1. Developments in Evolutionary Algorithms and Multi Disciplinary Optimisation A University of Sydney Perspective A University of Sydney Perspective

2. The Team Dr. K Srinivas - Leader Prof. J. Périaux – Advisor Prof. S W Armfield Dr. E. J. Whitney Mr. L. F. Gonzalez Mr. S. Nagarathinam Mr. D. S. Lee Dr. M Sefrioui

3. Overview General aspects of the program K. Srinivas Discussion of specific examples Mr. Luis Felipe Gonzalez

4. Motivation Multi Disciplinary Search Space – Large Multimodal Non-Convex Discontinuous Traditional Methods- Trade off between Conflicting Requirements

5. Evolutionary Algorithms Explore large search spaces. Robust towards noise and local minima Easy to parallelise Map multiple populations of points, allowing solution diversity. A number of multi-objective solutions in a Pareto set or performing a robust Nash game.

6. Multi-Objective Optimisation Maximise/ Minimise Subjected to constraints

7. Pareto Front

8. Drawback of EAs A typical aerodynamic optimisation relies on CFD and FEA on structures CFD Computation is time consuming Our research addresses this issue in some detail

9. Our Contribution Hierarchical Asynchronous Parallel Evolutionary Algorithms (HAPEA) Evolutionary Algorithms (HAPEA) Parallel Computing Asynchronous Evaluation Hierarchical Population Topology

10. Parallel Computing and Asynchronous Evaluation Evolution Algorithm Asynchronous Evaluator 1 individual Different Speeds

11. Asynchronous Evaluation Suspend the idea of generation Solution can be generated in and out of order Processors – Can be of different speeds Added at random Any number of them possible

12. Pareto Tournament Selection Create a tournament Where B is the selection buffer. If the new individual x is not dominated any other in the tournament ( Q ), then it is immediately accepted and inserted into the main population according to the replacement rules.

13. Hierarchical Population Topology Model 1 precise model Model 2 intermediate model Model 3 approximate model Exploration (large mutation span) Exploitation (small mutation span)

14. Multidisciplinary design problems involve search space that are multi-modal, non-convex or discontinuous. Traditional methods use deterministic approach and rely heavily on the use of iterative trade-off studies between conflicting requirements. Problems in Aerodynamic Optimisation (1)

15. Traditional optimisation methods will fail to find the real answer in most real engineering applications, (Noise, complex functions). The internal workings of validated in-house/ commercial solvers are essentially inaccessible from a modification point of view (they are black-boxes). Problems in Aerodynamic Optimisation (2)

16. NASA and US Air force and EAs [1] N. Madavan, Turbomachinary airfoil Design Optimization using Differential Evolution,[1] [2] Thomas A. Zang and Lawrence L. Green, Multidisciplinary Design Optimisation Techniques: Implications and opportunities for Fluid Dynamics Research.[2] [3] Illinois Genetic Algorithms Laboratory, U.S. Air Force Office of Scientific Research, F49620-97-1- 0050..[3]

17. Ackley MOEAs Examples Asynchronous Test Case – Sphere Function Optimisation of Analytical Test Functions

18. Test Functions: Ackley Increasing number of variables

19. Solved on a single population Asynchronous: Assign a small fictitious delay to each function evaluation. This will vary uniformly between two values fastest and lowest. Evaluate asynchronously. Synchronous: Assign the same delay to all individuals in advance. Wait until the slowest evaluation is completed, as it will occur in practice on a cluster of computers. Four unknowns=4), Stopping Condition = 0.0001, 25 runs. Configurations up to tslowest /tfastest = 5 Asynchronous Test Case – Sphere Function

20. Here our EA solves a two objective problem with two design variables. There are two possible Pareto optimal fronts; one obvious and concave, the other deceptive and convex MOEA Examples

21. Again, we solve a two objective problem with two design variables however now the optimal Pareto front contains four discontinuous regions

