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MULTI-DISCIPLINARY SYNTHESIS DESIGN AND OPTIMIZATION FOR MULTI-HULL SHIPS

ABSTRACT

Keywords: Multi-disciplinary Design and Optimization (MDO), Neural Networks,

Pareto Optimum Solutions

This paper1 describes a synthesis level multi-disciplinary design and optimization

(MDO) method developed for multi-hull ships. The method is unique in two

respects. First, it uses advanced multi-objective optimization methods (in its broad

scope), integrating powering, stability, sea keeping, hull forms definition, cost, and

payload capacity into a single design tool. Second, it uses neural networks as a

response surface method. More specifically, the paper discusses the use of neural

networks, trained based on sets of Computational Fluid Dynamics (CFD) data, for

estimation of powering and sea keeping through the optimization loop. The paper

presents details of the method and multi-objective optimization results in the form of

Pareto optimum solutions for multi-hull concepts

1 The latest version of this paper, which reflects progress during the last two years

is MULTIDISCIPLINARY SYNTHESIS OPTIMIZATION PROCESS IN

MULTIHULL SHIP DESIGN by Hamid Hefazi, Adeline Schmitz, Igor Mizine,

Steve Klomparens, and Stephen Wiley. This new paper is available from Igor

Mizine, [email protected].

Hamid Hefazi California State University,

Long Beach, Long Beach/USA

[email protected]

Adeline Schmitz

California State University,

Long Beach, Long Beach/USA

[email protected]

Igor Mizine

[email protected]

Geoffrey Boals

[email protected]

CSC

CSC Papers

2009

2


.

INTRODUCTION

The vast majority of current U.S. naval auxiliary ships are relatively large mono-hulls

with limited speed capabilities. The OSD guidance known by the rubric “10-30-30”

cites goals for the speeds at which deployments have to be executed that cannot be

met with existing transportation vehicles, particularly the ships on which over 90% of

the materiel needed by ground forces has to move. The desire for high-speed

transit capabilities has resulted in increased interest in non-traditional and multi-hull

platforms for naval missions. Multi-hull ships have many potential advantages over

mono-hull ships; however, their design procedures are not as mature. Further,

multi-hull ships also offer avenues of hydrodynamic design optimization that are not

found on mono-hull ships – such as optimizing of hull spacing or relative hull

proportions. Achieving many desirable sets of performances requires advances in

our ability to predict (and explore) hydrodynamic effects in conjunction with other

constraints such as dynamic structural loads when operating in high sea states and

cost.

Synthesis tools that are used to explore the ship design trade space in the concept

design phase (ASSET, PASS) have been around for many years and are used

widely by industry for mono-hull ships. While some synthesis tools have been

developed for multi-hulls, they are not nearly comparable in depth or level of fidelity

to the mono-hull tools. They are used to develop point solutions of ship designs to

populate and study the trade space, but the difference in the point designs are

determined by the design team. This process could be substantially enhanced by

the application of multi-disciplinary design and optimization (MDO) tools to the

design problem, and by further development of multi-hull synthesis tools.

Comprehensive, computational MDO tools however can be prohibitively expensive

considering the complexities that are involved in accurate analysis of

hydrodynamics, structural loads, cost, etc. Advanced multi-objective optimization

methods in conjunction with advances in our ability to accurately and efficiently

predict these performances are needed if these tools are to be of practical value to

the designer. Such advanced multi-disciplinary ship hull design/optimization tools

will be a valuable resource equally applicable to the design of future commercial or

military high speed vessels (dual-use). The advanced hull forms designed therewith

potentially offer the advantage of reduced drag at a given speed, and thus

increased fuel efficiency and range, and/or reduced structural weight and thus

increased cargo lift capacity while meeting stability and seakeeping criteria.

Most of the MDO works to-date are focused on application to mono-hulls. For

example, Zalek (2007) describes multi-criterion evolutionary optimization of ship

hullforms for propulsion and seakeeping. The problem formulation and development

is applicable to mono-hull frigate type naval surface vessels. Harries et al. (2001),

investigate optimization strategies for hydrodynamic design of fast ferries. A

commercial optimization system is used to integrate various CAD and CFD codes

for calm water resistance and seakeeping. The method is applied to Ro-Ro ferry.

Campana et al. (2007) present results of the MDO of the keel fin of a sailing yacht

3


. accounting for hydrodynamic and elasticity. Different MDO formulations are studied

in the context of global optimization (GO) frame work.

