Sep. 19, 2014
Hydrodynamic Shape Optimization
of Ships and Offshore Structures
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
Overview
Sep. 19, 2014
• 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
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
Sep. 19, 2014
Design Challenges – Knowledge Gap
Sep. 19, 2014
• knowledge of detail
marginally in early
design phases
L. Birk and T.L. McCulloch
Design Challenges – Knowledge Gap
Sep. 19, 2014
• knowledge of detail
marginally in early
design phases
• however, financial
impact of design
decisions is huge
L. Birk and T.L. McCulloch
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
Sep. 19, 2014
Closing the Knowledge Gap – How?
Sep. 19, 2014
• 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
Closing the Knowledge Gap – First Step
…for the time being:
Sep. 19, 2014
• Restriction to hull shape
development
• Integration of Computational
Fluid Dynamic tools
• Process control by optimization
algorithms
• New hull design philosophy
Shape Optimization Needs
Sep. 19, 2014
• 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, ...
Automated Hull Generation – The Idea
Traditional design
Sep. 19, 2014
Shape optimization
Parametric Model for Offshore Structures
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Generation of Components
Sep. 19, 2014
V,xc
Cross section curve
Frenet-Sweep operation
Form parameters
Cross section area curve
Component NURBS surface
51,250t Semisubmersible Hull
Sep. 19, 2014
51,250t Semisubmersible Hull
Sep. 19, 2014
Merged Hull
(only submerged part shown)
51,250t Semisubmersible Optimization
• 8 free variables
Sep. 19, 2014
51,250t Semisubmersible Optimization
Sep. 19, 2014
• 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)
Multi-Objective Optimization
free variables define
design space
Sep. 19, 2014
objective function is
vector valued
design space further
limited by constraints
What constitutes the optimum?
Multi-Objective Optimization
• Pareto (1906)
• Pareto frontier
• designs that are
at least in one
objective better
than all others
• non-dominated
solutions
Sep. 19, 2014
Optimization Algorithm – ε-MOEA
• ε-MOEA (Epsilon Multi-Objective Evolutionary Algorithm)
K. Deb et al. (2001, 2003)
• ε-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
Sep. 19, 2014
Estimated Pareto Frontier
Sep. 19, 2014
Estimated Pareto Frontier
Sep. 19, 2014
Estimated Pareto Frontier
Sep. 19, 2014
Estimated Pareto Frontier
Sep. 19, 2014
Ongoing Research at UNO
Sep. 19, 2014
• 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
Ship Hull Generation Process
Sep. 19, 2014
• 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:
position
• match curves of form at that station,
e.g. SAC controls area of the station
• local section control
sectional area
• Hull surface by lofting
• Objective and Constraints
design waterline
AP
• Curves are optimized for fairness
• Constraints are the form parameters
FP
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
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• Variational design, via Lagrangian Optimization
F = the Lagrangian Functional
f = the objective function(s)
h = constraints
λ = Lagrange multipliers
• 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)
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)
Sep. 19, 2014
Major Difficulties
• Initial guesses
• Harries (1998) exploited basic Bspline 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 initial
estimate to guess feasible
domains based on design choices
• Research is ongoing!
Sep. 19, 2014
starting curves are
drawn for a range of
form parameter tangent
values
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!)
Sep. 19, 2014
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
Sep. 19, 2014
Conclusions
Sep. 19, 2014
• 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
The End
Thank you for your
attention !
Sep. 19, 2014
Sep. 19, 2014
Expected Downtime Computation
x
Sep. 19, 2014
=
Short-term wave statistics representing a single design sea state
RAOs (linear) computed with WAMIT (J.N. Newman, MIT)
Long-term statistics of sea states
Sep. 19, 2014
Occurrences of short-term sea states (Hs, T0)
Wave scatter diagram
Graphical representation of
wave scatter diagram
Assessment Based on Long Term Statistics
Sep. 19, 2014
Estimation of downtime due to severe weather
a)
Specification of limit
(2sa ) S ,limit  1.0m
b)
Assessment by short-term wave
statistic for all zero-up-crossing
period classes T0j:
( 2 sa ) S
m0 S ( H S2 , T0 )
 4
 f (T0 )
2
HS
HS
(significant response amplitude
operator)
c)
Expected downtime:
Computation of maximum feasible
significant wave height:
1
 (2s )
H S ,limit (T0 )  (2sa ) S ,limit   a S
 HS



Account for all wind directions
• Compute expected downtime
for each wave direction
• Build a weighted average
Relative occurrence of wind direction
qb 
Sep. 19, 2014
Comparison of Hydrodynamic Properties
Sep. 19, 2014
Comparison of Hydrodynamic Properties
Sep. 19, 2014
Comparison of Hydrodynamic Properties
Sep. 19, 2014