance between the bottom tipthe fingers and the surface, the discharge coefficient forQadepends on the finger geometry through bothhe and thefinger orientation angleθ . The bag and cushion volumesVbandVc are modeled as lumped pneumatic capacitancesbeing included because the compressibility of the cushair has been shown to significantly affect dynamics uncertain operating conditions, and can be a source of dyninstability [20].

l

y

As shown in Fig. 2 withhc andhg being the craft basand surface heights above a suitable inertial datum,fluid dynamics is coupled to the skirt and craft dynamthrough mass conservation laws for the variableVb(α, γ )andVc(α, γ,hc,hg), and through the modulation ofhe . Thusthe system has three degrees of freedom,hc,α, andγ withinputhg(t) and outputhc(t). From the geometry of Fig. 2,

hs = L1 sinα +L2 sin(Φ + γ ), (1)

hg + he + hs = hc. (2)

With Lm being the length of the two dimensional model, tcushion footprint area is given by

Sc = Lm[Bb + 2

{L1 cosα +L2 cos(Φ + γ )}], (3)

whereBb is the width of the vehicle base between the sinner attachment points.

The nonlinear differential equations of the craft and sdynamics are derived using Lagranges equations andare [4]:

(A) hc equation:

Mchc +Ms[L1(α

2 sinα− α cosα)

+LM(γ 2 sinγM − γ cosγM)] +Mcg = pcSc; (4)

(B) α equation:

MsL1[L1α −LM sin(γM − α)γ 2

+LM cos(γM − α)γ − hc cosα − g cosα]

= pbV obα + (pb − pc)V ib

α + pcV fα ; (5)


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− hc cosγM − g cosγM] + Is γ

= pbV obγ + (pb −pc)V ib

γ + pcV fγ , (6)

whereIs is the moment of inertia about center of skirt maγM is the angle between center of mass of the skirthorizontal,LM is the distance between center of mass ofskirt and inner bag joint D,Mc is the total mass of the craincluding skirt, andMs is the mass of the skirt. The functionV obα ,V

ibα ,V

fα ,V

obγ ,V

ibγ , andV fγ are the rates, with respect

theα andγ , at which the surfaces ABC, CDE and CF sweout volumes as the skirt moves.

Considering the lift fans, for steady or quasisteady flthey are assumed to deliver air to the bag according tolaw

pb = fb(Qb)= pbe

{ξ − (ξ − 1)

(Qb

Qbe

)3}. (7)

In this expression the subscript “e” denotes equilibriumhovering values andξ is the pressure ratio correspondito Qb = 0; usually 1.2 � ξ � 1.4 to ensure adequate stastability. The form of Eq. (7) is chosen to reflect the fathat periodic flow reversal can occur, and that forQb < 0,dpb/dQb < 0 [13]. The flow from bag to cushion idescribed by

Qc =Ab sgn(pb − pc)√

2|pb − pc|ρ

, (8)

whereAb is the effective area of the orifice including thdischarge coefficient and the area of the orifice separathe bag and cushion. This form also allows flow reverthrough the bag orifices to occur. The flowQa escaping fromthe cushion to atmosphere is modeled by

Qa = Lphf (he, θ)sgn(pc)

√2 |pc|ρ

, (9)

whereLp is the total peripheral length of the skirt andhfis an effectiveleak height, which allows air leakage fromthe atmosphere into the cushion, when the pressure incushion is smaller than the pressure in the atmosphehas the nondimensional form [4]

hf = Bf fa(he

Bf, θ

), (10)

whereBf is the finger width, andθ is defined in Fig. 2. Thefunction fa is the product of the area between the bottof the fingers and the surface with a discharge coefficdependent onθ. As he decreases fromhe > 0, hf initiallydepends linearly onhe . Then, when surface contact occuat he = 0, further decrease inhe causeshf to decreasenonlinearly as the tips of the fingers (at F in Fig. 2) collapshutting off the flow [4].

t

The air in the bag and cushion is assumed to be compible, and at any instant in time the pressures are assumbe uniform throughout the volumes. Then, the bag andcushion air mass conservation laws take the form

Cbpb + Vb =Qb −Qc, (11)

Ccpc + Vc =Qc −Qa. (12)

In these equations,Cb andCc are the pneumatic capactances ofVb andVc, given respectively byCb = Vb/γPa andCc = Vc/γPa . Whereγ is the ratio of specific heats, whicis 1.4 for air. The termVb in Eq. (11) is associated with flexible skirt deformation under the action ofpb and termVc inEq. (12) is associated with both vehicle motion and flexskirt deformation under the action ofpc .