22. Results So Far… EvaluationsCPU Time Traditional 2311 224152m20m New Technique 504 490 (-78%) 48m 24m (-68%) The new technique is approximately three times faster than other similar EA methods. We have successfully coupled the optimisation code to different compressible and incompressible CFD codes and also to some aircraft design codes CFD Aircraft Design HDASS MSES XFOIL Flight Optimisation Software (FLOPS) FLO22 Nsc2ke ADS (In house) A testbench for single and multiobjective problems has been developed and tested

23. Applications So Far… (1) Constrained aerofoil design for transonic transport aircraft  3% Drag reduction UAV aerofoil design -Drag minimisation for high-speed transit and loiter conditions. -Drag minimisation for high-speed transit and takeoff conditions. Exhaust nozzle design for minimum losses.

24. Applications So Far… (2) Three element aerofoil reconstruction from surface pressure data. UCAV MDO Whole aircraft multidisciplinary design. Gross weight minimisation and cruise efficiency Maximisation. Coupling with NASA code FLOPS 2 % improvement in Takeoff GW and Cruise Efficiency  AF/A-18 Flutter model validation.

25. Applications So Far… (3) Transonic wing design Two Objectives UAV Wing Design Wind Tunnel Test on : Evolved Aerofoils Evolved Wings (in progress) Evolved Aircrafts (in progress)

26. Capabilities We are now confident of our ability to optimise real industrial/Aeronautical cases, which could be three- dimensional, having multi-objective criteria or related to multidisciplinary Design Optimisation (MDO).

27. Technical Resources: Parallel Computing Computer resources Access to a Dell Linux Cluster (Scalable Parallel) Theoretical Peak Performance: 1860 Gflops (or 1.82 Tflops) Sustain Performance Achieved: 1095 Gflops (or 1.07 Tflops) - using LINPACK measurement

28. Technical Resources Analysis Tools Aerodynamics/CFD FLUENT FLO22 (NASA Langley) HDASS (In house Navier-Stokes Solver) (2D Gridless solver) VLMpc ( Vortex lattice method) Structural Analysis Finite Element Analysis : Strand 7 Nastran CAD Solid Works, Autocad Aircraft Design FLight Optimisation System (FLOPS) NASA Langley AAA (DART corporation) ADS (In House)

29. Four Representative Examples Three Element Aerofoil Euler Reconstruction. Aerofoil Optimisation Multidisciplinary UAV Design Optimisation Multidisciplinary Wing Design Optimisation

30. Three Element Aerofoil Euler Reconstruction. Problem Definition: Rebuild from scratch the pressure distributions that approximately fit the target pressure distributions of a three element aerofoil set. Flow Conditions -Mach 0.2, - Angle of Attack 17 deg - Euler Flow, unstructured mesh

31. Design variables Fitness Function The fitness function is the RMS error of the surface pressure coefficients on all the three elements Multi-element aerofoil reconstruction problem The design variables are the position And rotation of the slat and flap Upper and lower bounds of position and rotation are and respectively

32. Implementation Population size: 40 Grid n x 2500 Single Population EA (EA SP) Hierarchical Asynchronous Parallel EA (HAPEA) Population size: 40 Viscous: Grid n x 2500 Viscous: Grid n x 2000 Viscous: Grid n x 1500

33. Pressure Distribution

34. Candidate and Target Geometries

35. Example of Convergence History. A better solution in lower computing time

36. Aerofoil Optimisation PropertyFlt. Cond. 1 Flt Cond.2 Mach0.75 Reynolds9 x 10 6 Lift0.650.715 Problem Definition: Find the Pareto set of aerofoils for minimum total drag at two design points, Compare to Nadarajah and RAE 2822.

37. Design Variables: Bounding Envelope of the Aerofoil Search Space Ten control points on the thickness distribution. 16 Design variables for the aerofoil Constraints: Thickness > 12% x/c Pitching moment > -0.065 Two Bezier curves representation: Six control points on the mean line.