Studies applicable to multi-hull ships include, Tahara et al. (2007) who present a

multi-objective optimization approach for a fast catamaran via a Simulation-Based

Design (SBD) framework. A variable fidelity concept is also presented which allows

for integration of accurate, yet time consuming RANS predictions together with fast

potential flow results for optimization. The MDO method only considers resistance

and seakeeping. Another study funded by the Office of Naval Research at

University of Michigan, Beck (2007) is also focusing on the hydrodynamic

(seakeeping and resistance) optimization of multi-hulls. Brown and Neu, (2008) in

the phase I of a study entitled Naval Surface Ship Design Optimization for

Affordability have applied a multi-objective optimization method to a number of case

studies using a simple ship synthesis model, and the US Navy’s Advanced Ship and

Submarine Evaluation Tool (ASSET) in the PHX ModelCenter (MC) design

environment, ASSET (2008), ModelCenter (2008). Their case studies include

LHA(R), a replacement for the US Navy amphibious assault ship, and DDG-51, a

destroyer class vessel. Phase II of their study will include response surface

modeling (RSM), a more detailed design of experiments (DOE) and focus on multi-

hull high speed ships.

Since 1998, CSULB, under programs funded by the Office of Naval Research

(ONR), Besnard et al. (1998), and the Center for Commercial Development of

Transportation Technology (CCDoTT) has been developing advanced automated

optimization methods and computational fluid dynamics (CFD) methods for

applications to fast ship design. Originally, the focus of these programs was shape

optimization of underwater hull forms, such as the Pacific Marine’s blended wing

body (BWB) which was optimized for its lift to drag ratio, Hefazi et al. (2002), Hefazi

et al. (2003). Having demonstrated the feasibility of automated hydrodynamic shape

optimization for lifting bodies using advanced methods such as neural networks,

Schmitz (2007), CSULB in collaboration with Computer Science Corporation (CSC)

initiated the current program to extend these technologies to multi-disciplinary

design and optimization (MDO) of multi-hull ships. Our approach is unique in its

broad scope and use of neural networks as a response surface method.

Generally, the MDO design system consists of synthesis design method (SDM),

hullforms definition and optimization sub-system, seakeeping, structural design

optimization, general & cargo arrangement design optimization, propulsion

machinery sub-systems and more local sub-systems such as: outfit, electrics,

handling systems, etc. Seakeeping, power, and payload are primary functional

relationships, which depending on the stage of the design, are analyzed at various

degrees of fidelity.

Two major challenges of MDO design system are:

MDO needs to formulate a design in which there are several criteria or design

objectives, some of which are conflicting.

Subsystem performance evaluations (such as powering, seakeeping, etc) are often

very complex and (computationally) intensive. Direct evaluation of these

4


. performances as part of the optimization process, may make the MDO method too

costly and out of reach of most practical design problems.

To overcome these limitations, our approach, uses advanced multi-objective

optimization methods such as Neighborhood Cultivation Genetic Algorithm (NCGA)

for optimization. Unlike traditional design spiral approaches, multi-objective

optimization keeps various objectives separate and concurrent in order to find the

best possible design, which satisfies the (opposing) objectives and constraints. To

address the subsystem performance evaluation challenge, artificial neural networks

are trained based on model tests or computed data bases and are used in the

optimization process to evaluate various subsystem performances. This innovative

approach replaces the use of highly idealized or empirical methods for evaluation of

subsystem performances (such as powering, seakeeping, etc) during the

optimization process.

The overall MDO process is schematically shown in Figure 1. It consists of various

“models” to evaluate powering, cost, stability, seakeeping, structural loads, etc. The

outcomes of these models are then used by a multi-objective optimization method

such as MOGA to perform optimization. The entire process is “managed” by

commercially available software, iSIGHT (2008), or ModelCenter (2008) designed

for optimization applications. Various models and subsystems are briefly described

in subsequent sections. Some of the applications of the method are presented in

section 6.

Figure 1: MDO process

SYNTHESIS LEVEL MDO MODEL

This model includes various design relationships for calculating areas, volumes,

sizes, weights, stability and costs of multi-hull (trimaran) ships. These relationships

are based on many technical literature sources and practical design experiences.

New D. V.

Initial Design Variables

Optimum Design

Neural Network for

Powering prediction

Define

Configuration

Optimum

?

YES

NO

Structural

design &

optimization

Stability and

Neural Network

for Seakeeping

Payload

capacity

determination

Cost

Model

Hull form

definition

model

5


. They are consistent with Navy’s, USCG, ABS regulations, and operational

requirements for specific planned applications. They are organized in various Excel

spreadsheets. Synthesis design model, in short, achieves a weight - buoyancy, and

required - available area/volume balanced design, with required propulsion and

auxiliary machinery and with a check on stability. The flow chart in Figure 2 shows

the synthesis model process. A comprehensive description of the SDM is given in

Hefazi (2006). The overall process includes the following calculations

Speed-power and endurance fuel calculations.

