lothar birk 1 and t. luke mcculloch 2

Sep. 19, 2014

Hydrodynamic Shape Optimizationof Ships and Offshore Structures

Lothar Birk1 and T. Luke McCulloch2

1) School of Naval Architecture and Marine Engineering University of New Orleans2) Bentley Systems, Inc. New Orleans (Metairie), LA

Sep. 19, 2014OverviewOverview

• Design optimization – Challenges and advantages

• Automated shape optimization

• Multi-objective optimization of a semisubmersible

• Ongoing work on• Parametric design of ship hulls

• Hydrodynamic analysis

• Conclusions

Sep. 19, 2014Design Challenges of Marine IndustryDesign Challenges of Marine Industry

• One-of-a-kind designs• limited design resources (time, money, engineers)

• less automation in comparison to aircraft or car industry

• no prototypes, less chance to correct design errors

Sep. 19, 2014Design Challenges – Knowledge GapDesign Challenges – Knowledge Gap

L. Birk and T.L. McCulloch

• knowledge of detail marginally in early design phases


L. Birk and T.L. McCulloch


• however, financial impact of design decisions is huge



• however, financial impact of design decisions is huge

• knowledge gap has to be closed to improve designs

Sep. 19, 2014Closing the Knowledge Gap – How?Closing the Knowledge Gap – How?

• Apply first principles based analysis as early as possible• requires more details of the design

• provides base for rational decisions

• Automate design processes• allows investigation of more design alternatives

• enables application of formal optimization procedures

Sep. 19, 2014Closing the Knowledge Gap – First StepClosing the Knowledge Gap – First Step

…for the time being: • Restriction to hull shape development

• Integration of Computational Fluid Dynamic tools

• Process control by optimization algorithms

• New hull design philosophy

Sep. 19, 2014Shape Optimization NeedsShape Optimization Needs

• Automated hull shape generation• non-interactive• driven by form parameters and parameter relations

• Performance assessment • objective functions (stability, seakeeping, resistance, maneuvering …)• compare different designs

• Constraints• ensure designs are feasible (technical, economical, …)

• Optimization algorithm(s)• control of the optimization process• search algorithms, gradient based algorithms,

genetic algorithms and evolutionary strategies, ...

Sep. 19, 2014Automated Hull Generation – The IdeaAutomated Hull Generation – The Idea

Traditional design Shape optimization

Sep. 19, 2014Parametric Model for Offshore StructuresParametric Model for Offshore Structures

Sep. 19, 2014Generation of ComponentsGeneration of Components

Component NURBS surface

Fre

net

-Sw

eep

op

erat

ion

Fo

rm p

aram

eter

s

Cross section curve

Cross section area curve

V,c

Sep. 19, 201451,250t Semisubmersible Hull51,250t Semisubmersible Hull

Sep. 19, 201451,250t Semisubmersible Hull51,250t Semisubmersible Hull

Merged Hull(only submerged part shown)

Sep. 19, 201451,250t Semisubmersible Optimization51,250t Semisubmersible Optimization

• 8 free variables

Sep. 19, 201451,250t Semisubmersible Optimization51,250t Semisubmersible Optimization

• Two objectives• Minimize displacement / payload ratio

• displacement is fixed, thus payload is maximized • payload assumed to be stored on deck

• Minimize estimated average downtime• acceleration in work area is restricted• analysis performed considering wave scatter diagram including wind

directions of target operating area

• Constraints:• require sufficient initial stability

at working and survival draft• several geometric restrictions

North-East Atlantic

(Marsden Square 182)

Sep. 19, 2014Multi-Objective OptimizationMulti-Objective Optimization

free variables definedesign space

design space furtherlimited by constraints

objective function isvector valued

What constitutes the optimum?

Sep. 19, 2014Multi-Objective OptimizationMulti-Objective Optimization

• Pareto (1906)

• Pareto frontier• designs that are

at least in one objective better than all others

• non-dominated solutions

Sep. 19, 2014Optimization Algorithm – Optimization Algorithm – εε-MOEA -MOEA

• ε-MOEA (Epsilon Multi-Objective Evolutionary Algorithm)K. Deb et al. (2001, 2003)

• ε-dominance

Sep. 19, 2014Multi-Objective Hull Shape OptimizationMulti-Objective Hull Shape Optimization

• Ideal solution

f1 = 5.125

f2 = 0

• initial population contains 400 designs

• a total of 2000 designs will be investigated

Sep. 19, 2014Estimated Pareto FrontierEstimated Pareto Frontier

Sep. 19, 2014Ongoing Research at UNOOngoing Research at UNO

• Form parameter driven ship hull design• More complex than offshore structure hulls• More stringent fairness requirements

• Hydrodynamics analysis• Wave resistance calculation• Integrate propeller selection / design

