SNAME 05

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Lothar Birk1 and T. Luke McCulloch2 1) School of
Naval Architecture and Marine Engineering
University of New Orleans 2) Bentley Systems,
Inc. New Orleans (Metairie), LA
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Overview

• 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

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Design 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

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Design Challenges Knowledge Gap

• knowledge of detail marginally in early design
  phases

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Design Challenges Knowledge Gap

• knowledge of detail marginally in early design
  phases
• however, financial impact of design decisions is
  huge

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Design Challenges Knowledge Gap

• knowledge of detail marginally in early design
  phases
• however, financial impact of design decisions is
  huge
• knowledge gap has to be closed to improve designs

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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

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Closing 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

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Shape 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,
  ...

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Automated Hull Generation The Idea
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Parametric Model for Offshore Structures
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Generation of Components
V,xc
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51,250t Semisubmersible Hull
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51,250t Semisubmersible Hull
Merged Hull (only submerged part shown)
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51,250t Semisubmersible Optimization

• 8 free variables

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51,250t 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 winddirections of target
  operating area
• Constraints
• require sufficient initial stability at working
  and survival draft
• several geometric restrictions

North-East Atlantic(Marsden Square 182)
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Multi-Objective Optimization
objective function is vector valued
free variables define design space
design space further limited by constraints
What constitutes the optimum?
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Multi-Objective Optimization

• Pareto (1906)
• Pareto frontier
• designs that are at least in one objective better
  than all others
• non-dominated solutions

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Optimization Algorithm e-MOEA

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

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Multi-Objective Hull Shape Optimization

• Ideal solution
• f1 5.125
• f2 0
• initial population contains 400 designs
• a total of 2000 designs will be investigated

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Estimated Pareto Frontier
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Estimated Pareto Frontier
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Estimated Pareto Frontier
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Estimated Pareto Frontier
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Ongoing 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

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Ship 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

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B-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.

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B-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 isnt that hard to do, conceptually)

F the Lagrangian Functional f the objective
function(s) h constraints ? Lagrange
multipliers
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Automatic 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)

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

• 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!

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Example 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!)

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Robust 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

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Conclusions

• 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

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The End
Thank you for your attention !
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Expected Downtime Computation
Short-term wave statistics representing a single
design sea state RAOs (linear) computed with
WAMIT (J.N. Newman, MIT)
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Long-term statistics of sea states
Occurrences of short-term sea states (Hs, T0)
Graphical representation of wave scatter diagram
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Assessment Based on Long Term Statistics
Estimation of downtime due to severe weather

1. Specification of limit
2. Assessment by short-term wave statistic for all
   zero-up-crossing period classes
   T0j(significant response amplitude
   operator)
3. Computation of maximum feasible significant wave
   height

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Account for all wind directions

• Compute expected downtime for each wave
  direction
• Build a weighted average

Relative occurrence of wind direction
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Comparison of Hydrodynamic Properties
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Comparison of Hydrodynamic Properties
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Comparison of Hydrodynamic Properties