Multi-Disciplinary Optimization with Minamo
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1 EXCELLENCE IN SIMULATION TECHNOLOGIES Multi-Disciplinary Optimization with Minamo Ingrid Lepot Numerical Methods and Optimization Group, Cenaero CESAR Training Workshop, Mar 18, 2009
2 Surrogate Based Optimization Objective Predicted Optimum Approximate model Initial Accurate Results Design Variable
3 Surrogate Based Optimization ONLINE modeling Objective Predicted Optimum Artificial Neural Networks Radial Basis Functions Kriging Approximate model Initial Accurate Results Design Variable
4 Adaptive Sampling Capability
5 Surrogate Assisted Optimization Workflow User Specifications Approximate Model ANN, RBF, Kriging, Optimization EA, gradient-based, DATABASE Accurate Model CFD / Structure / Exp. /... ONLINE modeling END Performance Check
6 Derivative Free Optimization with Minamo Multi-modal function 4 design variables Less than 100 iterations Local Minima Minamo Software Functionalities Space filling DoE techniques: LHS, Voronoï tessellations, Latinized Voronoï tesselations Auto-adaptive DoE Single Objective Algorithms: GAs, GAs/Gradient methods with surrogate models Multiple Objectives Algorithms: Objective summation, Pareto GA, Pareto GA with surrogate model Constraints: Transformed into penalties, handled directly by GA Parallel: Any queuing system Uncomputable objective functions Easy simulation Coupling Quantitative Variance Analysis CAD: Efficient shape parameterization, Direct CAD access
7 Monitoring/steering/analysis peripheral tools Response surfaces reliability through leave-k-out cross-validation Constraints activity monitoring Quantitative Variance Analysis tool (ANOVA): Sobol sensitivity indices estimation Data mining utilities for high-dimensional output, self organizing maps
8 Minamo as Optimus Plug-in with Online Modeling Base mono-objective optimization capabilities integrated and available as Useropt
9 Direct CAD Access Master script (Python or C++, called by Minamo) CAD Model Ref. mesh Modified CAD model Modified CAD Model Ref. mesh Mesh CAPRI client Simmetrix Linux Windows TCP/IP CAPRI server IGG/AutoGrid 5 CATIA V5 UG Pro/E
10 CATIA V5 to 3D Unstructured CFD Mesh import CAPRI session = CAPRI.Session.Instance( CatiaV5 ) session.start() model = session.loadmodel( Wing ) volume = model.volumeat(1) volume.retesselate(0, 0, 2.0, 178.0, 0.0, 0.0) volume.exportgmsh( ref.msh ) session.stop() import Simmetrix Simmetrix.Session.Instance().Start() model = Simmetrix.DiscreteModel( ref.msh ) mesh = Simmetrix.Mesh(model) mesh.setglobalmeshsize(200.0) for face in [1, 5, 7, 8, 9]: mesh.setlocalmeshsize(face, 20.0) mesh.modifysurfacemesh() mesh.generatevolumemesh() mesh.exportgmsh( mesh.msh ) Simmetrix.Session.Instance().Stop()
11 CAD-based Wing MDO CAD : CATIAV5 Parallel Aeroelastic Computation Argo + Samcef Automatic Mesh Generation
12 MS Airfoil Optimization AC1 wing tip section Bernstein third order polynomial parameterization (7 parameters) Leading edge radius Trailing edge angle Maximum thickness Maximum thickness location Camber at the leading edge Camber at the trailing edge Camber at the middle of the airfoil
13 MS Airfoil Mesh
14 Lift-over-drag Maximization (constrained Cm)
15 Convergence (from DOE with 30 samples)
16 Hierarchical blade shape parameterization Stagger Angle Camber Chord Lean Lean Sweep Sweep
17 HP Compressor Rotor design (engine wear) Efficiency - Mass flow 0,92 TE TE Isentropic Efficiency Isentropic efficiency 0,91 0,9 0,89 0,88 0,87 0,86 0,85 0,84 0.2% Optimal geometry with open gap Optimal geometry with nominal gap Initial geometry with nominal gap Initial geometry with open gap 0,83 28,6 28, ,2 29,4 29,6 29, ,2 Mass Mass Flow flow 0.4 kg/s Comparison of both geometries 2 gap values/2 operating points TE Initial geometry Optimal geometry
18 ANOVA Sobol indices First order sensitivities and interaction volume (if required higher order sensitivities) quantification 0,3 0,25 Relative Importance of Parameters Section 5 first camber parameter Sobol Indices 0,2 0,15 0,1 0,05 0 camber_s1_1 camber_s1_3 camber_s2_2 camber_s3_1 camber_s3_3 camber_s4_2 camber_s5_1 camber_s5_3 camber_s6_2 stacking_s1_x stacking_s3_x stacking_s5_x stacking_s1_y stacking_s3_y stacking_s5_y stagger_s1 stagger_s3 Stagger_S5 Shift_S1 Shift_S3 Shift_S5 Axial_Chord_S1 Axial_Chord_S3 Axial_Chord_S5 Interaction Isent_Eff_Large_Gap_1.10 Isent_Eff_Small_Gap_1.10 Isent_Eff_Large_Gap_1.13 Isent_Eff_Small_Gap_1.13 Illustration on NEWAC optimization accounting for engine wear
