1. Sep. 19, 2014 Hydrodynamic Shape Optimization of Ships and Offshore Structures Lothar Birk 1 and T. Luke McCulloch 2 1) School of Naval Architecture and Marine Engineering University of New Orleans 2) Bentley Systems, Inc. New Orleans (Metairie), LA

2. Sep. 19, 2014 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. Sep. 19, 2014 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

4. Sep. 19, 2014 Design Challenges – Knowledge Gap L. Birk and T.L. McCulloch knowledge of detail marginally in early design phases

5. Sep. 19, 2014 Design Challenges – Knowledge Gap L. Birk and T.L. McCulloch knowledge of detail marginally in early design phases however, financial impact of design decisions is huge

6. Sep. 19, 2014 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

7. Sep. 19, 2014 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. Sep. 19, 2014 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

9. Sep. 19, 2014 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. Sep. 19, 2014 Automated Hull Generation – The Idea Traditional designShape optimization

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

12. Sep. 19, 2014 Generation of Components Component NURBS surface Frenet-Sweep operation Form parameters Cross section curve Cross section area curve V,  c

13. Sep. 19, 2014 51,250t Semisubmersible Hull

14. Sep. 19, 2014 51,250t Semisubmersible Hull Merged Hull (only submerged part shown)

15. Sep. 19, 2014 51,250t Semisubmersible Optimization 8 free variables

16. Sep. 19, 2014 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 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)

17. Sep. 19, 2014 Multi-Objective Optimization free variables define design space design space further limited by constraints objective function is vector valued What constitutes the optimum?

18. Sep. 19, 2014 Multi-Objective Optimization Pareto (1906) Pareto frontier designs that are at least in one objective better than all others non-dominated solutions

19. Sep. 19, 2014 Optimization Algorithm – ε-MOEA ε-MOEA (Epsilon Multi-Objective Evolutionary Algorithm) K. Deb et al. (2001, 2003) ε-dominance

20. Sep. 19, 2014 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

21. Sep. 19, 2014 Estimated Pareto Frontier

22. Sep. 19, 2014 Estimated Pareto Frontier

23. Sep. 19, 2014 Estimated Pareto Frontier

24. Sep. 19, 2014 Estimated Pareto Frontier

25. Sep. 19, 2014 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. Sep. 19, 2014 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. Sep. 19, 2014 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.

28. Sep. 19, 2014 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. Sep. 19, 2014 Automatic Differentiation Object Oriented Implementation Each variable stores value, gradient (1 st order derivatives), and Hessian matrix (2 nd 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. Sep. 19, 2014 Major 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 initial estimate to guess feasible domains based on design choices Research is ongoing! starting curves are drawn for a range of form parameter tangent values

31. Sep. 19, 2014 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. 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

33. Sep. 19, 2014 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. Sep. 19, 2014 The End Thank you for your attention !

35. Sep. 19, 2014

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

37. Sep. 19, 2014 Long-term statistics of sea states Occurrences of short-term sea states (H s, T 0 ) Wave scatter diagram Graphical representation of wave scatter diagram

38. Sep. 19, 2014 Assessment Based on Long Term Statistics a)Specification of limit b)Assessment by short-term wave statistic for all zero-up-crossing period classes T 0j : (significant response amplitude operator) c)Computation of maximum feasible significant wave height: Estimation of downtime due to severe weather Expected downtime:

39. Sep. 19, 2014 Account for all wind directions Compute expected downtime for each wave direction Build a weighted average qq Relative occurrence of wind direction

40. Sep. 19, 2014 Comparison of Hydrodynamic Properties

41. Sep. 19, 2014 Comparison of Hydrodynamic Properties

42. Sep. 19, 2014 Comparison of Hydrodynamic Properties