Evolutionary Algorithms in modefrontier

Evolutionary Algorithms in modefrontier Carlo Poloni Univ. Trieste Italy 1 PRESENTATION OUTLINE Some concept on OPTIMIZATION what we need and what we can do Some considerations about Evolutionary Algorithms some hystory & state of the art Some examples Optimisation of a composite wing - Fluid/Structure interaction Marc, StarCD, Nastran Optimisation of Gas Turbine performance Tascflow Optimisation of hot-stamping process Abaqus 2

Design Office Needs Today Product Development: Pre-design CAD use CAE for verification Testing Production The design is almost frozen after Pre-design Modification after CAE are costly Analyst work often frustrating: usless information, criticism for inaccuracies, cost of computing not visible in product innovation 3 Design Office Needs Pre-design Parametric CAD Extensive CAE FRONTIER Testing Production Build parametric models Make rational design data-flow USE all best company skills from the beginning Optimise the product and produce innovation Reduce time to market with better products 4

The use of Design Optimisation means: Formulate a logic analysis process Execute simulations or experiments efficiently IT infrastructure (Intranet) Logic and Optimisation Algorithms Archive in an organized way sensible data in an easyly accessible way (through a web browser) Take rational decisions on the best compromise between cost and performances 5 Optimisation needs An Optimisation task: requires several repetition of the complete computation cycle parameterise all computation flow involving commercial software and/or in-house utilities need of flexible utilities to extract relevant information control parameters input files objectives to optimise output files needs to control the global computation time use the best optimisation approach among several (RMS, DOE, MOGA, ANN ) send and control many jobs on a hybrid network parallelise optimisation steps needs to get insight on system behaviour (N-dimension space), allowing the designer to make the right decision contribution of parameters Pareto dominance 6

Global Optimisation Strategy Multi Objective Genetic Algorithm for global exploration Local Hill Climbing for improvements Approximation Training Data Derivatives Interpolation techniques for data synthesis Multi Objective Genetic Algorithms for design space exploration Simplex for local search Gradient based methods for accurate refinements 7 FRONTIER Product Properties ALL platforms are supported Browser based technology JAVA, XML, RMI, CORBA Capability of handling any computing services files or API (Application Protocol Interface) from CFD to MS-EXCEL Optimisation Algorithms Multi-Objective Genetic Algorithm, Simplex Gradient based methods DOE (Design of Experiments) FRONTIER allows the user to extract the maximum of information allowed by the user-defined CPU budget Decision Support tools Multi Criteria Decision Making Design Data visualization Statistical tools for Design Data Analysis (robust design) Design Data filtering Response Surface Models Polynomial (1st, 2nd order) Exponential k-nearest Kriging Gaussian Process Neural Networks 8

Evolutionary Algorithms, some hystory In USA: 1973 J.Holland first systematic work on Genetic Algorithm 1989 Book by D.E.Goldberg In Europe: 1969 I.Rechenberg and H.P.Schwefel first paper on Evolution Strategy 1992 Book by H.P. Schwefel Since then 2 major worldconferences are organised each year on the unified name: Evolutionary Algorithm Now moveing to even more wider name of computational intelligence At European level: INGENET Genetic Algorithms in Engineering applications A Framework IV Thematic Network (1997-2001) Evolutionary Algorithm EUROGEN conferences 9 A simple Algorithm do ng gener at i on do ni nd i ndi vi dual s translate bits into variables comput e obj ect i ves => int erface t o anal ysi s end do Do some st at i st i cs on t he popul at i on i ndi vi dual s do Cr eat e a new popul at i on: by cr oss over : sel ect i ndi vi dual and reproduce Select Modify end do end do by mut at i on: sel ect i ndi vi dual s and mu t a t e 10

State of the art EA SGA simple genetic algorithm ES µ,λ evolution strategy with µ individuals λ offsprings Self Adaptive Algorithms (tuning parameters are updated during the evolution) Hystorical algorithms, Robust but expencive New development, even more robust Hybrid Algorithms ( Evolutinary / Gradient opeartors ) New development, efficient but less robust Self Adaptive Algorithms with embedded meta-modelling Efficient and Robust, latest development 11 One application: 3D wing Optimisation Reference Airfoil: Onera M6 wing Mach number 0.84 Reynolds number 10e 6 12

Objectives and Variables 3D case! Variables:! Coordinates of spline control points in CATIA! Objectives:! MAX CL! MIN CD! MIN CM Computed by Star CD 13 Optimisation logic INPUT StarCD StarCD CATIA CATIA script script OUTPUT OUTPUT 14

Optimisation Run Optimiser: MOGA 30 x 10 15 Optimisation run Min Cd Constraints on: Cl > 0.133 Cm <0.0472 Wing Volume 16

Results Onera M6 Cl Cd Cm Onera M6 0.133 0.0436 0.0472 Optimized 0.133 0.0384 0.0466 Optimized -12% Drag 17 Results Onera M6 Cl Cd Cm Onera M6 0.133 0.0436 0.0472 Optimized 0.133 0.0384 0.0466 Optimized -12% Drag 18

3D wing Optimisation General Remark CATIAv5 PROSTAR- STARCD PROSTAR design chain has been succesfully tested The optimisation run found significant improvement over existing solution (Onera M6 wing) Courtesy 19 Example (1): fluid structure interaction Design of a composite wing CFD Code STAR-CD Structural code MARC GEOM_INIT CFD CFD_to_FEM FEM_to_CFD FEM OUTPUT Conv? Coupling StarCD & MARC 20

