Design Optimization of Ship Propellers by Means of Advanced Metamodel- Assisted Evolution Strategies

Transcription

1 Design Optimization of Ship Propellers by Means of Advanced Metamodel- Assisted Evolution Strategies Michael Emmerich*, Jochen Hundemer+, Mihai-Christian Varcol+ Boris Naujoks++ and Moustafa Abdel-Maksoud+ *LIACS, Leiden University, The Netherlands ++Systems Analysis, Informatik, Universität Dortmund, Deutschland +Laboratory for Ship Technology, UniDuisburg-Essen, Deutschland ERCOFTAC 2006, Las Palmas de Gran Canaria, Spain tems Analysis Group Dortmund IST Duisburg LIACS

2 Application Study in Ship Propellor Design Metamodel-Assisted ES Problem Domain Algorithmic Design Test on Artificial Landscapes Ship Propeller Design: Design Problem Model CFD Simulation for Ship Propeller Optimization ( 2 von 18

3 Design Optimization Algorithm: Metamodel-Assisted EA

4 Design Optimization Black-box Optimierungssoftware System Variables Objective- and Constraint values Preprocessing Postprocessing Simulator for Ship Propeller Optimization ( 4 von 18

5 Difficulties for Design Optimization Time consuming simulation model (stability, fluid-dynamics etc.) High number of variables, multimodal objective function (many local optima) Metal-Forging Computational Fluid Dynamics Chemical Reactor Design Electromagnetic Compatibility for Ship Propeller Optimization ( 5 von 18

6 Evolution Strategies Evolution strategies Excellent optimization techniques for high-dimensional search spaces Self-adaptation of step-sizes to the local topology of function But: need many evalutations Metamodel-assisted evolution strategies Partial replacement of precise evaluations by approximate evaluations Metamodel (Surrogate Model) is used prescreen/reduce offspring population for Ship Propeller Optimization ( 6 von 18

7 Metamodel-Assisted Evolution Strategy Key Articles + ca. 15 Papers, 1 PhD Thesis on MAES for Ship Propeller Optimization ( 7 von 18

8 Metamodell-assisted assisted Direct Optimization Direct Optimization Algorithm Decision variables Qualities, Constraints Time-consuming simulation ariables Estimation of qualities/constraints Interpolation Variables Neighboring Datapoints Metamodel (or: Emulator) Evaluation Database for Ship Propeller Optimization ( 8 von 18

9 variate approximate, filt evaluate, replace for Ship Propeller Optimization ( 9 von 18

10 Filter with constant output size Offspring population reduced offspring population for Ship Propeller Optimization ( 10 von 1

11 Gaussian Random Fields kly correlation (high q) Strong correlation (low q) for Ship Propeller Optimization ( 11 von 1

12 Gaussian Random Field Metamodels (Kriging) Conditional PDF: for Ship Propeller Optimization ( 12 von 1

13 Filter with constant output size Offspring population reduced offspring population for Ship Propeller Optimization ( 13 von 1

14 ernative criteria for detecting promising solution for Ship Propeller Optimization ( 14 von 1

15 Results on 20-D D sum of squares Evolution Strategy Evolution Strategy +Metamodel (+Confidence Measu for Ship Propeller Optimization ( 15 von 1

16 Results on Ackley s Problem for Ship Propeller Optimization ( 16 von 1

17 Results on 10-D D Ackley Function Evolution Strategy Metamodel+ES Metamodel+ Confidence Measu ES for Ship Propeller Optimization ( 17 von 1

18 Quality indicators for filters Validation of the model Selectivity Inversiontest for Ship Propeller Optimization ( 18 von 1

19 Ackley 20- (lower boun Validation of lower confidence bound precision for Ship Propeller Optimization ( 19 von 1

20 ross-validated approximation error (CE) vs Distance to Local Optimum CE ==> Error of Metamodel shrinks with distance to local optimum ONLINE LEARNING CAPABILITY for Ship Propeller Optimization ( 20 von 1

21 Application in Ship Propeller Design

22 Targets Optimization of a propeller under given boundary conditions Automatic Adaptation of a given Propeller to changed conditions Generation of solution candidates by affine transformations of original geometry Simulation of the potential theoretic fluid flow around the propeller for Ship Propeller Optimization ( 22 von 1