38. Implementation Hierarchical Asynchronous Parallel EA (HAPEA) Exploitation Population size = 30 Exploration Population size = 15 Intermediate Population size = 20 Model 1 Grid= 215 x 36 Model 2 Grid=99 x 16 Model 3 Grid= 71 x 12 To solve this and other problems standard industrial flow solvers are being used. In This case MSES (Euler+BL ) M. Drela

39. Pareto Front Transonic Aerofoil Design Problem Flight Condition 1 Compromise

40. Aerofoil Optimisation Results Aerofoilc d [c l = 0.65 ] c d [c l = 0.715 ] Traditional Aerofoil RAE2822 0.01470.0185 Conventional Optimiser [Nadarajah [1]] 0.0098 (-33.3%) 0.0130 (-29.7%) New Technique0.0094 (-36.1%) 0.0108 (-41.6%)  For a typical 400,000 lb airliner, flying 1,400 hrs/year:  3% drag reduction corresponds to 580,000 lbs (330,000 L) less fuel burned. q [1] Nadarajah, S.; Jameson, A, " Studies of the Continuous and Discrete Adjoint Approaches to Viscous Automatic Aerodynamic Shape Optimisation," AIAA 15th Computational Fluid Dynamics Conference, AIAA-2001-2530, Anaheim, CA, June 2001.

41. UAV Conceptual Design Optimisation Problem Minimise two objectives: Gross weight  min(WG) Endurance  min (1/E) Subject to: Takeoff lenght < 1000 ft, Alt Cruise > 40000 ROC > 1000 fpm, Endurance > 24 hrs With respect to: external geometry of the aircraft Mach = 0.3 Endurance > 24 hrs Cruise Altitude: 40000 ft

42. Design Variables In total we have 29 design variables Design VariableLower Bound Upper Bound Wing Area (sq ft)280330 Aspect Ratio S1825.2 Wing Sweep (deg) 0.08.0 Wing Taper Ratio0.280.8 13 Configuration Design variables Camber Twist Wing

43. Design Variables Camber Twist Horizontal Tail Area (sq ft) 65.085.0 HT Aspect Ratio3.015.0 HT Taper Ratio0.20.55 HT Sweep (deg)12.015.0 Vertical Tail Area (sq ft) 11.029.0 VT Aspect Ratio1.03.2 VT Taper Ratio0.280.62 VT Sweep (deg)12.034.0 Fuselage Diameter 2.65.0 Tail Fuselage

44. Design Variables: Bounding Envelope of the Aerofoil Search Space Ten control points on the thickness distribution. 16 Design variables for the aerofoil Constraints: Thickness > 12% x/c Pitching moment > -0.065 Two Bezier curves representation: Six control points on the mean line.

45. Mission profile

46. Structural & weight analysis A compromise on fidelity models Vortex induced drag: VLMpc Viscous drag: friction Aerofoil Design Xfoil pMOEA (HAPEA) Optimisation Aircraft design and analysis Aerodynamics FLOPS FLOPS (Modified to accept user computed aerodynamic data) Design Tools

47. Implementation Population size: 20 Grid 141x 74x 36 on aerofoil, 20 x 6 on Vortex model Grid 109x 57x 27 on aerofoil, 17 x 6 on Vortex model Grid 99x 52x 25 on aerofoil, 15 x 6 on Vortex model

48. Convergence history for objective one

49. Pareto optimal region Objective 1 optimal Objective 2 optimal Compromise

50. Sample of Pareto Optimal configurations Pareto Member 0 Pareto Member 14 Pareto Member 16 Pareto Member 19

51. Mach Number0.69 Cruising Altitude10000 ft ClCl 0.19 Wing Area2.94 m 2 Minimisation of wave drag and wing weight MOO of transonic wing design for an Unmanned Aerial Vehicle (UAV)

52. Lift distribution is replaced by concentrated loads The local stress has to be less than the ultimate shear stress. In this case for Aluminum Alloy Procedure AerodynamicsPotential Flow Solver (FLO22) Structural Analysis Wing Weight approximated as the sum of the span-wise cap weight to resist the bending moment  