3.2. The linearized equations

Numerical solutions of above equations reveal substanonlinear effects on frequency response with the msource of such effects being the modulation of cushionflow from the cushion to atmosphere associated with ssurface contact as expressed in Eq. (10). Neverthelessresults presented in Chung and Sullivan [3,4] suggestover the frequency range of interest, the small disturbanclinear response of the craft is at least qualitatively realisHence to provide further insight into properties of tbag and finger skirt, linear analysis is used to examinnumber of factors not easily addressed by direct numesimulation.

The nonlinear equations in the previous sectionlinearized about an equilibrium or craft operating contion. These linearized equations are transformed toLaplace domain. Withs = σ + jω being the Laplace variable, the transform of a linearized variableδX(t) is de-noted by(X(s). For a system having inputX(t) andoutput Y (t), the corresponding frequency response fution is denoted by(Y(jω)/(X(jω). For the two dimen-sional skirt model with capacitance effects, it isXT =[α, γ , α, γ,pb,pc, hc, hc] with the inputhg(t). Then thereare eight first order differential equations that are two eqtions for the vehicle heave dynamicshc , two equations eacfor the skirt displacementsα andγ , and one equation eacfor the pneumatic capacitances of the bag and cushionumes. The set of these simultaneous differential equacould be expressed in a state-space matrix form as follo

Hx =Rx + T u, (13)

where x = [δα, δγ , δα, δγ, δpb, δpc, δhc, δhc]T and u =[δhg, δhg]T. Then the linearized equations for ACV headynamics can be represented in a compact state-space

x =Ax +Bu, (14)

whereA= H−1R andB = H−1T . The outputs of a lineasystem can be related to the state variables and the inpthe state equation

Y = Cx, (15)


nde-ons

rect

en-io o

en

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dualtions ofthe

tudeest

, the

where theC matrix depends on the system input aoutput choices, andY is the set of outputs. From the statspace matrices, the measurement of craft heave respto the ground input can be obtained by(hc/(hg . Thedynamic stability of the system can be determined by diexamination of the system eigenvalues.

3.3. Application of genetic algorithm

The design variables in the skirt system are the dimsions of outer bag and inner bag, and the pressure ratbag and cushion;L1,L2,L3,L4,Lob, andpb/pc . The givendesign restrictions are the total vehicle mass and the dim

e

f

-

sions of vehicle’s hard structure;Mc,Lc,Bc,Db , andHb.They are fixed during the optimization process.

Binary coding is applied because all design variableseasily represented in binary values and it is easier to intewith main algorithm. In this coding method, each parameuses the four bits to represent its value. Thus one indivihas the total 24 bits to represent the entire potential solupoint because there are total six different parameterskirt geometry and pressure ratio being optimized. Forfitness value, the individual whose second peak magniof frequency response curve is the least will get the bfitness value. For the case of second peak frequencysame principle is applied.

Fig. 3. Overall flow of the GA on skirt optimization problem.


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Table 1Parameters used in the GA on skirt optimization problem

Population size 30 individualsMax. generations 180 stepsLength of an individual 24 bitsElitist reservation 10% of population sizeCrossover methods Single Point Crossover

Two Point CrossoverRandom Crossover

Mutation methods Single bit mutationTwo bit mutation

Properties of skirt being optimized L1,L2,L3,L4,Lob,pb/pc

There are several constraints for the realistic desMost of all, vehicles must be stable. In order to reflect tconstraint, the penalty function will examine the eigenvalof the skit system from the linearized equations of motiThe next constraint is the skirt bounce of vehicles. Tskirt bounce can be prevented or reduced by settingproper pressure ratio of the bag and cushion. If the presratio is out of the proper range which is 1.0–1.6 [13], ththe penalty function will assign the penalty values to sindividuals. The third constraint is about the hover-gSince the motion of vehicles is computed at the equilibriconditions, the hover-gap should be the positive valuelast, there is an allowable range for the modificationdimensions in the bag and finger skirt geometry. Ifdimensions are out of this range, then the shape of frequresponse curve becomes unrealistic, and it is even imposto compute the frequency response plots with thosedimensions. This allowable range is determined byexperiments, experience, and trial-and-error process.

In this paper, three different crossover operatorssimultaneously applied due to the unique characteristieach one. Those three different operators are the scrossover, two point crossover, and random crossove14]. For the diversity of individuals, two different mutatioprocesses are again simultaneously performed. Thosemethods are the single bit mutation and two bit mutatThen, 10% of the best individuals are kept during egenetic process without any interference or modificationthe elitist replacement technique. As shown in Table 1population is consisted of 30 individuals and the genprocess is stopped after 180 steps of generation. Tvalues were determined after many experiments. The oproperties in this table are already explained earlierFig. 3 the overall flow of GA on the optimization othe bag and finger skirt system is depicted, and shthat optimization process is performed on interactionthree essential components. They are the genetic proparameter estimation, and mathematical model of skirtorder to validate the GA codes, several experimentstests have been performed. Those experiments rangeda simple function optimization to complicated optimizatiproblems.

