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- 1. Lecture “Aerodynamic design of Aircraft” in University of Tokyo 20th January, 2014 Engineering Optimization in Aircraft Design Masahiro Kanazaki Tokyo Metropolitan University Faculty of System Design Division of Aerospace Engineering kana@sd.tmu.ac.jp Follow me!: @Kanazaki_M
- 2. Resume ~ Masahiro Kanazaki March, 2001 Finish my master course at Graduated school of Mechanical and Aerospace Engineering, Tohoku university March, 2004 Finish my Ph.D. at Faculty at Graduated school of Information Science, Tohoku university April, 2004-March, 2008 Invited researcher at Japan Aerospace Exploration Agency April, 2008- , Associate Professor at Division of Aerospace Engineering, Faculty of Engineering, Tokyo Metropolitan University Dr. information science Experimental evaluation based design optimization Aerodynamic design for complex geometry using genetic algorithm Aerodynamic design of highlift airfoil deployment using highfidelity solver Multidisciprinaly design optimization
- 3. Contents(1/2) 1. What is engineering optimization? ~ Optimization, Exploration, Inovization 2. Optimization Methods based on Heuristic Approach i. How to evaluate the optimality of the multi-objective problem. ~ Pareto ranking method ii. Genetic algorithm (GA) iii. Surrogate model，Kriging method iv. Knowledge discovery – Data mining，Multi-variate analysis 3. Aircraft Design Problem i. Fundamental constraints ii. Evaluation of aircraft performance iii. Computer aided design
- 4. Contents(1/2) 4. Examples i. Exhaust manifold design for car engines ~ automated design of complex geometry and application of MOGA ii. Airfoil design for Mars airplane ~ airfoil representation/ parameterization iii. Wing design for supersonic transport ~ multidisciplinary design iv. Design exploration for nacelle chine installation
- 5. 5 What is engineering optimization? ~ Optimization, Exploration, Inovization
- 6. What is optimization？(1/4) 6 Acquire the minimum/ maximum/ ideal solution of a function Such point can be acquired by searching zero gradient Multi-point will shows zero gradient, if the function is multi-modal. Are only such points the practical optimum for real-world Optimization is not automatic problem? Objective function Objective function decision making tool. Proper problem definition Knowledge regarding the design problem Design variable(s) Design variable(s)
- 7. What is optimization？(2/4) Mathematical approach Finding the point which function’s gradient=0 →Deterministic approach Local optimums Assurance of optimality Gradient method (GM) Population based searching (=exploration) →Heuristic method Global exploration and global optimums Approximate optimum but knowledge can acquired based on the data set in the population Evolutionary strategy (ES) 7
- 8. What is optimization？(3/4) Real-world design problem/ system integration （Aerodynamic, Stricture, Control） Importance of design problem definition Efficient optimization method Post process, visualization（similar to numerical simulation） In my opinion, Engineering optimization is a tool to help every engineers. We (designers) need useful opinion from veterans. Significance of pre/post process Consider interesting and useful design problem! 8
- 9. What is optimization？(4/4) Recent history of “optimization” Finding single optimum (max. or min.) point （Classical idea） “Design exploration” which includes the optimization and the data-mining Multi-Objective Design Exploration: MODE: Prof. Obayashi） Innovation by the global design optimization (Inovization: Prof. Deb) Principle of design problem(Prof. Wu) 9
- 10. 10 Optimization Methods based on Heuristic Approach
- 11. Optimization Methods based on Heuristic Approach 11 Example which show the importance of knowledge Since 2002,,, Development of new aircraft… Innovative ideas Efficient methods are required. Mitsubishi Regional Jet（MRJ） In Boeing Boeing767 Announcement of development “sonic cruiser” in 2001 Market Sonic Cruiser shrink due to 9.11 Because they have been had much knowledge regarding aircraft development, it was easy for them to change the plan. Boeing787 Reconsider their plan to 787
- 12. Optimization Methods based on Heuristic Approach Aerodynamic Design of Civil Transport Design Considering Many Requirement High fuel efficiency Low emission Low noise around airport Conformability Computer Aided Design For higher aerodynamic performance For noise reduction ↔ Time consuming computational fluid dynamics (CFD) Efficient and global optimization is desirable. 12