Area/volume calculations including required length, height and volume for

machinery spaces for required propulsion plant and auxiliary machinery.

Required tankage volume for required endurance fuel.

Determines remaining hull area/volume available for payload items.

Sizes superstructure and deckhouse above the main deck to exactly provide

area/volume for the remainder of required payload and crew.

Electric load calculations.

Weight and center of gravity calculations.

Required vs. available GM per USCG windwheel criteria.

COST MODEL

The build strategy and cost estimate analysis for multi-hull (trimarans and

catamarans) and mono-hull ships is performed using SPAR Associates proprietary

cost estimating model called PERCEPTION ESTI-MATE. SPAR’s PERCEPTION

ESTI-MATE cost model has evolved over nearly two decades of algorithm

development and shipyard return cost data collection and evaluation, perception

Esti-mate (2008).

The cost models’ approach for an estimate is based first upon the composition of

the hull’s structural components (decks, bulkheads, shell, double bottoms, etc.),

then the ship systems (mechanical, piping, electrical, HVAC, etc.), and finally other

ship characteristics. Factors considered, and applied, if relevant, are the general

build strategy for on-unit, on-block and on-board construction; the type of shipyard

and its established product line, its facilities and production capabilities; and the

expected competence of the shipyard to plan and manage its resources, costs, and

schedules.

Each cost model employs a comprehensive set of cost estimating relationships, or

CERs. They reside on SPAR’s estimating system called PERCEPTION ESTI-

MATE and represent a wide cross-section of current and historical shipyard

construction costs at many levels of detail. Adjustments can be made (and were

made for the HALSS estimate) as necessary to reflect differing shipyard productivity

factors, construction methods, and material costs. These CERs, while parametric in

nature, focus on a specific area of cost (labor and material) and each reflects the

specific material and the manufacturing and assembly processes required.

Specialized CERs focus on structural component fabrication, assembly, and

6


. erection for installation of propulsion systems and for various support activities. The

CERs are based on many different metrics, such as weld length, deck area,

compartment volumes, number of crew (by type crew), kW of propulsion (by type),

etc. Hull structural component costs are based upon component weight by type of

structure and material.

The cost estimates, applicable to a lead ship, are believed to be fair representations

of anticipated true costs based upon the design information. Material costs have

been adjusted to reflect a common year (2007) value. This assumes that for a

multi-year program, appropriate contract escalation clauses have been defined to

index actual costs relative to the base year.

The cost estimates are based upon typical contract cost and schedule performance

for three types of shipbuilders and shipbuilding processes: so-called Virtual

Shipyard (US National Ship Research Program (NSRP) terminology), Dual Use

Shipyard, and Large US Mid Tier Shipyard, as well as shipyards in other countries.

USING NEURAL NETWORKS IN NUMERICAL OPTIMIZATION

As mentioned earlier, a unique feature of our approach is the utilization of artificial

neural networks as a response surface method (RSM) to replace time consuming

and costly direct CFD calculations of powering and seakeeping in the optimization

loop. The method has wide range of other potential applications and is briefly

reviewed here.

The modern approach used in the design of a complex system (the ship or

component inside the ship) usually includes at some level an optimization. In

practical cases, the design tool may either be an optimization or design-of-

experiment software, or a set of test cases identified by an experienced designer

interested in conducting trade studies. The analyses performed at each subsystem

level rely, in general, on a combination of semi-analytical models, advanced

numerical methods such as computational fluid dynamics (CFD) and finite element

analysis (FE), and use of existing databases.

7


. Monohull-Trimaran

Design Synthesis Model

Design Input?Crew

?Cargo & Other Payload

?Range

?Launch & Operations Limits

?Rules & Standards

?Electric Power Required

Speed –PowerSpeed for Installed Power

Or

Power for Required Speed

Area –Volumes•Machinery Spaces

•Hull Tanks

•Deckhouse

•Superstructure

Electric LoadIn Transit

Load/Unload

Select Gen Size

7 Weapons Weight

6 Outfit Weight

5 Auxiliaries Weight

4 Command Weight

3 Electric Weight

2 Propulsion Weight

1 Structure Weight

8 Deadweight Weight

Output & FeasibilityWeight vs. Displacement

Speeds Requirements

Stability

(Seakeeping Ranks)

