Lothar Birk 1 and T. Luke McCulloch 2

1. 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

2. 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

3. 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 Design Challenges of Marine Industry

4. knowledge of detail marginally in early design phases Design Challenges – Knowledge Gap L. Birk and T.L. McCulloch

5. knowledge of detail marginally in early design phases however, financial impact of design decisions is huge Design Challenges – Knowledge Gap L. Birk and T.L. McCulloch

6. 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 Design Challenges – Knowledge Gap

7. 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

8. Restriction to hull shape development Integration of Computational Fluid Dynamic tools Process control by optimization algorithms New hull design philosophy Closing the Knowledge Gap – First Step …for the time being:

9. 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, ...

10. Shape optimization Traditional design Automated Hull Generation – The Idea

11. Parametric Model for Offshore Structures

12. Cross section area curve Component NURBS surface Form parameters Frenet-Sweep operation Cross section curve Generation of Components V,xc

13. 51,250t Semisubmersible Hull

14. 51,250t Semisubmersible Hull Merged Hull (only submerged part shown)

15. 8 free variables 51,250t Semisubmersible Optimization

16. 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 51,250t Semisubmersible Optimization North-East Atlantic(Marsden Square 182)

17. Multi-Objective Optimization objective function is vector valued free variables define design space design space further limited by constraints What constitutes the optimum?

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

19. ε-MOEA (Epsilon Multi-Objective Evolutionary Algorithm)K. Deb et al. (2001, 2003) ε-dominance Optimization Algorithm – ε-MOEA

20. Ideal solution f1 = 5.125 f2 = 0 initial population contains 400 designs a total of 2000 designs will be investigated Multi-Objective Hull Shape Optimization

21. Estimated Pareto Frontier

22. Estimated Pareto Frontier

23. Estimated Pareto Frontier

24. Estimated Pareto Frontier

25. 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

26. 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

27. 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. B-Spline Example

28. 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 isn’t that hard to do, conceptually) F = the Lagrangian Functional f = the objective function(s) h = constraints λ = Lagrange multipliers

29. 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)

30. 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! Major Difficulties • starting curves are drawn for a range of form parameter tangent values

31. 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!)

32. 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

33. 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

34. The End Thank you for your attention !

36. x = Expected Downtime Computation Short-term wave statistics representing a single design sea state RAOs (linear) computed with WAMIT (J.N. Newman, MIT)

37. Wave scatter diagram Long-term statistics of sea states Occurrences of short-term sea states (Hs, T0) Graphical representation of wave scatter diagram

38. Expected downtime: Assessment Based on Long Term Statistics Estimation of downtime due to severe weather • Specification of limit • Assessment by short-term wave statistic for all zero-up-crossing period classes T0j:(significant response amplitude operator) • Computation of maximum feasible significant wave height:

39. Compute expected downtime for each wave direction Build a weighted average qb= Account for all wind directions Relative occurrence of wind direction

40. Comparison of Hydrodynamic Properties

41. Comparison of Hydrodynamic Properties

42. Comparison of Hydrodynamic Properties