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Multidisciplinary Design Optimization of Supersonic Transport Wing Using Surrogate Model
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Multidisciplinary Design Optimization of Supersonic Transport Wing Using Surrogate Model

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Presented at 27th ICAS at Nice, 2010

Presented at 27th ICAS at Nice, 2010

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  • 1. 27th ICAS at Nice on 22th SeptemberSession : Supersonic Aircraft Concepts“Multidisciplinary Design Optimization of Supersonic Transport Wing Using Surrogate Model” Naoto Seto (Tokyo Metropolitan University)
  • 2. Outline Background Objectives Design Approaches Design Target and Design Variables Objective Functions and Constraints Results Conclusions
  • 3. Background 1 Short time travel is one of the biggest demands.  SuperSonic Transport (SST) is expected to meet the demand above. Studies in several institutes all over the world SSBJ of AERION Silent SST of JAXA QSST of SAI Many problems to be solved  Flight cost  Environmental problems Trade-off  Aerodynamic performances How should be next generation SST designed with many problems ?
  • 4. Background 2 Multidisciplinary Design Optimization (MDO) is the key technique InformationTechnological interests pool Aerodynamics Sonic boom Structure Materials Propulsions …etc Effects of variables Trade-off (Multi-validate analysis) (*GA, *DoE) Global trends MDO with global exploration will (Data mining) help knowledge discovery*GA : Genetic Algorithm*DoE : Design of Experiment
  • 5. Objectives Development of efficient MDO tool for SST wing in conceptual design Features about proposed MDO1. Low CFD calculation cost  Full potential equation with panel method  Kriging model2. Construction of global design information pool  Trade-off :Multi-Objective Genetic Algorithm  Effects of design variables :ANalysis Of VAriance  Global trends about design variables :Parallel Coordinate Plot
  • 6. Design Approaches
  • 7. Design Approaches (design procedure) Initial sampling based on LHS* Surrogate model construction (Kriging model) Exploration of non-dominated solutionsAdditional samplings on Kriging model using MOGA No Convergence ? Yes Constructing design information pool (ANOVA, PCP)*Latin Hypercube Sampling
  • 8. Design Approaches (exploration of non-dominated solutions)  Multi Objective Genetic Algorithm (MOGA)  One of evolutionary algorithm  Searching global non-dominated solutions with multi-point explorations →Many evaluations are required. CFDKriging modelOne of surrogate modelInterpolating and searching local extremes ˆ (x i )     (x i ) y Global model Localized deviation from the global model
  • 9. Design Approaches (exploration of non-dominated solutions) Kriging model includes uncertainty at the predicted points. Expected Improvement (EI) considers the balance between optimist and the error.  EI is expressed below (for maximization problem) E I x   z  ( f max  z ) dz , n :standard distribution,  normal density s :standard error  f  ˆ  y  f max  ˆ  y  ( f max  y ˆ )   max   s    s   s  : Kriging model : Maximum values from sampling The larger EI value has the larger possibility to be optimum solutions →Additional samplings are based on EIs’ maximization Jones, D. R., “Efficient Global Optimization of Expensive Black-Box Functions,” J. Glob. Opt., Vol. 13, pp.455-492 1998.
  • 10. Design Approaches (design information) Analysis of Variance (ANOVA) One of multi-validate analysis for quantitative information IntegrateThe main effect of design variable xi: i ( xi )     y( x1 ,....., xn )dx1 ,..., dxi 1 , dxi 1 ,.., dxn   ˆ variance where:      y( x1 ,....., xn )dx1 ,....., dxn ˆ Total proportion to the total variance: pi   2 p2  y(x1,....,xn ) dx1...dxn 35% ˆ p1where, ε is the variance due to design variable xi. 65% Main effect
  • 11. Design Approaches (design information) Parallel Coordinate Plot (PCP) One of statistical visualization techniques from high-dimensional data into two dimensional data. Design variables and objective functions are set parallel in the normalized axis. PCP shows global trends of design variables. 1.0 0.8 0.6 0.4 0.2 0.0 Upper bound of ith design variables and objective functions Normalization Lower bound of ith design variables x(dvi ) - min(dvi ) P i and objective functions max(dvi ) - min(dvi )