53. Design Variables 16 Design variables on three span wise aerofoils 9 Design variables on three span wise aerofoil section 57 design variables +

54. Minimum thickness Position of Maximum thickness Fitness functions Constraints & Objective Functions

55. Approach one : Traditional EA with single population model Computational Grid 96 x 12 x 16 Approach two : HAPEA Exploitation Population size = 30 Exploration Population size = 30 Intermediate Population size = 30 Grid size 96 x 12 x 16 Grid size 72 x 9 x 12 Grid size 48 x 6 x 8 Six machines were used in all calculations Implementation

56. The algorithm was run five times for 2000 function evaluations and took about six hours to compute Pareto fronts after 2000 function evaluations HAPEA approach Single population approach

57. Convergence history for objective one

58. Aerofoil sections for Pareto Member 0 12, 20 Top view of wings on Pareto set Results

59. Aerofoil sections for Pareto member ten (PM10)

60. Wing span pressure coefficient distribution Aspect Ratio = 3.5 MACH = 0.69 YAW = 0.0 ALPHA = 0.920 L.E Sweep = 10.2 deg L.E Sweep 2 = -1.9 deg CD = 0.0013 Pareto Member 10

61. Top and side view Pareto Wing 10 Top View Side View

62. Work in Progress Master of Engineering  Rotor Blade design and Optimisation using evolutionary Techniques  Adaptive Transonic Wing/Aerofoil Design and MDO using Evolutionary Techniques  Grid-less Algorithms for Design and optimisation in Aeronautics Undergraduate Projects  Transonic wing design using DACE (Design of Experiments-approximation Theories)  An empirical study on DSMC for within evolutionary Optimisation

63. The Challenge The use of higher fidelity models is till prohibitive, research on surrogate modeling/approximation techniques is required. MDO is a challenging topic, the last few year have seen several approaches for Design and optimization using Evolutionary techniques but research indicate that it is problem dependent and it is still an open problem. Access to Dell Linux Cluster is limited for benchmarking purposes. Use of higher fidelity models is still prohibitive.

64. A robust framework for Aeronautical MDO Long term vision Conceptual design Preliminary design Detailed Design CAD Integration Approximation Techniques (RSM….?), Optimiser Set (EAS, gradient hybrid) Higher Fidelity Models Database of Case Studies) Parallelization Strategies Multidisciplinary Analysis

65. Limitations Higher fidelity analysis codes Funding Limited access to Dell Linux Cluster for benchmarking purposes. Use of higher fidelity models is still prohibitive.

66. Outcomes (1) The new technique with multiple models: Lower the computational expense dilemma in an engineering environment (three times faster) Direct and inverse design optimisation problems have been solved for one or many objectives. Some Multi-disciplinary Design Optimisation (MDO) problems have been solved. The algorithms find traditional classical results for standard problems, as well as interesting compromise solutions. In doing all this work, no special hardware has been required – Desktop PCs networked together have been up to the task.

67. Outcomes (2) No problem specific knowledge is required  The method appears to be broadly applicable to different analysis codes. Work to be done on approximate techniques and use of higher fidelity models

68. Acknowledgements The authors would like to acknowledge Professor Steve Armfield and Dr Patrick Morgan at The University of Sydney for providing the facilities on using the cluster of computers. The authors would like to thank Arnie McCullers at NASA LARC for providing the FLOPS code. The authors would like to thank Professor M. Drela, B. Mohammadi and NASA for providing the MSES, Nsc2ke and FLO22 codes respectively. Also to Professor K. Deb for discussions on developments and applications of MOEA during his visit to The University of Sydney in 2003. The authors would like also acknowledge contribution of MER students S. Nagarathinam and D.S. Lee, with some of the slides and figures for this presentation.