• Goal of Research• Hull definition description based on typical design coefficients• Control of displacement distribution (impact on performance)• Optimization of hull fairness / surface quality• Robust hull generation

Sep. 19, 2014Ship Hull Generation ProcessShip Hull Generation Process

• Shape generation via form parameter driven optimization (Harries)

• Curves of form: SAC, design waterline, profile,… tangents, etc.• built from design specifications (form parameters)• curves of form control form parameters of station curves

• Station curves:• match curves of form at that station,

e.g. SAC controls area of the station• local section control

• Hull surface by lofting

• Objective and Constraints• Curves are optimized for fairness• Constraints are the form parameters

position

sectional area

design w aterline

FPAP

Sep. 19, 2014B-Spline ExampleB-Spline Example

• Start with basic curve• make a good guess

(close to what you want)• this is non-linear optimization!

Result depends on starting curve

• Enforce desired constraints• We forced the end curvature to

zero,• Many other constraints have been

coded.• Automatic differentiation takes

care of the derivative details.

Sep. 19, 2014B-Spline Design by Form ParametersB-Spline Design by Form Parameters

• Variational design, via Lagrangian Optimization

• Necessary condition for optimum results in system of nonlinear equations

• Solution using Newton-Iteration (gradient driven – takes lots of derivatives)

• Implement automatic differentiation to make life easy (and isn’t that hard to do, conceptually)

F = the Lagrangian Functional

f = the objective function(s)

h = constraints

λ = Lagrange multipliers

Sep. 19, 2014Automatic DifferentiationAutomatic Differentiation

• Object Oriented Implementation

• Each variable stores value, gradient (1st order derivatives), and Hessian matrix (2nd order derivatives)

• Overload (re-define) basic operators

• Overload any needed analytic functions

• Calculate the floating point value of any analytic expression

• Calculate the gradient and Hessian of the expression, analytically, with floating point accuracy

• Compute anything analytic! (No errors due to numerical differentiation)

Sep. 19, 2014Major DifficultiesMajor Difficulties• Initial guesses

• Harries (1998) exploited basic B-spline properties to define initial curve

• Robustness / feasibility of solution• Hardest part of form parameter design• Inequality constraints,

least squares objectives, and fuzzy logic have all been tried

• Use the equations for initialestimate to guess feasible domains based on design choices

• Research is ongoing!

starting curves are drawn for a range of form parameter tangent values

Sep. 19, 2014Example: Hull with Well Defined KnuckleExample: Hull with Well Defined Knuckle

• Curves of form • sectional area curve

(SAC)

• design waterline, and

• enforcing a corner condition

• Created transverse curves to match the form curves at the station in question

• Only final lofted hull is shown

• Bulb is also based on form parameters(size exaggerated!)

Sep. 19, 2014Robust Performance EvaluationRobust Performance Evaluation

• Wave resistance• inviscid flow• panel method• nonlinear free surface

condition• free trim and sinkage• useful for forebody

optimization• Propeller design

• lifting line• integrated into performance

evaluation

Sep. 19, 2014ConclusionsConclusions

• Integration of parametric design, hydrodynamic analysis and optimization algorithms enables design optimization

• Design optimization can help to close the knowledge gap

• Proven concept for offshore structures

• Methods for robust, automated creation of design alternatives are a necessity

Sep. 19, 2014The EndThe End

Thank you for your Thank you for your attention !attention !

Sep. 19, 2014

Sep. 19, 2014Expected Downtime ComputationExpected Downtime Computation

x =

Short-term wave statistics representing a single design sea state

RAOs (linear) computed with WAMIT (J.N. Newman, MIT)

Sep. 19, 2014Long-term statistics of sea statesLong-term statistics of sea states

Occurrences of short-term sea states (Hs, T0)

Wave scatter diagram

Graphical representation of wave scatter diagram

Sep. 19, 2014Assessment Based on Long Term StatisticsAssessment Based on Long Term Statistics

a) Specification of limit

b) Assessment by short-term wave statistic for all zero-up-crossing period classes T0j:

(significant response amplitude operator)

c) Computation of maximum feasible significant wave height:

m0.1 )2( , limitSas

)( ),(

4 )2(

020

20 Tf

H

THm

H

s

S

SS

S

Sa

1

,0,

)2()2( )(

S

SalimitSalimitS H

ssTH

Estimation of downtime due to severe weather

Expected downtime:

Sep. 19, 2014Account for all wind directionsAccount for all wind directions

• Compute expected downtime for each wave direction

• Build a weighted average

qRelative occurrence of wind direction

Sep. 19, 2014Comparison of Hydrodynamic Properties Comparison of Hydrodynamic Properties

lothar birk 1 and t. luke mcculloch 2

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