Conceptual Ship Design using MSDO Rob Wolf John Dickmann Ryan Boas Engineering Systems Division ESD.77

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1 Conceptual Ship Design using MSDO Rob Wolf John Dickmann Ryan Boas Engineering Systems Division ESD.77 John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 1

2 Outline Motivation Single Objective optimization Sensitivity analysis Pareto Front Calculations: OMOE Summary Follow-on issues John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 2

3 Why Ship Design Optimization? Issue: Institutional angst over and desire for ships with innovative performance attributes * Difficulty: Most new design efforts yield same old designs or (best case) nearest neighbor variants MSDO and (specifically) heuristic algorithms may be able to help achieve breakthrough *Everybody wants to go FAST and carry a lot of STUFF (Military AND commercial issue) John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology

4 Model Relationships Initial Inputs Pareto Front {J sys } Optimization Algorithm (genetic/gradient) {J sys } {J} Performance Analysis {x o } {J} Empirical Ship Model Main Check Hull Parameters Payloads Deckhouse Machy System Tankage Hull Geometry Weight Balance Check Hull Parameters (2 nd iter.) Stability Electrical System Volume Balance Propulsive Power Balance Cost Model John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 5

5 Validation Input (FFG-7) Inputs (Design Vector) Value Inputs (Design Vector) Value Length between perpendiculars (ft) 48 Engine choice 6 Beam (ft) 44.8 Engine/propeller combination 2 Prismatic coefficient.6 Generator choice (New stats entered) Maximum section coefficient.75 Number of generators 4 Number of hull decks 2 Fuel Weight (lton) 55 Number of deckhouse decks Deckhouse mat'l (Al=1, steel=2) 2 Average hull deck height (ft) 9.77 KG Margin 1 Average deckhouse deck height (ft) 8.58 Collective Protection System None Bilge height (ft) 9.5 Volume factor.5 John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 6

6 Validation Output Ship Design Parameters Objective Function(s) Output Model FFG-7 Frigate % Difference Draft (ft) % Station Depth (ft) % Station 1 Depth (ft) % Station 2 Depth (ft) % Full Load Weight (lton) % Installed P ower (hp) % Average kw Load (kw) % Average kw load wi th % margin (kw) kw Error 2.15%?? (>) Area Error -.29%?? (>) Volume Error -..26%?? (>) Stability Meas ure (GM/B) % Cost ($M) 48.5 Max Sustained Spe ed (kts) ~8.68% Range (nm) * ~42 ~4.% RAW1 *Range % difference significant because of model simplification (constant specific fuel consumption) John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 7

7 Conceptual Representation of N-dimensional Design Space Feasible areas Plus: Discrete variables make feasible space very rugged John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 8

8 Single Objective Optimization Design space extremely complex Many constraints Mostly discrete variables (outside of hull form) Necessitated focus on a small part of the design space to test gradient based optimization method Optimizer: MATLAB fmincon (SQP) Optimized function: Speed Excellent results for limited exploration of design space: Design Variables: Objective: Length Beam Cp Cx Fuel Speed John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 9

9 Genetic Algorithm - Implementation GA Optimization Toolbox, NC State Floating Point and Binary implementations Used in tuning and comparison with gradient methods Special Operators (Floating Point) Mutation: Boundary, Uniform, Non-uniform (Gaussian), Multi-nonuniform Crossover: Arithmetic, Heuristic, Simple GOSET, Purdue University Used for multi-objective optimization Special Operators Elitism: Non-dominated population members retained on subsequent generations, up to 5% of population Diversity Control: Population members close together on front must share fitness thus spreading the front John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 1

10 GA Tuning Test Run: Populations: 2-1 Mutation Rates: 1- Average of five runs Speed Avg V s Time GA termination criteria: 1 Generations.1% of best Gradient Based solution Avg Time Generations Avg Gen MR Pop Avg John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 11

11 Gradient vs. GA Optimization Comp Design Variables: Objective: Gradient Optimization Genetic Algorithm-1 Time Length L/B Cp Cx Fuel Speed 2s s Highlights: GA computational time ~x Gradient Solution essentially identical John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 12

12 Sensitivity Analysis/Scaling Scaling issues DVs range across 4 orders of magnitude Difficulty scaling to O(1): Optimizer output would not rescale back to physical dimensions for simcode Solution: Scaled all to the same order vice O(1) Constraint Scaling Large variation in constraint dimensions makes comparison of sensitivity coefficients difficult Conclusion: should scale constraints in order to make sensitivity analysis useful/easier to understand. Needed to scale for Part A; Dedicated scaling analysis arrived with same factors. John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 1