,

Fig. 4. Overall performance of GA on Waban-Aki skirt optimization.

4. Results of GA optimization on the bag and fingerskirt

4.1. Optimization on Waban-Aki skirt

In Fig. 4, the overall performance of GA on skoptimization is shown. The upper two lines in the figurepresent the second peak frequency and magnitudbest solution obtained in each generation step. Sincetradeoff exists between the second peak frequencymagnitude, GA is trying to find the optimal point whethose two properties meet the best condition without losany particular side. The third line which is located atbottom of the figure represents the average penalty vof whole population at each generation step. This line dnot have a convergence for most of optimization problesince the stochastic optimization method like GA has alwthe perturbation in the results. That is why this line issmooth, but rather be disturbed slightly at every generastep.

The optimized skirt should satisfy the several stabilityquirements and the main objective – improved ride quaTable 2 shows the dimensions and other properties of oinal skirt system and optimized skirt system. AccordingMantle, he explained some significant factors which imprthe stability in heave motion [13]. It is recommended for sbility of vehicle to increase the hover gap height and flrate. In Table 2, it shows that the hover gap height oftimized skirt is increased from 3.6 mm to 3.9 mm andflow rate of that is also increased from 95.088 m3 s−1 to97.161 m3 s−1. Hence the stability of optimized skirt sytem is improved. However, the pressure ratio is decreafrom 1.2 to 1.1. This change degrades the stability of vecle, but there are many factors interacted together in ordproduce better stability. GA tries to find the solution whifalls into the best optimized conditions even though somfactors could not be met. For the loss of pressure ratio,


Table 2Properties of the original and optimized skirt systems in Waban-Aki

Waban-Aki

Mc (kg) Lc (m) Bc (m) Db (m) Hb (m)

Original skirt 36,740 21 8.6 1.39 0.975Optimized skirt 36,740 21 8.6 1.39 0.975

Ms (kg) L1 (m) L2 (m) L3 (m) L4 (m)

Original skirt 932.27 0.180 2.02 1.69 1.10Optimized skirt 932.43 0.164 1.90 1.70 1.08

Lob (m) 0 (rad) pce (Pa) Qe (m3 s−1) pbe/pce

Original skirt 2.60 0.576 2,000 95.088 1.2Optimized skirt 2.64 0.600 2,000 97.161 1.1

he (m) αo (rad) γo (rad) Hc (m) hso (m)


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compensation for stability was made from the improvemof other skirt properties. For example, the outer bag lenis increased from 2.6 m to 2.64 m. This change eventucontributes the vehicle’s stability by providing more flebility and the ability to absorb more energy caused fromground or during the vehicle’s heave motion. Other dimsions such as the length and angles related to the fingebag are also changed to provide better stability and ride qity. Finally, eigenvalues of the system and other constrconditions are checked and satisfied.

Fig. 5 shows the frequency response curves for ornal and optimized skirts. The second peak magnitudefrequency of original model are found as 20.8 units a24.7 rad s−1, while those of optimized model are obtainas 6.6 units and 21.2 rad s−1. Thus the second peak manitude and frequency are reduced significantly throughoptimization process. The percentages of reduction in thparameters are 68.3 and 14.2%, respectively. This resudicates that the magnitude of disturbance during the vcle’s heave motion is reduced more than a half of that in

Fig. 5. Frequency response curves for the original and optimizedban-Aki.

d

original skirt system and its frequency is away from the ssitive range.

4.2. Optimization on LCAC skirt

LCAC is also chosen as another example of a bagfinger skirt optimization with GA. All the properties ooptimized and original skirts of LCAC are shown in TableIn Fig. 6, GA found the optimal point of solution after 4generation steps. This is quite fast convergence compto the Waban-Aki skirt optimization. The reason is thatoriginal vehicle has the properties closed to the optimal palready, so that it takes less time to reach that point. It isknown from the fact that the magnitude of optimization lemade on the skirt of LCAC is less than the case of WabAki. Nevertheless GA produced a quite significant reducon the second peak magnitude and frequency of LCAC ssystem.

Fig. 6. Overall performance of GA on LCAC skirt optimization.