- 13. Optimization Methods based on Heuristic Approach Multi-objective → Pareto ranking Real-world problem generally has multi-objective. If a lecture is interesting but its examination is very difficult, what do you think? ・・・・ などなど Multi-objective problem The optimality is decided based on multi-phase Example) How do you get to Osaka from Tokyo? Pareto-solutions Fare Non-dominated solutions Pareto optimum Time In engineering problem ex.) Performance vs. Cost Aerodynamics vs. Structure Performance vs. Environment → Trade-off 13
- 14. Optimization Methods based on Heuristic Approach 14 Ranking of multi-objective problem ～ Pareto Ranking Lets consider minimization f1, f2 Pareto ranking method by Prof. Deb → Non-dominated Sorting
- 15. Optimization Methods based on Heuristic Approach Heuristic search：Multi-objective genetic algorithm (MOGA) Inspired by evolution of life Selection, crossover, mutation Many evaluations ⇒High cost x1 x2 x3 x4 x5 Parent Child Blended Cross Over - α 15
- 16. Optimization Methods based on Heuristic Approach 16 For high efficiency and high the diversity GA is suitable for parallel computation （ex: One PE uses for one design evaluation.） Distributed environment scheme/ Island mode （ex: One PE uses for one set of design evaluations.）
- 17. Optimization Methods based on Heuristic Approach Island model is similar to something which is important factor for the evolution of life. Continental drift theory What do you think about it? 17
- 18. Optimization Methods based on Heuristic Approach Surrogate model Polynomial response surface Identification coefficients whose existent fanction Kriging method Interpolation based on sampling data Model of objective function Standard error estimation (uncertainty) Co-variance y (xi ) (xi ) Space global model localized deviation from the global model 18
- 19. Optimization Methods based on Heuristic Approach Sampling and Evaluation Initial designs Simulation Surrogate model construction Initial model Kriging model Exact Additional designs Evaluation of additional samples Multi-objective optimization and Selection of additional samples Termination? No Yes Improved model Image of additional sampling based on EI for minimization problem. Genetic Algorithms Knowledge discovery Knowledge based design , DR Jones, “Efficient Global Optimization of Expensive Black-Box Functions,” 1998. s ：standard distribution, normal density ：standard error 19
- 20. Optimization Methods based on Heuristic Approach Heuristic search：Genetic algorithm (GA) Inspired by evolution of life Selection, crossover, mutation BLX-0.5 EI maximization → Multi-modal problem Island GA which divide the population into subpopulations Maintain high diversity 20
- 21. Optimization Methods based on Heuristic Approach 21 We can obtain huge number of data set. What should we do next? Visualization to understand design problem →Datamining, Multivariate analysis To understand the design problem visually Three kind of techniques regarding knowledge discovery Graphs in Statistical Analysis → Application of conventional graph method Machine learning → Abductive reasoning Analysis of variance→Multi-validate analysis
- 22. Optimization Methods based on Heuristic Approach Parallel Coordinate Plot (PCP) One of statistical visualization techniques from highdimensional data into two dimensional graph. Normalized design variables and objective functions are set parallel in the normalized axis. Global trends of design variables can be visualized using PCP. 22
- 23. Analysis of Variance One of multivariate analysis for quantitative information 23 Integrate Optimization Methods based on Heuristic Approach The main effect of design variable xi: ˆ i ( xi ) y( x1 ,....., xn )dx1 ,..., dxi 1 , dxi 1 ,.., dxn variance ˆ y( x1 ,....., xn )dx1 ,....., dxn μ1 where: Total proportion to the total variance: pi i xi dxi 2 ˆ y ( x1 ,...., xn ) dx1 ...dxn 2 where, εis the variance due to design variable xi. Proportion (Main effect)
- 24. Optimization Methods based on Heuristic Approach Self-organizing map for qualititative information Proposed by Prof. Kohonen Unsupervised learning Nonlinear projection algorithm from high to two dimensional map Design-objective Multi-objective Two-dimensional map （Colored by an component, N component plane, for N dimensional input.） 24