  • 12. Design Target and Design Variables
  • 13. Design Target Three-dimensional geometry of supersonic main wing  Other components geometry fuselage, tail planform are same as 2.5th Silent SuperSonic Technology Demonstrator (S3TD) Specifications Fuselage 13.8m MTOW 3500kg Sref 21m2 Cruse M 1.6 Cruse altitude 14km 2.5th design by JAXA
  • 14. Design Variables 14 design variables Table 1 Design space Upper Lower Design variable bound bound Sweepback angle at inboard dv1 57 (°) 69 (°) section Sweepback angle at outboard dv2 40 (°) 50 (°) section dv3 Twist angle at wing root 0 (°) 2(°) dv4 Twist angle at wing kink –1 (°) 0 (°) dv5 Twist angle at wing tip –2 (°) –1 (°) dv6 Maximum thickness at wing root 3%c 5%cRoot & kink airfoil NACA 64series dv7 Maximum thickness at wing kink 3%c 5%cTip airfoil bi-convex dv8 Maximum thickness at wing tip 3%c 5%c dv9 Aspect ratio 2 3 Tip airfoil Supersonic- dv10 Wing root camber at 25%c –1%c 2%c linearly-interpolation leading edge dv11 Wing root camber at 75%c –2%c 1%c Kink airfoil dv12 Wing kink camber at 25%c –1%c 2%c spline-interpolation Subsonic- dv13 Wing kink camber at 25%c –2%c 1%c leading edge dv14 Wing tip camber at 25%c –2%c 2%c Root airfoil
  • 15. Objective Functions and Constraints
  • 16. Objective Functions Three objective functions in this studymaximize L/ Dminimize ΔP (On boom carpet) ΔPminimize Wwing subject to Design C L = 0.105 Time[ms] maximize K-means method ˆ - L / Dmax y ˆ - L / Dmax y • EIL / D = ( ˆ - L / Dmax )Φ( y ) + sφ( ) Additional sampling points s s maximize clusters ΔP - ˆ y ΔP - ˆ y EI1 • EIΔP = ( ΔP - y min ˆ )Φ( min ) + sφ( min ) s s maximize Wwingmin ˆy Wwingmin - ˆ y EI2 • EIWwing = (Wwingmin - ˆ )Φ( y ) + sφ( ) s s
  • 17. Evaluations of L/D and ΔP CAPAS* developed in JAXA Aerodynamic performance  Sonic-boom intensity  Compressible potential equation  Correction of shock wave with panel method (PANAIR) by Whitham’s theory  2  2  2  PANAIR data 2 F ( x)  CP ( M  1) 2  2  2 0 2 x y z x     1 r F x   : Velocity potential 2 3 Thomas’s waveform parameter method   M 2-1 pressure[psf]   1.4Computational CP distributions r : propagation distancegeometry Time[ms] *CAPAS (CAD-based Automatic Panel Analysis System)
  • 18. Evaluation of wing weight Inboard wing (multi-frame structure)  Aluminum material  Minimum thickness of skin & frame (0<thickness<20mm, every0.1mm) Outboard wing (full-depth honeycomb sandwich structure)  Composite material  Stack sequence  Fiber angle θ ; [0/ θ/- θ/90] ns, θ=15, 30, 45, 60, 70deg  Number of laminations n  n  N  25 Solver is MSC NASTRAN 2005R (FEM model)  Strength requirements  Aluminum material:Mises stress < 200MPa at all FEM nodes  Composite material: Destruction criteria < 1 at all FEM nodes on each laminate  Computational conditions  Symmetrical maneuver +6G, Safety rate: 1.25 PANAIR data  Estimated load on the main wing (symmetrical maneuver) × (safety rate) × (aerodynamics load)
  • 19. Constraint Trim balance C. G.  C.P. is identical to C.G. at target CL C.P. →12 evaluations are required to decide the angle of horizontal tail.  Realistic cruise condition Angle of horizontal tail Blue area (main wing and horizontal tail) were changed in this study. Cl target CL Cd x
  • 20. Results
  • 21. Results (samplings) 75 points were sampled for constructing a initial Kriging model. Additional samplings were carried out three times.  32 additional samples  Total number of samplings is 107. Calculation time for one sample  One hour for the CAPAS evaluations  15 minutes for the NASTRAN evaluations Calculation environment  General work station : 1CPU (Xeon 2.66MHz)
  • 22. Results (solution space about objective functions) Wwing  24 non-dominated solutions from L/D ΔP[psf] AoA [kg] final data Design A 7.02 1.19 612 2.5  Most of additional samplings formed Design B 6.08 0.97 502 2.7 non-dominated solutions Design C 5.60 1.53 276 2.6 Design D 6.77 1.09 691 2.6 Design A (best L/D) Design B (best ΔP) Design C (best Wwing) Design D (compromised) Wwing[kg]ΔP[psf] Optimum direction L/D ΔP[psf]
