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The CO2 Project (Design with Constraint Solving)

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  1. The CO2 Project(Design with Constraint Solving) Laurent ZIMMER DASSAULT AVIATION Research and Future Business Division laurent.zimmer@dassault-aviation.fr

  2. Context • A National Research Project • Labelled by a network for Software Development of the French Ministry of Research • Granted by the French Ministry of Economy, Finance and Industry FJCP WORKSHOP 25-27/10/94

  3. Context • 6 partners • 2 Industrial • 2 Informatics Labs • 2 Engineering Labs FJCP WORKSHOP 25-27/10/94

  4. Purpose • To develop in parallel • A (mainly) interval constraint-based software dedicated to engineering design called CE : • Modelling • Solving • A relating design methodology: • inverted and integrated design • constraint formulation FJCP WORKSHOP 25-27/10/94

  5. Basic Principle Classical Design Process I.I. Design Process Concept Model Req. DV DV+PV Calculus Calculus PV PV Requirements ... Sol 1 Solution Sol2 Sol N Point to Point design Set-based design (Toyota) FJCP WORKSHOP 25-27/10/94

  6. Methodology • To test the approach through many case studies: • Academic case studies • preliminary aircraft vehicle design • Industrial case studies • mechanical design problem • design of an Air Conditioning System (ACS) FJCP WORKSHOP 25-27/10/94

  7. Software Development • Every 6 months Release • Initial version of the tool: • Hull consistency with decomposition (HC3) • Interval arithmetic directly implemented with the floating point arithmetic instructions of the C++ compiler (outer rounding) • infinite numbers are not processed FJCP WORKSHOP 25-27/10/94

  8. First Case-Study Global Unmanned Aircraft Preliminary Design

  9. Problem Description • Requirements resulting from mission profile: • Range, cruise speed, cruise altitude, volume of payload .. • Constraint Model: • 51 variables,35 equations and 26 inequalities, • 5 Geometrical Design Variables : • Body diameter, Wing span, Wing root chord • Wing thickness/chord ratio, Wing aspect ratio FJCP WORKSHOP 25-27/10/94

  10. trapezoidal T delta L Swl arrow PossibleDesigns TiCRaT = T / L wing thickness/chord ratio Swl wing leading sweep angle FJCP WORKSHOP 25-27/10/94

  11. Some tests • T1: Dimensioning (VC -> VP) • to fix the geometrical variables • Range = f(MachNo) • T2: Reverse Computing • MachNo = f(Range) • T3:Parametric Study • Range=f(Swl) FJCP WORKSHOP 25-27/10/94

  12. T1 • H = 5000 FJCP WORKSHOP 25-27/10/94

  13. T2 • H = 5000, Range = 3496 FJCP WORKSHOP 25-27/10/94

  14. T3 FJCP WORKSHOP 25-27/10/94

  15. Results • T1 is OK • T2 is OK but not very efficient • T3 is OK however parametric study is to automate FJCP WORKSHOP 25-27/10/94

  16. reverse calculus vs direct parametric study FJCP WORKSHOP 25-27/10/94

  17. Revised version • A correct Interval Arithmetic Library implemented on a robust floating point library • (Gaol F. Goualard 2000) • A new propagation architecture implementing up-to-date consistency algorithms • (L. Granvilliers & M. Christie) • Some specialised solving strategies • parametric studies • optimisation (min, iterative approximating S. Preswitch 99) FJCP WORKSHOP 25-27/10/94

  18. Second Case-Study Pressure Device Design

  19. Stiffened Plate Pressure 2,5 Bar Plate Stiffener Purpose • Design of a Pressure device FJCP WORKSHOP 25-27/10/94

  20. ny type de raidisseur h nx Design problem of a stiffened plate • Design variables • Thickness of the plate • Type of stiffeners, • Type of material, • number of longitudinal and lateral stiffeners • Design challenge • Increasing the mechanical resistance without decreasing the cost of the resulting product FJCP WORKSHOP 25-27/10/94

  21. Constraint Formulation • Not only analytical functions ! • Like: • Cost models • Use of components of the shelf • A global physical model of the behaviour of the plate FJCP WORKSHOP 25-27/10/94

  22. Cost models (*******************************************************************) (* Définition du process de fabrication *) (*******************************************************************) (* Temps de Découpe de la tôle *) h<=8E-3 -> T1=1/2; h>8E-3 -> T1=(1/2)*(L1+L2); T1>0; (* Cassure des raidisseurs *) hauteur<=1E-2 -> T2=ny*(nx+1)/20; hauteur>1E-2 -> T2=ny*(nx+1)/10; T2>0; Need of a trigger mechanism to express Experience or Business rules FJCP WORKSHOP 25-27/10/94

  23. Carrés22 à carrés200 IPE80 à IPE600 Components of the shelf Catalogue of stiffeners Steel, Iron, Iron cast, Titanium .. Catalogue of materials FJCP WORKSHOP 25-27/10/94

  24. Catalogues FJCP WORKSHOP 25-27/10/94

  25. Global Physical Model Finite Elements Model FJCP WORKSHOP 25-27/10/94

  26. Global Physical Model Casebase Learning Approximation by a set of analytical functions FJCP WORKSHOP 25-27/10/94

  27. Feedback • The case study has been processed • The processing of non analytical knowledge is not easy : • Finite Elements models • Interpolation tables • existing programs • .. • It is a real bottleneck for ICP FJCP WORKSHOP 25-27/10/94

  28. And Nowwe are working onan industrial case study An Aircraft Air Conditioning System Design

  29. Half closed motorised Air conditioning cycle FJCP WORKSHOP 25-27/10/94

  30. Close/Half-Close Cycle Design Atmosphere Cabin Main Heat Exchanger Turbine Turbo reactor motor Compressor Pre-cooling Heat Exchanger switch on Atmosphere FJCP WORKSHOP 25-27/10/94

  31. T7 entre –40 °C et 71 °C • Schéma d’architecture global du SCA Section d’ entrée Ai Ouvert Fermé FJCP WORKSHOP 25-27/10/94

  32. Variability in the Design Problem • Possible free parameters: • Motor Power • Ram Air section • Heat exchangers characteristics • Design is hard FJCP WORKSHOP 25-27/10/94

  33. RAM AIR Lx Lz MAIN AIR Ly Cross-Flow Heat Exchangers FJCP WORKSHOP 25-27/10/94

  34. Dimensioning Heat Exchangers • Lx, Ly, Lz • Type of Exchange Surfaces • different types • different properties (5) • Type of Exchangers • Cross-Flow, Multi-pass ... FJCP WORKSHOP 25-27/10/94

  35. equations FJCP WORKSHOP 25-27/10/94

  36. State Space Configuration Altitude 16500 m M=0.6 7500 m M=0.65 6000 m M=0.3 3000 m M=0.6 Temps FJCP WORKSHOP 25-27/10/94

  37. Partial results • We are able to dimension the ACS in a given configuration • if we enlarge the search space: • type of exchange surfaces • type of exchangers • number of configurations • then we address a problem currently out of scope FJCP WORKSHOP 25-27/10/94

  38. Conclusion • A lot of research effort remain to do if we want to fully address the field of Design • Interesting themes : • Hard mixed integer and real non linear problems • Large search spaces of numerical underconstraint problems • Decision Support FJCP WORKSHOP 25-27/10/94

  39. Decision Support • Model of soft flexible interval constraints • Easy and relevant engineer ’s preferences expression • Automatic generation of Pareto Frontier FJCP WORKSHOP 25-27/10/94