- 25. Optimization Methods based on Heuristic Approach How SOM is working. Input data, (X1, X2, …., XN), Xi: vector (objective functions) : Designs Xi i=1, 2,…..N W 1.Preparation Prototype vector is randomized. 2.Search similar vector W that looks like Xi Each prototype vector is compared with one input vector Xi. 3.Learning1 W is moved toward Xi. W = W +α(Xi- W) 4.Learning2 W’s neighbors are moved toward Xi. Map can be visualized by circle grid, square grid, Hexagonal grid, … 25
- 26. How to apply to the aircraft design 26 Several constraints should be considered. In aircraft design, following constraints are required. Lift=Weight Trim balance Evaluation High-fidelity solver, Low-fidelity solver Experiment CAD How to represent the geometry. NURBS, B-spline PARSEC airfoil representation
- 27. 27 Ex-i： Exhaust manifold design for car engines
- 28. Ex-i: Exhaust manifold design for car engines Engine cycle and exhaust manifold Air Muffler Air cleaner Catalysis Intake manifold 排気マニホールド Exhaust manifold Intake port Exhaust port Intake valve Exhaust valve 燃焼室 Remove Nox/Cox Higher temperature Smoothness of exhaust gas Higher charging efficiency charging efficiency(%)=100× Volume of intake flow/Volume of cylinder 28
- 29. Ex-i: Exhaust manifold design for car engines Exhaust manifold Lead exhaust air from several camber to one catalysis Merging geometry effect to the power Chemical reaction in the catalysis is promoted at high temperature. 29
- 30. Ex-i: Exhaust manifold design for car engines Evaluations Engine cycle: Empirical one dimensional code Exhaust manifold : Unstructured based three-dimensional Euler code 30
- 31. Ex-i: Exhaust manifold design for car engines Geometry generation for manifold 1. Definition of each pipe 2. Detection the merging line 3. Merge pipes 31
- 32. Ex-i: Exhaust manifold design for car engines Objective function 排気マニホールドの最適設計 Minimize Charging efficiency Maximize Temperature of exhaust gas Design variables Merging point and radius distribution of pipes merging3 p2 p1 merging1, 2 p2 p2 Definition of off-spring for merging point and radius 32
- 33. Ex-i: Exhaust manifold design for car engines A (Maximum charging efficiency) Charging efficiency (％) A C 90 87.5 D B (Maximum temperature) B Initial 85 C 1490 1500 1510 Temperature (K) 1520 D 33
- 34. 34 Ex-ii) Airfoil design for Mars airplane ~ airfoil representation/ parameterization
- 35. Ex-ii) Airfoil design for Mars airplane Image of MELOS Ikeshita/JAXA Exploration by winged vehicle Propulsion Aerodynamics Structural dyanamics ・Atmosphere density: 1% that of the earth ・Requirement of airfoil which has higher aerodynamic performance 35
- 36. Ex-ii: Airfoil design for Mars airplane Airfoil representation for unknown design problem B-spline curve, NURBS High degree of freedom Parameterization which dose not considered aerodynamics PARSEC(PARametric SECtion) method* Parameterization based on the knowledge of transonic flow Define upper surface and lower surface, respectively Suitable for automated optimization and data mining Camber is not define directly. → It is not good for the airfoil design which has large camber. *Sobieczky, H., “Parametric Airfoils and Wings,” Notes on Numerical Fluid Mechanics, pp. 71-88, Vieweg 1998. 36
- 37. Ex-ii: Airfoil design for Mars airplane Modification of PARSEC representation** Thickness distribution and camber are defined, respectively. Theory of wing section Maintain beneficial features of original PARSEC Same number of design variables. Easy to understand by visualization because the parameterization is in theory of wing section ** K. Matsushima, Application of PARSEC Geometry Representation to High-Fidelity Aircraft Design by CFD, proceedings of 5th WCCM/ ECCOMAS2008, Venice, CAS1.8-4 (MS106), 2008. 37
- 38. Ex-ii: Airfoil design for Mars airplane 38 Parameterization of modified PARSEC method The center of LE radius should be on the camber line, because thickness distribution and camber are defined, respectively. Thickness distribution is same as symmetrical airfoil by original PARSEC. Camber is defined by polynomial function. Square root term is for design of LE radius. Thickness 6 z t an x 2 n1 2 n 1 Camber 5 zc b0 x bn x n n 1 ＋
- 39. Ex-ii: Airfoil design for Mars airplane Formulation Objective functions Maximize maximum l/d Minimize Cd0（zero-lift drag） subject to t/c=target t/c (t/c=0.07c) Evaluation Structured mesh based flow solver Baldwin-Lomax turbulent model Flow condition (same as Martian atmosphere) Density=0.0118kg/m3 Temperature=241.0K Speed of sound=258.0m/s Design condition Velocity=60m/s Reynolds number：20,823.53 Mach number：0.233