  • 23. Results (configuration comparison) Each champion sample is compared to the compromised. Design A Design B Larger sweep back Thinner root airfoil *Red dot line is the compromised (Design D) Design C Thinner root airfoil of Design A Advantage of the reducing wave dragFlap tail angle Larger inboard sweep back angle of Design B Ideal equivalence area distribution Flap tail angle of Design C Reducing aerodynamics load on the main wing
  • 24. Evaluation of wing weight evaluations Inboard wing (multi-frame structure)  Aluminum material  Minimum thickness of skin & frame (0<thickness<20mm, every0.1mm) Outboard wing (full-depth honeycomb sandwich structure)  Composite material  Stack sequence  Fiber angle θ ; [0/ θ/- θ/90] ns, θ=15, 30, 45, 60, 70deg  Number of laminations n  n  N  25 Solver is MSC NASTRAN 2005R (FEM model)  Strength requirements  Aluminum material:Mises stress < 200MPa at all FEM nodes  Composite material: Destruction criteria < 1 at all FEM nodes on each laminate  Computational conditions  Symmetrical maneuver +6G, Safety rate: 1.25 PANAIR data  Estimated load on the main wing (symmetrical maneuver) × (safety rate) × (aerodynamics load)
  • 25. Results (waveform on the ground)  Each champion sample is compared to the compromised. *Red dot line is the compromised (Design D) Less differentDesign A among Design A, B, and D Large different between Design C and D L/D ΔP[psf] Wwing[kg]Design B Design A 7.02 1.19 612 Design B 6.08 0.97 502 Design C 5.60 1.53 276 Design D 6.77 1.09 691Design C Severe trade-off between ΔP & Wwing
  • 26. Results (Overview about ANOVA) 70% 45% *a1 *a2 *a3 73%dv1 inboard sweep dv8 tip t/cdv2 outboard sweep dv9 aspect ratiodv3 root twist dv10 root camber(25%c) Proper range indv4 kink twist dv11 root camber(75%c) design space?dv5 tip twist dv12 kink camber(25%c)dv6 root t/c dv13 kink camber(75%c)dv7 kink t/c dv14 tip camber(25%c)
  • 27. Results (Overview about PCP) Best 5 samples about L/DExtracting useful data about each objective function for the better visualization *p1 Best 5 samples *p2 about ΔP24 non-dominated solutions data Best 5 samples about Wwing *p3
  • 28. Results (design information of better L/D)*PCP was carried out from best five samples about L/D Root camber(dv10, 11) & kink camber(dv12, 13)  ANOVA Design A upper Kink twist(dv4) & root t/c(dv6)  PCP lower→Small drag around root & sufficient lift around kink *a1 *p1
  • 29. Results (design information of better ΔP)*PCP was carried out from best 5 samples about ΔP Inboard sweep(dv1) & root camber(dv10) & kink camber(dv14)  ANOVA Design B Kink twist(dv4) & root t/c(dv6) & kink t/c(dv7)  PCP upper lower→Ideal equivalence area (Ae) distribution *a2 *p2
  • 30. Comparisons about equivalence area distribution 2.5 2.0Equivalence area 1.5 1.0 Design A Design B 0.5 Design C Design D Darden 0.0 0 2 4 6 8 10 12 x(m)
  • 31. Results (design information of better Wwing)*PCP was carried out from best 5 samples about Wwing Root t/c(dv6) & AR(dv9) & root camber(dv10) & kink camber(dv12, 13)  ANOVA Design C Inboard sweep(dv1) & tip twist(dv5) & kink t/c(dv6)upper  PCP lower→Low aerodynamic load on the wing *a3 *p3
  • 32. Conclusions Efficient MDO tool for conceptual design  MOGA with Kriging model  MOGA with Kriging model took about 10 days for the total task  MOGA without Kriging model would take about 160 days in this study  Trade-off among each objective function →Severe trade-off between ΔP and wing weight  ANOVA ANOVA found the design variables which have effects on each objective functions.  PCP PCP showed the global trend of design variables.  Better L/D → root & kink camber  Better ΔP → inboard sweep back angle  Better wing weight → aspect ratio & root t/c Efficient exploration Useful design information pool
  • 33. Acknowledgement• I wish to thank Dr. Yoshikazu Makino, and Dr. Takeshi Takatoya, researchers in Aviation Program Group/Japan Aerospace Exploration Agency, for providing their CAE program and large support. I would like to thank my paper adviser, Prof. Masahiro Kanazaki, for his guidance, and support.• My presentation is supported by the grant from JSASS (Japan Society of Aeronautics and Space Science).