Cost

Balances:—Cargo Area/Volume

—Electric Power

—Tankage Volume

—Machinery Installation

VariablesDimensions

Hulls Configuration

Hull Forms integral parameters

Internal spaces arrangement

Hull Forms Generation?Basic hull forms lines and profiles

?Assumed Displacement

Table of offsets & Hydrostatics

Figure 2: Synthesis Model Process

Such optimization or trade study usually has to be able to handle a large number of

design variables and explore the entire design space. Advanced analysis tools for

function evaluation such as CFD and FE are very demanding in terms on computing

requirements and when they are used, the cost associated with their use, both in

terms of man and computing power required, usually limits the exploration of the

design space. Regression models like neural networks (NN) can be used to reduce

some of these limitations. They basically seek to reduce the time associated with

extensive computations by estimating the functions being evaluated in the

optimization loops.

Figure 3 shows how neural networks can be inserted in the design process by

generating a database outside the design loop or make use of a large available

database and then use those to train one or several NNs. In practical terms, the

introduction of NNs allows extracting the time-consuming or difficult operations

(performing an advanced numerical analysis or extracting information from a large

and evolving database) from the design loop while still keeping their influence on

the outcome of the design process via the NN. The cost has thus been moved (and

possibly reduced in the process) to the training set generation (if it was not already

available) and to the training of the network. The result is a NN which can estimate

the function or functions over the design space it has been trained on. This ability to

quickly evaluate new designs allows in turn for the use of global optimization tools

such as Genetic Algorithms instead of having to rely on local optimization methods

or exploring a restricted part of the design space.

8


. The neural network methodology that is developed is a constructive algorithm

based on cascade correlation (CC). Instead of just adjusting the weights in a

network of fixed topology, cascade correlation begins with a minimal network, then

automatically trains and adds new hidden units one-by-one in a cascading manner.

This architecture has several advantages over other algorithms: it learns very

quickly; the network determines its own size and topology; it retains the structure it

has built even if the training set changes; and it requires no back-propagation of

error signals through the connections of the network. In addition, for a large number

of inputs (design variables), the most widely used learning algorithm, back-

propagation, is known to be very slow. Cascade correlation does not exhibit this

limitation. This supervised learning algorithm was first introduced by Fahlman and

Lebiere (1990).

Figure 2: System design loop utilizing Neural Networks. The NN’s are generated

outside the design loop based on computationally extensive models and/or large

databases.

The original CC algorithm has been modified in order to make it a robust and

accurate method for function approximation. The modified algorithm, referred to as

modified cascade correlation (MCC) in this paper, is an alternative committee NN

structure based on a constructive NN topology and a corresponding training

algorithm suitable for large number of input/outputs to address the problems where

the number of design parameters is fairly large, say up to 30 or more. Details of the

MCC algorithm are presented in Schmitz (2007). The method has been validated

using a mathematical function for dimensions ranging from 5 to 30, Schmitz (2007),

Besnard et al. (2007). Overall results indicate that it is possible to represent

complex functions of many design variables, with average error of close to 5%. The

number and distribution, within the design space, of training data points have some

impact on the accuracy of the network predictions. Our validation studies suggest

also that an optimum number of training data points is approximately 100*N where

N is the number of design variables. Furthermore a Latin Hypercube distribution of

the data points within the design space also tends to improve accuracy.

In practical applications such as optimization loops, this approximation is much

better than resorting to empirical or highly idealized approximation of complex

function evaluations such as powering or seakeeping of multi-hull ships. The NN

approach allows the optimization process to utilize the results of highly

sophisticated CFD or experimental analysis in the process without limitations

imposed by computational costs.

Subsystem 1 Semi-analytical

model

Design Tool

(DOE or optimization)

New Design

Subsystem 2 NN-2

Subsystem 3 NN-3

Objective(s) & Constraints

Training set generation for subsystem 2

analysis

Subsystem 2 NN-2

Large database for subsystem 3

analysis

Subsystem 3 NN-3

9


. MDO SUBSYSTEMS

HULLFORMS DEFINITION

At the present stage of this work, in order to allow practical applications by average

users at an early stage of design, it is decided that the MDO process and all its

models must be able to run on a workstation computer but be scalable to operate

on a server type system. Therefore a commercially available CAD based hullform

definition program is most appropriate. The naval architecture tools of Rhinoceros

and Rhino Marine, that is similar to Fast Ship, have been selected for this purpose,

RhinoMarine (2008). The standard, Rhino Marine process requires the user to

manually enter the waterline heights and to select the hullform that the hydrostatics

is to be performed. This manual procedure is replaced by an automated procedure

in order to allow for incorporation into our optimization application. The process

starts with selection of a parent hullforms for center hull and side hulls. A geometric

modeler interface automatically produces a model of scaled proportions to that of

the desired parent hull selection through the optimization loop. Using RhinoMarine,

the geometric modeler also produces various hydrostatic data and the minimum

wetted surface as output. This information is incorporated into the synthesis design

model for stability calculations.