19 HP Compressor Rotor Hub Design Geometry (Fixed) single mobile row CATIA v5 parameterized hub endwall Per individual 2 operating points computed: 1 close to peak efficiency and 1 close to the stability limit (elsa simulation / 2.2 M. grid points / tip clearance modeling / RANS k-l Smith turbulence model) Objective 1st Mono-point optimization to freely search the design space Maximize isentropic efficiency (free of constraint) Two-point optimization Maximize isentropic efficiency at design point Constraint on Total-to-Total pressure ratio at close to stall point Manufacturing constraints - Mass flow/outlet angle monitoring
20 Parameterization CATIA v5 R17 16 parameters Series of B-spline curves Design between LE and TE 6 main control points in the blade channel that can move radially, axially and/or circumferentially 3D surfaces that follow the blade curvature
21 Design Convergence History Large DoE scatter - Stabilization after about 50 design iterations: 2 different promising design families pointed out, satisfying the manufacturing constraints LOO Reliability Assessment: Isentropic efficiency correlation coefficient (DoE) (optimization)
22 Overall Performance Results First mono-point optimization highlighted a marked total pressure drop close to stall Need for robust multi-point design Two-point design: Performance gain at the design point Efficiency increase by 0.4 % Mass flow increase only by 0.4% (DoE scatter > 1%) Total-to-total pressure ratio preserved close to stall Very moderate outlet flow angle alteration Gain should be preserved in a stage environment Checked and confirmed (3D RANS simulations)
23 Total relative pressure just downstream the blade Optimized design Axisymmetric reference Marked losses decrease almost until 50% Local (low mass flow BL zone) losses increase
24 Relative Mach number in the B2B plane (23.6% span) Optimized design Axisymmetric reference Visible reduction of the wake Marked decrease of the relative Mach number downstream the shock, in the region of flow acceleration
25 Aero(-acoustic) open rotor optimization Multi-point aerodynamic blade shape optimization for cruise/take-off fixed or variable blade restaggering
26 SuMo/AutoGrid/elsA/Minamo chain Maximization of propulsive CR while retaining thrust for both operating points 96 parameters Reference geometry Modified geometry Farfield handled as a meridian technological effect
27 Key player in noise generation: Rotor 1 tip vortex trajectory/ Rotor 2 LE Acoustic cost function implemented to be handled for noise TO multi-objective optimization
28 Techno-economical composite door optimization Shape optimization Material optimization Manufacturing cost minimization Geometry Angles & dimensions Addition or removal of stiffeners or structural parts Position changes Materials Laminate definition (number of plies, stacking sequence, ply orientation, fibre volume fraction, nature of constituents) Cost parameters Materials, process, complexity, dimensions, manpower, tooling cost Shape & materials are linked to the manufacturing process which defines conditions of feasibility
29 Numerical framework - Software Multi-objective, multi-constraint optimization with a large number of discrete, integer & continuous variables Optimization Minamo CAD Catia V5, Solidworks Direct access to CAD CADNexus CAPRI Meshing Simmetrix Materials database In-house FE Solver Samcef, Nastran Dedicated cost model Gallorath SEER-DFMTM In-house libraries CADMesh, Composites Optimization Tool
30 Connections and workflow Material properties modification CATIA V5 CAD Master Model modification Minamo Post-processing Excel Material properties modification CAD Connexion software In-house tools Material properties SOLVER : SAMCEF Composite structure optimization with direct CAD access, mixed integer/real design variables
31 Pareto front Front de Pareto SOLUTION 1 Cost Function (euros) SOLUTION 2 ZONE de conception avec respect de masse < 45 kg. 900 SOLUTION Max Displacement Skin (mm)
32 Development Perspectives Sampling and meta-modeling Further development of auto-adaptive sampling Kriging + Expected Improvement Criterion Surrogate models coupling: local/global - weighted average RBFN adaptive fine tuning Support Vector Machines Optimization - Hybridization: Investigation of adequate GA gradient based method (surrogate based) switching. Exploitation of collective knowledge with multi-parent crossovers (UNDX). Gradient knowledge (SPSA, FDSA, ) to be incorporated in genetic operators, e.g. gradient-based mutation.
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