- 40. Ex-ii: Airfoil design for Mars airplane Design variables Upper bound Lower bound dv1 LE radius 0.0020 0.0090 dv2 x-coord. of maximum thickness 0.2000 0.6000 dv3 z-coord. of maximum thickness 0.0350 0.0350 dv4 curvature at maximum thickness -0.9000 -0.4000 dv5 angle of TE 5.0000 10.0000 dv6 camber radius at LE 0.0000 0.0060 dv7 x-coord. of maximum camber 0.3000 0.4000 dv8 z-coord. of maximum camber 0.0000 0.0800 dv9 curvature at maximum camber -0.2500 0.0100 dv10 z-coordinate of TE -0.0400 0.0100 dv11 angle of camber at TE 4.0000 14.0000 0.35 for t/c=0.07c
- 41. Ex-ii: Airfoil design for Mars airplane Design result (objective space) Multi-Objective Genetic Algorithm: (MOGA) Baseline Des_moga#3 Des_moga#1 Des_moga#2 Trade-off can be found out. 41
- 42. Ex-ii: Airfoil design for Mars airplane α vs. l/d, α vs. Cd, α vs. Cl Better solutions could be acquired. 42
- 43. Ex-ii: Airfoil design for Mars airplane Optimum designs and their pressure distributions Des_moga#1 Des_moga#3 Des_moga#2 43
- 44. Ex-ii: Airfoil design for Mars airplane Visualization of design space by PCP 44
- 45. Ex-ii: Airfoil design for Mars airplane Visualization of design space by PCP (sorted by max l/d) l/d>45.0 45
- 46. Ex-ii: Airfoil design for Mars airplane Visualization of design space by PCP(sorted by Cd0) Cd0<0.0010 46
- 47. Ex-ii: Airfoil design for Mars airplane max min maxl/d 54.2988 23.1859 SOGA th25 0.0700 0.0102 47 MOGA th75 0.1046 0.0035 maxl/d 49.3560 25.7858 Cd0 0.0335 0.0091 th25 0.0700 0.0677 th75 0.0539 0.0214 Cd0<0.0010 l/d>45.0 Larger LE thickness (th25)→same trend compared with baseline Larger maxl/d should be smaller (dv4(zxx)) (Larger curvature)→TE thickness (th75) becomes smaller， Smaller Cd0should be larger (dv5)，dv4(zxx)→ thickness of TE (th75) becomes larger.
- 48. 48 Ex-iii) Wing design for supersonic transport ~ multi-disciplinary design
- 49. Ex-iii: Wing design for supersonic transport 49 Supersonic Transport (SST) Concord(retired) One of SST for civil transport Silent Supersonic Transport Demonstrator 3TD) Flying across the Atlantic about three(S(S3TD) Silent Supersonic Transport Demonstrator hours High-cost because of bad fuel economy Noise around airport Sonic-boom in super cruise Next generation SST SAI: Supersonic Aerospace International LLC. For trans/intercontinental travel With high aerodynamic performance SAI’s QSST Without noise, environmental impact, and sonic-boom Development of small aircraft for personal use. JAXA Concept of SST for commercial airline is desirable. Aerion
- 50. Ex-iii: Wing design for supersonic transport 50 Development and research of SST in Japan (conducted by JAXA) NEXST1 Silent Supersonic Transport Demonstrator (S3TD) Flight of unpowered experimental model in 2005. Low drag design using CFD Low boom airframe concept multi-fidelity CFD Exploration using genetic algorithm Conceptual design of supersonic business jet. Requirement of high efficient design process
- 51. Ex-iii: Wing design for supersonic transport 51 Design method Efficient Global Optimization (EGO) Genetic , Kriging model Analysis of variance (ANOVA) Self-organizing map (SOM) Evaluations Full potential solver，MSC.NASTRAN Design problem for JAXA’s silent SST demonstrator # of design variables(14) # of objective functions(3) Aerodynamic performance Sonic boom Structural weight
- 52. Ex-iii: Wing design for supersonic transport Design variables 52 Table 1 Design space. Design variable Upper bound Lower bound dv1 Sweepback angle at inboard section 57 (°) 69 (°) dv2 Sweepback angle at outboard section 40 (°) 50 (°) 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 dv7 Maximum thickness at wing kink 3%c 5%c dv8 Maximum thickness at wing tip 3%c 5%c dv9 Aspect ratio 2 3 dv10 Wing root camber at 25%c –1%c 2%c dv11 Wing root camber at 75%c –2%c 1%c dv12 Wing kink camber at 25%c –1%c 2%c dv13 Wing kink camber at 25%c –2%c 1%c dv14 Wing tip camber at 25%c –2%c 2%c
- 53. Decision of angle of horizontal tail (HT) ⇒ total of 12 CFD evaluations Setting aerodynamic center same location with center of gravity Realistic aircraft’s layout 53 C. G. Angle of horizontal tail Cl Objective functions Maximize L/D Minimize ΔP Minimize Ww at M=1.6, CL =0.105 Trim balance Location of aerodynamic center Ex-iii: Wing design for supersonic transport target Cl Cd x
- 54. Ex-iii: Wing design for supersonic transport 54 Design exploration results by EGO DesA DesB DesA DesB DesC DesC Many additional samples around non-dominated solutions Extreme Pareto solutions (to be discussed later): DesA achieves the higest L/D, DesB achieves the lowest ΔP, and DesC achieves the lowest Ww. ⇒ Why they are optimum solutions?