13 Multi-Objective Optimization Computational efficiency of empirical algorithm allowed full combinatorial mesh exploration ~7M designs Even so, exploration limited by large number of discrete variables GA optimization run generated wide exploration of design space Population size: 1 Generations: 5 Pareto filtering conducted using OMOE (scale: -1) OMOE =.15(Range)+.(Speed)+.55(Combat Capability) John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 14

14 Comparison of Pareto Fronts OMOE E O M O Combinatorial Mesh Genetic Algorithm Best of Both Cost Cost ($M) 25 2 John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 15

15 Pareto Front vs. Propulsion Comb. Pareto Front-OMOE Two LM6 Single Shaft ; Two GT- 5-2 Single Shaft Single GT- Single Shaft 6-1; 5-1; Four LM6 7-4 Two Shafts Four LM Two Shafts Two Diesel- Two 2-2 Shaft Single Diesel- Single Shaft OMOE Cost ($M) John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 16

16 Multi-Objective Optimization: Issues Weighting factors in OMOE OMOE =.2(Range)+.(Speed)+.55(Combat Capability) Coefficients determine which designs get pushed to Pareto Front Normalization method for individual MOEs Performance range of interest or Full design range Example: Speed 42-5 kt. Full design range: 25-5 kt. John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 17

17 Summary Gradient-based optimization is superior in continuous sections of the design space But many DVs in this problem are discrete GA yields more, and more superior, solutions At the cost of tuning effort and computational time GA allows for better exploration of the full design space in comparison to Gradient or Combinatorial Mesh methods for this problem Scaling of variables and constraints is an issue OMOE methods drive Pareto designs John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 18

18 Research Issues How best to combine Gradient search with GA search Scaling Factors and impact on optimization The Ordering Question Does this method really provide us with new information? The validity of OMOE as a design decision tool (?) Choice of weighting factors impacts ability to penetrate convex areas of the Pareto Front MOE normalization method impacts designs that get filtered out to the Pareto Front Should design filtering be done on individual MOEs as a separate step prior to OMOE consideration? This is the intersection with Operational Analysis: What are speed and range worth in combination with other desired attributes not addressed in this optimization? John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 19

19 Questions? John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 2

20 Background/Pedigree of the Model MIT Math Model Evolution Empirically based Ships built since end of WW-II Ships from LT Versions FORTRAN (1976) MATHCAD (199s) MATLAB (2) Validated against Standard Warship design tool: ASSET John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 21

21 Design Clusters Eng Code/Type Engine-Shaft Code/Combination Combat Package Code/Type 2 Diesel basic+uav 5 LM basic+uav+uuv 6 LM25* basic+uav+uuv+peng (4) 7 LM6 25 basic+uav+uuv+peng (8) 41 basic+uav+uuv+2nd Gun+Peng (4) 42 basic+uav+uuv+2nd Gun+Peng (8) 48 basic+uav+uuv+helo+2nd Gun+Peng (8) *(DDG-51 Style) John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 22

22 Pareto Front vs. Propulsion Comb. Two LM6 7-2 Single Shaft 6-2; Two GT- 5-2 Single Shaft Single GT- Single Shaft 6-1; 5-1; Four LM6 7-4 Two Shafts Four LM Two Shafts Two Diesel- Two 2-2 Shaft Single Diesel- Single Shaft OMOE Cost ($M) John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 2

23 Pareto Front vs. Combat Package / / OMOE Cost ($M) John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 24

24 Impact of OMOE/MOE Normalization* Choose a single point along the Pareto Front: $5.4M Vary weighting factors across from -1 in steps of.1 MOE normalization across performance range of interest Calculate how design changes at that point: Range Speed CombatCap OMOE variation can result in 5 possible designs at the Pareto Front *This filtering was conducted for a single Cost: $5.4M John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 25

25 Impact of OMOE/MOE Normalization* Same Cost point: $4.5M Change MOE normalization to: Full range of design values Vary OMOE weightings as before Range Speed CombatCap *This filtering was conducted for a single Cost: $5.4M John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 26

26 Contour Plot: Range-Speed-Cost 7 Cost John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 27

27 Iso-Contours: Cost vs. Speed/Combat Cost $M John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 28

28 Surface Plot John Dickmann,Rob Wolf, Ryan Boas, Massachusetts Institute of Technology 29

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