Example (1): fluid-structure interaction Objectives! MIN mass! MIN deformation! MAX Lift! MIN Drag! MAX Lift/Drag ratio Profile NACA4412 C/L = 10 C L Coupling StarCD & MARC 21 Example (1): fluid-structure interaction Variables! Parabolic variation of thickness (3 variables)! Relative thickness of layers (2 variables)! Fibers orientation (3 variables)! Materials:! VICOTEX 1454/48%/G1051 (epoxy+carbon bidirectional)! NCHM 1748/38%/M46J (epoxi+carbonio unidirectional) Coupling StarCD & MARC 22

Example (1): fluid-structure interaction Tipo di accoppiamento Hard coupled Soft coupled ALE (Arbitrary Lagragian Eulerian) DMM (Dinamic Mesh Methods) Closely-coupled* loosely-coupled Pressure values are passed to the structural code Displacements are passed to the CFD code Interpolation is needed Coupling StarCD & MARC 23 Example (1): fluid-structure interaction INPUT CFD-FEM FEM StarCD Prostar FEM-CFD FEM-CFD MARC Script OUTPUT CONV.? Coupling StarCD & MARC 24

Example (1): fluid-structure interaction Computed conf. Prot.1 Prot.2 Prot.4 Rigid Var.1 45.0 10.0 18.8 Var.2 43.7 27.6 18.9 Var.3 90.0-74.4-44.6 Var.4 44.3 72.9-44.6 Var.5 87.4-58.8-44.6 Var.6 0.0012 0.0025 0.0016 Var.7 0.0006 0.0008 0.0011 Var.8 0.0005 0.0004 0.0007 Mass 0.226 0.356 0.341 Lift 0.03048 0.03196 0.02632 0.03132 Drag 0.00351 0.00376 0.00302 0.00358 Def. 15.51 24.79 151.91 Eff. 8.71 8.50 8.81 8.77 Best performances are obtained using the deformable structure! Coupling StarCD & MARC 25 Example (1): fluid-structure interaction Prot.4 - MAX efficiency root increased load tip decreased load Coupling StarCD & MARC 26

Example (1): fluid-structure interaction Prot. 2 MAX lift, low efficiency root increased Load tip increased Load Coupling StarCD & MARC 27 Design problem An existing gas-turbine axial wheel must be improved, therefore: the static pressure ratio is given hub and shroud shape are given inlet is given, exit angle should match the stator the efficiency should be possibly improved the number of blades possibly reduced the mass of the blade (centrifugal forces) be reduced profile thickness increased (cooling) 28

Simulation set-up Problem simplification: GEOMETRY: no tip clearance PHYSICS: steady state analysis MESH: 95200 nodes with NI=70 (inlet to outlet) NJ=40 (periodicity) NK=34 (hub to shroud) BC: periodic, moving walls, inlet: pressure, turbulence, temperature and velocity distribution; CPU for one analysis: 4 hours on one processor PENTIUM III 550Mhz, 128Mbyte 29 Optimisation set-up General Requirements: the geometric input parameters must not yield excessive distortion all simulations have to run to the same convergence level radial stacking has to be fixed expansion ratio has to be fixed Objectives: minimise the number of blades minimise the taper ratio hub to shroud maximise profile thickness maximize efficiency Constraints: new efficiency > old efficiency mean exit angle < original blade +1 mean exit angle > original blade -1 max exit angle < original blade +5 min exit angle > original blade - 5 Variables: # of blades (1 parameter) profile thickness (%of increment, 1 parameter) tapering (linear, 1 parameter) angles of 5 profiles from hub to shroud (5 parameters) profile shape at 90% radius (4 parameters) 30

Geometry parameterisation profile thickness (% of increment, 1 parameter) + = tapering (linear, 1 parameter) angles of 5 profiles from hub to shroud (5 parameters) profile shape at 90% radius (4 parameters) + = 31 Design Logic Input variables output variables Input files output files applications transfer files logic controls objectives $ constraints 0o0 32

Optimisation strategy Initial screening MOGA 36 x 10 (320 simulations considering repeated analysis) 4 objectives analysis of results 12 processors Linux 4.4 days cluster First refinement running 12 TASCFlow MOGA 30 x 10 (184 simulations) simulations concurrently 2 Objectives handled by FRONTIER analysis of results 2.5 days Final Optimisation Single objective, 30 x 10 (168 simulations) One optimal geometry found 2.3 days 33 Initial screening Original blade eff. Eff. Thic. #Bla. #Bla. Tap. The first optimisation run shows: from 84 to 90 blades efficiency improvements are possible profile thickness can be increased tapering can be introduced #Bla. 34

First run Pareto solutions Eff. Thic. #Bla. #Bla. Tap. #Bla. 2 parameters and objectives can now be fixed: 84 Blades 6% Tapering 35 Refinement with 2 Objectives Thic. Thic. Original blade 4 solutions are not dominated 84 blades, 6% Tapering, 25% thicker, efficiency 0.927 Eff. Eff. 36

Final Optimisation 84 Blades, 6% Tapering, 12.5% Increased Thickness (both side, suction and pressure side, total 25%) Efficiency 0.928 37 Optimisation final results Parameter Original Blade Optimized blade # blades 90 84 Taper 100% 94% Thickness 100% 125% Efficiency 92.00% 92.80% Expansion ratio 2.11 2.10 Outflow angle 59.87 59.0131 Reaction rate 0.3579 0.4102 38

Results Original Optimised 39 Conclusion Evolutionary Algorithms are one component of the design optimisation process Recently developed algorithms are robust and efficient But the design otimisation process, whatever is the algorithm, is not a push-button-get-result process but is a knowledge acquisition, knowledge exploitation, decision-making process that, to be effective must have all the following ingredients: Parametric models Mathematical algorithms Flexible IT infrastructure 40