POWERING

As mentioned earlier, throughout the optimization loop, the powering (coefficient of

residual resistance) is evaluated with a trained neural network. The neural network

approach encompasses three steps:

1. Generation of the training set (TS) & validation set (VS).

2. Neural network training to obtain a NN “evaluator(s)”.

3. Integration of the trained NN evaluator(s) in the optimization process.

A training set (TS) is a set of known data points (design variables and their

associated values, such as objective function(s) and constraints). The training

algorithm attempts to achieve an output, which matches these inputs. A validation

set (VS) is a set which, unlike the TS, is not used for training, but rather is used for

stopping the training. The purpose of the VS is to avoid over-fitting which can occur

with the MCC algorithm. Accurate prediction of the training data is not a valid

measure of NN accuracy. Theoretically it is possible to drive this error to zero. How

well the network represents data that it has not been trained on (VS) is a proper

representation of accuracy. In the absence of access to an existing

comprehensive powering data base for multi-hull configurations of interest

(trimaran), in this study the TS data was generated using the MQLT, Amromin et al.

(2003). Based on a quasi linear theory, MQLT is a CFD code, which has been

verified by comparison with trimaran model test results and proved to be reliable to

assess complex problem of multi-hull interference, Mizine et al. (2004). In view of

reduced CFD cost due to application of neural networks, methods with higher level

of fidelity (such as RANS) can also be used for generating TS data. The TS

database in this work consists of 578 number of CO values computed for three

design variables (separation, stagger and length of center hull). Seventeen

additional data points are used as validation set. The training program is a C++

software in which the MCC algorithm is programmed. The outcome of the training is

a NN in the form of an executable in which the proper number of hidden units and

corresponding weights – found during training – have been implemented. This

10


. executable is integrated in the optimization process. The CO determines the

powering requirement and the numbers of engines required which is used by the

SDM model.

SEAKEEPING

Similar to the powering, neural networks are used to predict seakeeping

performance in the MDO process. Using advanced numerical motions analysis, a

TS has been generated using a series of geometrical configurations to evaluate and

log the effects of size, stagger and separation of the side hulls on the motions of the

vessel.

The hull form and hydrostatic conditions were developed with the program

FASTSHIP. The hydrodynamic analysis has been performed with the WASIM

software, Wasim (2008). WASIM is a hydrodynamic program for computing global

responses and local loading on displacement vessels moving at any forward speed.

The simulations are carried out in the time domain, but results may also be

transformed to the frequency domain using Fourier transformations. WASIM is

capable of both linear and non-linear time domain simulations. However, it has been

assumed that the non-linear hydrostatic effects on this trimaran hull form are

negligible, and the motions analysis has been performed with a linear simulation.

The training set data base consists of trimarans ranging from 100 m to 300 m in

length. To evaluate the impact of the geometrical hull variations on the trimaran, the

analysis has been performed with various longitudinal and transverse relative

locations of the side hulls, as well as displacement ratios between the side hull and

the main hull. The stagger of the side hull describes the longitudinal location of the

side hulls relative to the main center hull. The separation describes the transverse

spacing between the side main hulls. An example of a configuration (stagger and

separation) is shown in Fig 4 and 5.

Figure 4 – Stagger Case 0.00

11


.

Figure 3- Separation Case 9.075 / 25.00 = 0.36

Overall sixteen ship responses for trimaran vessel are evaluated. They include roll,

pitch, vertical and transverse accelerations, bending moment, shear force, propeller

emergence, etc. These responses are evaluated at sea states 4, 5, 6 and 7, three

speeds of 15, 25 and 35 knots and 5 headings of 0, 45, 90, 135 and 180 degrees.

Hull configurations consisted of the following variations:

Stagger of side hulls 0.00, 0.24, 0.40 & 0.80

Separation of side hulls 0.36, 0.75, 1.25

Overall vessel size 150m, 200m, 250m & 300m

Displacement ratio (side hull/center hull) 0.1015

The range of these parameters were decided upon after reviewing the initial results

in order to avoid studying options that were undesirable or unreasonable. These

configurations represent a total of 48 hull variations for both vessel types for 60

environments leading to a total of 2,880 data points for the training set (for each of

the 16 criteria). Details of computations and analysis of results are presented in

Hefazi et al. (2008).