Table 3Properties of the original and optimized skirt systems in LCAC

LCAC

Mc (kg) Lc (m) Bc (m) Db (m) Hb (m)

Original skirt 150,000 27 14 1.807 1.267Optimized skirt 150,000 27 14 1.807 1.267

Ms (kg) L1 (m) L2 (m) L3 (m) L4 (m)

Original skirt 1,913 0.270 3.03 2.535 1.65Optimized skirt 1,902 0.280 3.12 2.350 1.75

Lob (m) 0 (rad) pce (Pa) Qe (m3 s−1) pbe/pce

Original skirt 3.90 0.576 3,893 380.0 1.20Optimized skirt 4.20 0.589 3,893 379.9 1.18

he (m) αo (rad) γo (rad) Hc (m) hso (m)


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The results show the reduced air gap height from 38.8to 23.0 mm. This change contributes the instability ofhicle. However, the optimized system produced the cpensation for this instability by generating longer outer blength and changes in other skirt geometry. The flowof optimized skirt is found almost same as the original ssystem. Pressure ratio of bag and cushion is also obtaas slightly reduced value compared to the original one.nally eigenvalues of the system prove that the overallbility of skirt system is satisfied by producing all negatvalues. Other design and stability constraints are also sfied. The percentages of reduction in second peak magnand frequency between the original and optimized skirt stems are computed as 47 and 7%, respectively. The reduin both of characteristics definitely contributes for improvride quality and stability. This frequency response curvillustrated in Fig. 7.

4.3. Effect of various skirt masses on optimization

The effect of different skirt masses on optimization wGA is also tested. According to Chung et al. [3,4], reduc

Fig. 7. Frequency response curves for the original and optimized LCA

-

the skirt mass can be used to modify an undesirable hresponse. The original skirt material is an elastomer cofabric composite and its area density is 2.8 kg m−2. Thesecond skirt material is an arbitrary chosen material wharea density is 1.4 kg m−2. Unlike previous experiments foskirt optimization, GA has now two different skirt materichoices. Hence, design variables include the continuparameters as well as discontinuous ones, while in prevexperiments only continuous parameters were consideThen the lengths of individual and computation timeincreased compared to previous experiments. The objefunction is also changed to evaluate and assign the prfitness value. Since it is not possible to reduce bothmagnitude and frequency of second peak at the sameobjective function is modified so that it will produce thlowest second peak magnitude without any concerninterest about its frequency range. The reason is that mreduced magnitude of second peak does not disturbcomfort even though it is in the sensitive frequency rang

In this new experiment, GA selected the new skmaterial which is the half area density of original one

Fig. 8. Frequency response curves for different skirt mass conditioWaban-Aki.


Table 4Second peak magnitude and percentage of reduction for each system

Waban-Aki

2nd peak magnitude Percentage of(unit) reduction (%)

Original system without optimization 20.80 0Optimized system with fixed skirt mass 6.60 68.3Optimized system with various skirt masses 1.76 91.5

LCAC

2nd peak magnitude Percentage of(unit) reduction (%)

Original system without optimization 14.64 0Optimized system with fixed skirt mass 7.69 47Optimized system with various skirt masses 0.90 93.9

n on

ase ofededs ofthekirtbyced

t intheis

itudelityof

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asall

ngerell

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RG-

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Fig. 9. Frequency response curves for different skirt mass conditioLCAC.

order to produce the second peak magnitude as lowpossible. In Figs. 8 and 9, the second peak magnitudWaban-Aki and LCAC is reduced significantly, comparto the original system and the optimized system with fixskirt mass. Table 4 summarizes such reductions in termpercentage. This is very important result and implies thatride comfort can be improved further using the reduced smaterial density. This characteristic should be noticedthe manufacturers of ACVs, and the research for advanmaterial of skirt should be carried on.

5. Conclusions

The optimized skirt system produced the incrementhe outer bag length, in the hover gap height, and inflow rate for better ride quality and stability. Moreover, thskirt system had a greatly reduced second peak magnand frequency so that it provided improved ride quacompared to the original skirt system. The optimizationskirt system with various material choices was also carout by GA. The result of experiment indicated that GA cfurther optimize the skirt system with the reduced skirt a

density. This reduced skirt mass improved ride qualitywell as met the stability conditions by producing a very smmagnitude of second peak. In conclusion, the bag and fiskirt of both ACVs produced the better ride quality as was the stability through the optimization process by GA.

In future work, the skirt model will be modified to reflect more characteristics of real world behavior includdistributed mass model and standing wave form of instaneous outer bag shape. The codes of GA are also goinrefine for more effective and efficient performance so tit can produce the solution faster. The constraint conditfor the skirt optimization will be expanded further to contamore realistic conditions.

Acknowledgements

This research was supported by an NSERC grantPIN227747. This support is gratefully acknowledged.

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optimization of an air cushion vehicle bag and finger skirt using genetic algorithms

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