69. Questions…

70. ADDITIONAL SLIDES

71. Funding Sought DIRECT COSTS Personnel Postgraduate Student (PhD) / Research Associate$20,000.00 Total Personnel (a)$20,000.00$21,000.00 Equipment Computer Resources$4,000.00$0.00 Total Equipment (b)$4,000.00$0.00 Travel Two trips to AIAA and US conferences sites.$2,500.00 Total Travel (c)$2,500.00 TOTAL DIRECT COSTS (e)$26,500.00$23,500.00 INDIRECT COSTS PIs and any researcher Level A or above x multiplier The University of Sydney $2,000.00 $5,000.00 TOTAL INDIRECT COSTS (f)$2,000.00 TOTAL COSTS (h)$28,500.00$25,500.00

72. Justification of Funding Requested Personnel: A postgraduate student stipend. Experimental work at the University labs. The intellectual content makes it suitable as a two- year project for a PhD student and the successful candidate will be required to be proficient in a wide range of CFD and optimisation techniques. Equipment: Provision of a PC, that will be put in place at the university labs, the requirements of this PC are for high performance parallel computing resources. These characteristics are essential in order to compute high fidelity models on the CFD and structural analysis. Travel: Travel expenses, including airfare, accommodation and meals to attend to AIAA conferences in the US. The U.S. Air force is asked to contribute half the cost of producing journal papers and registration to conferences. Indirect Costs: Indirect Costs have been calculated for The University of Sydney and using the standard multiplier for laboratory research (1.25).

73. USYD and AFRL Possible areas of collaboration within AFRL divisions: AFRL/VAA: Aeronautical Science Division VAAA: The Aerodynamic Configuration Branch VAAC: The Computational Sciences Branch VAAI: Aerospace Vehicles Integration and Demonstration Branch VAS: Structures Division AFRL/VASD: Design and analysis methods branch Computational Fluid Dynamics Aerodynamics Aero thermodynamics Airframe-Propulsion Integration Airframe-Weapons Integration Stability and Control Flight Vehicle Performance Flow Diagnostics Aero Configuration Integration

74. Evolutionary Design Optimisation Problem Definition HAPEA Optimser Setup Do While Convergence not reached Create and evaluate initial population Generate and evaluate new candidates Evaluation of Candidates Compute the flow around the aerofoil sections and obtain a Cdo estimate for the wing Create drag polar on the candidate geometry Satisfying trim conditions. Analyze each configuration using FLOPS) Compute Objective Functions Evolve/ modify design variables on optimiser until stopping criteria is met.

75. Aircraft Design and Analysis The FLOPS (FLight OPtimisation System) solver developed by L. A. (Arnie) McCullers, NASA Langley Research Center was used for evaluating the aircraft configurations. FLOPS is a workstation based code with capabilities for conceptual and preliminary design of advanced concepts. FLOPS is multidisciplinary in nature and contains several analysis modules including: weights, aerodynamics, engine cycle analysis, propulsion, mission performance, takeoff and landing, noise footprint, cost analysis, and program control. FLOPS has capabilities for optimisation but in this case was used only for analysis. Drag is computed using Empirical Drag Estimation Technique (EDET) - Different hierarchical models are being adapted for drag build up using higher fidelity models.

76. Aerodynamic Analysis Control Points

77. Design Variables: Bounding Envelope of the Aerofoil Search Space Two Bezier curves representation: Six control points on the mean line. Ten control points on the thickness distribution. Constraints: Thickness > 12% x/c Pitching moment > -0.065 16 Design variables for the aerofoil

78. Aerofoil Characteristics cl = 0.65 Delayed drag divergence at high Cl Delayed drag divergence at low Cl Aerofoil Optimisation (2) Aerofoil Characteristics cl = 0.715

79. Aerofoil Characteristics M = 0.75 Delayed drag rise for increasing lift. Aerofoil Optimisation (2)

80. DescriptionLower BoundUpper Bound Wing Aspect Ratio3.507.00 Break to root taper0.650.80 Break to tip taper0.200.45 Wing Chord inboard Sweep, deg 10.0020.00 Wing Chord outboard Sweep, deg -20.000.00 Twist at root, deg0.003.00 Twist at Break, deg0.00 Twist at Tip, deg0.00 Break location0.200.35 Design Variables