The seakeeping approach is based on computing a seakeeping index as described

in Hefazi et al. (2008). This “seakeeping index” is then be minimized as one of the

objective functions in the multi-objective optimization process. The motion and

seakeeping criteria for the vessel while under transit conditions, needed to compute

the index, have been derived from the seakeeping criteria for the transit and patrol

mission for a NATO Generic Frigate, Eefsen et al. (2004). The limits for the transit

condition are listed in Table 1 as single amplitude RMS values of roll motion; pitch

motion, vertical and lateral acceleration, bottom slamming and propeller emergence.

Table 1: Transit Criteria

Parameter Limit Value

Roll Angle 4.0 deg

Pitch Angle 1.5 deg

Vertical Acceleration 0.2 g

12


. Lateral Acceleration 0.1 g

Bottom Slamming Index 20 per hour

Propeller Emergence Index 90 per hour

The roll angle criterion for the transit condition is independent of the roll period. The

pitch angle criterion is independent from the pitch period of the vessel.

APPLICATIONS

HALSS MODEL

The MDO method to-date has been applied to several High Speed Sealift Ship

(HSS) concepts such as basic Army and USMC requirements for JHSS, and High

Speed Connector (HSC) such as basic JHSV, where multi-objective optimization is

necessary. Furthermore, each requirement has its distinct constraints which are

generally derived from mission requirements. Their purpose is to avoid exploring

unreasonable designs. A very detailed study has been conducted in order to

determine the best approach for application of the method. Results indicate that a

careful optimization process, including selections of proper algorithms and proper

initial population, have to be followed in order to obtain complete and meaningful

results. This process and results (pareto optimum) are described in detail, Hefazi et

al. (2008).

The application of the synthesis level MDO tool consists of

Definition of the design space, constraints and measure(s) of merit.

Running the MDO program to search the multi-dimensional design space using

single or multi-objective optimization algorithms.

Construction of feasible and Pareto optimum solution sets.

Subsystem requirement definition corresponding to optimum measure(s) of merit.

Two cases are reported here. Other applications of the method can be found in

Hefazi et al. (2008). The first case is application to a Sealift Alternative Ship

concept. HALSS is an airlift large ship concept capable of C130 operations. Table 2

and 3 contain the design variables, their description and design space limits and

design constraints.

Table 2: Design variables for HALSS

Design

Variable

Lower

Bound

Upper

Bound

Description

Lch 250.0 320.0

Center Hull Length on Waterline

Bch 20.0 28.0

Center Hull Beam on Waterline

Tch 10.0 12.0

Center Hull Draft

Lsh 100.0 200.0

Side Hull Length on Waterline

Bsh 4.0 8.0

Side Hull Beam

Tsh 7.5 10.0

Side Hull Draft on Waterline

13


. Dch

24.0 32.0 Center Hull Depth

α 0.5 1.0

Separation

β 0.15 0.35

Stagger

Table3: List of constraints imposed on the HALSS model

Constraint Lower

Bound

Upper

Bound

Description

WSch 0 17279.0

Center Hull Wetted Surface

WSsh 600.0 90000.0

Side Hull Wetted Surface

ch

bC 0.55 0.90

Center Hull Block Coefficient

ch

pC

0.625 1.0 Center Hull Prismatic Coefficient

ch

mC 0.675 0.95

Center Hull Maximum Section Coefficient

sh

bC 0.4 1.8

Side Hull Block Coefficient

sh

pC

0 1.8 Side Hull Prismatic Coefficient

sh

mC 0.7 1.8

Side Hull Maximum Section Coefficient

Wtdisplbal 0 3000

Weight-Displacement Balance

Maxspeedboost 33.0 200.0

Maximum Speed Boost

The objectives of the optimization for this case are to maximize the dead weight to

displacement ratio (Dwtdisplratio), maximize the maximum speed boost

(Maxspeedboost), and maximize the seakeeping index (Skpp).

Initially, each objective function (Dwtdisplratio, Maxspeedboost, and Skpp) is

optimized individually using a Multi-island Genetic Algorithm (MIGA). MIGA is a

global search algorithm and is distinguished from other genetic algorithms in that

each population of individuals is divided into several sub-populations called

“islands” upon which all genetic operations are performed separately.