- 55. Ex-iii: Wing design for supersonic transport ANOVA: effect of dvs L/D ΔP Effect of root camber Effect of sweep back angle at wing root Effect of root camber ⇒ influence on aerodynamic performance of inboard wing at supersonic cruise Wwing Sweep back is effective to boom intensity.
- 56. Ex-iii: Wing design for supersonic transport 56 Trade-off between objective function L/D (size of square represents BMU(Beat Matching Unit)) ΔP Compromised solution Wwing Trade-off Angle of HT Compromised solution can be observed. L/D↓, Wwing↓, and Angle of HT↑ ⇒Lift of the wing is relative small. 14 Colored component plane for design variables ⇒ Which dvs are important?
- 57. Ex-iii: Wing design for supersonic transport Comparison of component planes L/D ΔP Wwing Angle of HT Larger sweep back ⇒ Low boom, high L/D (low drag) Sweep back@Inboard Camber@Kink25%c Camber@Root25%c Small camber at LE and large camber at TE Sweep back@Outboard ⇒ Low boom, high L/D (high lift) Camber@Kink75%c Blue box: Chosen by similarity of color map, Green box: Chosen by ANOVA result 57
- 58. Ex-iii: Wing design for supersonic transport Computational efficiency ・CAPAS evaluation in 60min./case (including decision of angle of HT) 75 initial samples + 30 additional samples = total of 105 samples 105CFD run×60min.=105hours (about 4-5days) If we use direct GA search with 30population and 100 generation, total of 3000CFD run is needed. If we use only high-fidelity solver (ex. 10hours/case), it takes total of about 4050days. 58
- 59. 59 ex-iv) Design exploration of optimum installation for nacelle chine
- 60. Ex-vi: Design exploration for nacelle chine installation 60 Nacelle chine: For improve the stall due to the interaction of the vortex from the nacelle/ pylon and the wing at landing. Nacelle installation problem: It is difficult to evaluate complex flow interaction by CFD. ⇒ Introduction of experiment based optimization
- 61. Ex-vi: Design exploration for nacelle chine installation61 Design method Efficient Global Optimization(EGO) Experiment Model’s half-span: 2.3m Flow speed: 60m/s
- 62. 62 62 Ex-vi: Design exploration for nacelle chine installation # of design variables: 2 Radius θ Longitudinal length: χ 0.4cnacelle ≤ χ ≤ 0.8cnacelle 30 (deg.) ≤ θ ≤ 90 (deg.) Objective function (1) maximize: CLmax
- 63. Ex-vi: Design exploration for nacelle chine installation63 Sampling result Initial samples Additional samples χ
- 64. Ex-vi: Design exploration for nacelle chine installation64 Sampling result (w/ additional samples) Initial samples Additional samples Improvement of accuracy around optimum region χ
- 65. Ex-vi: Design exploration for nacelle chine installation65 Projection of surrogate model to the CAD data 15 wind tunnel testing(approximately 7hours)
- 66. Conclusion Today’s lecture is engineering optimization. “Optimization” is mathematical techniques to acquire minimum/ maximum point. Formulation/ visualization are important → How to formulate interesting and useful design problem. Design methods for real-world problem Evolutionary algorithm is useful for multi-objective problem Surrogate model to reduce the design cost Application to aircraft design Proper objectives, constraints and evaluation method (It is most difficult issue for designers!)

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