23 Boundary Conditions Free-stream velocity determines thrust Fixed diameter of propeller Cavitations has to be avoided (constraint) Restrictions to the geometry for Ship Propeller Optimization ( 23 von 1

24 Decision variables Distribution of slope over the radius of the propellor Profile-depth Number of revolutions ================================= 9 Parameters Curvature/Profile thickness for Ship Propeller Optimization ( 24 von 1

25 Objectives Maximization of Efficiency! Maximal difference of thrust: 4% Maximal cavitation: < 3% of the propellor-surface Penalty Terms for boundary conditions: f = η + a max( 1 T T desired 0.04,0) 2 + b max( A A cavitation total 0.03,0) 2 for Ship Propeller Optimization ( 25 von 1

26 CFD Simulation Potential-theoretical Solver 3D-Boundary Elements Method (BEM) ρ ρ ρ V ( p) n = 0 µ wake, i = µ upper, i µ lower, i Boundary conditions on the surface Kutta-Condition at the edge Potentials σ 1 ρ ρ Φ = = Π da, σ n V 4 r A Dipoles Φ = σ 4Π A z 3 r Sources da for Ship Propeller Optimization ( 26 von 1

27 Determination of forces Pressures from local velocities ρ dp ρ 2 2 ρ = ( V V ) n 2 Prandtl-Kármán Approach for turbulent motions c = Re f -0.2 for Ship Propeller Optimization ( 27 von 1

28 CFD Simulation for Ship Propeller Optimization ( 28 von 1

29 CFD Method Measure for Cavitation: Ratio of surface with insufficient steam pressure Further work... Pod-engine simulations Computation of jet engines Instationary computations Interaction with vortices behind ships for Ship Propeller Optimization ( 29 von 1

30 Design Optimization Study

31 Setup of MAES Optimizer (15+5<100)-Metamodel-Assisted ES Lower Confidence Bound used as filter criterion Other criteria have been tried, but less successful 100 evaluations by means of CFD solver evaluations of metamodel based on local Kriging model with 2d euclidian neighbors for Ship Propeller Optimization ( 31 von 1

32 Wageninger B-Serie Results without Cavitation A E /A 0 : 0,7 Slope-ratio: 1,13 Vorgabe: Thrust: Diameter: Thrust: 0,83 m/s 1 m 185 N No. revolutions: 0,8-1,5 /s Propeller at ideal operating point for Ship Propeller Optimization ( 32 von 1

33 Original η = 66,7% n = 1 /s Results without cavitation New Solutio η = 67,7 n = 1 for Ship Propeller Optimization ( 33 von 1

34 lope ,2 0,4 0,6 0,8 1 r / R Results without cavitation Original Original New Veränderung Profiltiefe / mm Original New Original Profile-Depth Veränderung 0 0,2 0,4 0,6 0,8 1 r / R Resultat: Minimization of propellor area less friction Compensation through higher angle of attac for Ship Propeller Optimization ( 34 von 1

35 Wageninger B-Serie Given: A E /A 0 : 0,7 Slope-ratio: 1,13 Results with Caviation Speed: Diameter: Desired-Thrust: 8,74 m/s 4,68 m 554,4 kn No. Of revolutions: 1,92-2,1 /s for Ship Propeller Optimization ( 35 von 1

36 ginal 73,28% 2,01/s /A ges = 0,4% 460 kn Results with Cavitation New soluti η=72,5 n = 2,10 A kav /A ges = T = 534 for Ship Propeller Optimization ( 36 von 1

37 Steigung / mm ope ,2 0,4 0,6 0,8 1 r / R Resultat: Results with Cavitation Original Veränderung as a side-effect the area of propeller is minimized compensation through higher angle of attack and higher no. revolutions Approximation to an elliptic shape Original New Profiltiefe / mm Original New Original Veränderung 0 0,2 0,4 0,6 0,8 Profile Depth r / for Ship Propeller Optimization ( 37 von 1

38 Conclusions Metamodel-Assisted Evolution Strategies with LCB filter well suited for optimization task Generation of propeller variants by affine transformation Potential-solvers are employed for evaluations Optimization of propellers seems possible: efficiency and cavitation improve Outlook More potential in the method if curvature could be controlled (not possible with affine transformations, maybe 3D freeform parameterization?!) Further validation of the potential solver, prototype models... Further acceleration of MAES by means of hybridization Pareto optimization instead of aggregate objective for Ship Propeller Optimization ( 38 von 1