After both objective functions are optimized individually using MIGA, 100 individuals

from each optimization are chosen and concatenated to create a new population

such that all its members are feasible (no constraints are violated) and the entire

design space is spanned. This new population serves as the initial population for

the multi-objective genetic algorithm (MOGA). This operation is performed in order

to obtain a suitable initial population to begin the multi-objective optimization.

Next, a MOGA which, similarly to MIGA is a global search method, is run using

Neighborhood Cultivation Genetic Algorithm (NCGA). NCGA utilizes an initial

population upon which standard genetic operations of mutation and crossover are

performed such that a “pareto set” is constructed. A set is said to be “pareto

optimal” when no individual can be made better off without another being made

worse off. Unlike MIGA, where only one objective is to be optimized, NCGA

simultaneously attempts to optimize multiple objectives, resulting in trade-offs being

made between them.

14


. The results of the NCGA optimization with three objective functions are presented in

Figures 6 and 7; Fig. 6 shows the pareto front for Maxspeedboost vs. Dwtdisplratio

and Fig. 7 shows a three-dimensional representation of the Pareto set.

Table 4 presents the maximum values found for Maxspeedboost, Dwtdisplratio, and

Skpp using NCGA. Point 1 corresponds to maximum Maxspeedboost and is

represented by the white triangle in Figures 6. Point 2 corresponds to maximum

Dwtdisplratio and is represented by the gray square in Figure 6. Point 3

corresponds to maximum Skpp.

Figure 8 shows a frontal (a) and top (b) view of the HALSS where the left (or top)

side corresponds to point 1 in Table 5, and the right (or bottom) side corresponds to

point 2 in Table 4.

32.5

33

33.5

34

34.5

35

35.5

36

36.5

37

37.5

38

0.28 0.3 0.32 0.34 0.36 0.38

Dwtdisplratio

Ma

xsp

ee

db

oo

st (k

no

ts)

NCGA Pareto

Dead Weight to Displacement Ratio

Maximum Speed Boost

Figure 6: HALSS model NCGA optimization results (Dwtdisplratio vs.

Maxspeedboost)

15


.

Figure 7: 3D representation of HALSS NCGA optimization results

Table 4: Maximum values for Maxspeedboost, Dwtdisplratio, and Skpp

Point Lch Bch Tch Lsh Bsh Tsh α β Maxspeedboost Dwtdisplratio Skpp

1 313.28 22.53 11.08 180.56 5.35 8.09 0.81 0.32 37.44 0.31 0.98

2 276.92 27.46 11.08 161.29 7.90 8.64 0.77 0.15 33.03 0.37 0.97

3 319.94 26.66 11.04 119.18 4.12 8.65 0.74 0.15 36.12 0.33 0.98

(a) Frontal View (b) Side View

Figure 8 Comparison of two designs from extreme ends of the design space. The

design on the right maximizes Dwtdisplratio. The design on the left maximizes

Maxspeedboost.

JHSV MODEL

The second case reported here are the results of optimization for the Sealift Ship for

Joint High Speed Vessel (JHSV) type mission requirements. This mission

requirement includes:

Transit speed: Not less than 25kn Crew: 44

Boost range: Not less than 1,200nm Troops, berthed: 150

Transit range: Not less than 4,700nm Troops, seated: 312

Vehicle weight: Not less than 635t Total accommodations: 506

Vehicle area: Not less than 1,858m^2

Table 5 and 6 contain the design variables, their description and design space limits

and design constraints for JHSV trimaran model

Table 5: List of design variables for the JHSV trimaran model

Design Variable

Lower Bound

Upper Bound

Description

Lch 100.0 150.0

Center Hull Length on Waterline

Bch 7.5 12.0

Center Hull Beam on Waterline

Tch 3.5 10.0

Center Hull Draft

Lsh 40.0 65.0

Side Hull Length on Waterline

Bsh 3.0 6.0

Side Hull Beam

Tsh 1.5 4.0

Side Hull Draft on Waterline

16


. Dch

9.0 12.0 Center Hull Depth

α 0.75 1.5

Separation

β 0.0 0.35

Stagger

Table 6: List of constraints imposed on the JHSV Trimaran model

Constraint Lower Bound

Upper Bound

Description

WSch Center Hull Wetted Surface

WSsh Side Hull Wetted Surface ch

bC 0.550 0.625

Center Hull Block Coefficient

ch

mC 0.675 0.800

Center Hull Maximum Section Coefficient

sh

bC 0.500 1.000

Side Hull Block Coefficient

sh

mC 0.700 1.800

Side Hull Maximum Section Coefficient

Wtdisplbal -300 300

Weight-Displacement Balance

Maxspeedboost 35.0 200.0

Maximum Speed Boost

The objectives of the optimization for this case are to maximize the dead weight to

displacement ratio (Dwtdisplratio), maximize the lift to drag ratio and maximize the

cost. The optimization is run using the Darwin Genetic Algorithm in PHX

ModelCenter environment, ModelCenter (2008). Figure 9 shows the results of the

optimization in the form of Pareto optimal solutions.

Figure 9: The results of optimization using the Model Center Darwin genetic

algorithm

Table 7 shows the specifications of the extreme corners of the pareto surface.

Detailed comparisons of various design points and their implications are currently

17


. on-going and will be reported later. Overall however, results presented here show

that the MDO method can determine the significant impact of various criteria. This

provides valuable, input for functional and design space exploration analysis. The

presented MDO tools allow systematic parametric study of different requirements

and design options by means of optimization routine and synthesis design modeling

procedures.

Table 7: Extreme design points identified as the corners of the pareto surface

Point Lch Bo Lsh α β Maxspeedboost Dwtdisplratio Lift To

Drag

Production

Cost

1 118.3 19.9 40.1 0.75 0.35 36.6 0.41 29.53 89.6

2 152.6 26.7 65.0 1.50 0.31 36.8 0.35 43.46 97.5

3 100.3 21.0 42.9 0.80 0.15 36.1 0.44 20.21 94.4

CONCLUSION AND FUTURE WORK

CCDoTT/CSC team has made substantial progress in developing comprehensive,

practical computational tools for applications to multi-hull vessels. The MDO tools

allow systematic parametric study of different requirements and design options by

means of optimization routine and Synthesis Design Modeling procedures. The

method has been applied to several High Speed Sealift applications for testing. A

number of possible extensions of the method are under study and review. They

include future development of an advanced structural optimization sub-system to

investigate the impact of variations in the vessel configurations on the structural

design and weight. The structural MDO will use the loads generated by the

hydrodynamic analysis to evaluate the impact of changes in the vessel configuration

on the structure, for example, the structural implications of the pinching and prying

moments induced on the side hull for vessels with various breadths. The current

hullforms definition sub-system is based on scaling a selected parent hull from an

existing hullforms library. Incorporation of a parametric, non-dimensional offset

representation of the ship hulls in the MDO along with means to transform offsets

for variations in block and midship coefficients, center of buoyancy, widths and

depth of transom length, area of bulb, etc are another significant improvement that

are being considered. Enhanced seakeeping computations to include more training

set data for trimarans and also catamarans are currently underway. Finally, the

synthesis design model (SDM) utilized in this work has been developed in house

over the course of past three years with focus on multi-hull applications. Ideally this

SDM model could be incorporated with the US Navy’s Advanced Ship and

Submarine and Evaluation Tool (ASSET). Integration of our multi-objective

optimization, neural networks and an advanced SDM such as ASSET will provide a

powerful design tool applicable to both military and commercial applications.

18


.

ACKNOWLEDGMENT

This work is supported by the US Office of Naval Research, under cooperative

agreement No. N00014-04-2-0003 with the California State University, Long Beach

Foundation Center for the Commercial Deployment of Transportation Technologies

(CCDoTT). The authors would like to sincerely thank the program manager Dr.

Paul Rispin and Mr. Dan Sheridan from ONR for their support, and many important

inputs. Mr. Steve Wiley from CSC has been the primary developer of the SDM. His

experience with many Navy and commercial ships have been essential

contributions to this work. We also thank Viking Systems of Annapolis Maryland for

pioneering the systematic seakeeping calculations for multi-hulls. Their professional

contribution helped to incorporate these comprehensive results in MDO process.

Finally we would like to thank CCDoTT’s Principal Investigator Mr. Stan Wheatley,

program coordinator Mr. Steven Hinds, and program administrator Ms. Carrie

Scoville for their supports.

Glossary of Acronyms:

ABS - American Bureau of Ships

CFD - Computational Fluid Dynamics

HSS - High Speed Sealift Ship

JHSS - Joint High Speed Sealift Ship

JHSV - Joint High Speed Vessel

LWT - Light Weight

MCC - Modified Cascade Correlation

MDO - Multi-disciplinary Design and Optimization

MOGA – Multi-objective Genetic Algorithm

MIGA – Multi-island Genetic Algorithm

NN- Neural Network

NLPQL - Sequential Quadratic Programming

NCGA – Neighborhood Cultivation Genetic Algorithm

TS – Training Set

VS – Validation Set

USCG – US Coast Guard

USMC- US Marine Corp

19


.

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