MULTIDISCIPLINARY AIRCRAFT DESIGN AND OPTIMISATION USING A ROBUST EVOLUTIONARY TECHNIQUE WITH VARIABLE FIDELITY MODELS The University of Sydney L. F. Gonzalez E. J. Whitney K. Srinivas Pole Scientifique J. Périaux 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, New York,USA, 30 Aug - 1 Sep 2004,
Outline • Introduction – Problems in aeronautical design and optimisation – The need for Evolutionary algorithms • Theory – Evolution Algorithms (EAs). – Multidisciplinary –Multi-objective Design – Hierarchical Asynchronous Evolutionary Algorithm (HAPEA). • Application • Mathematical Test functions • Two real world examples • Conclusions
Multidisciplinary aircraft design and optimisation • Aircraft Deign is multidisciplinary in nature and there is a strong interaction between the different multi-physics involved (aerodynamics , structures , propulsion) • A tradeoff between aerodynamic performance and other objectives becomes necessary.
Problems in Aerodynamic Optimisation (1) • 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 (2) • Traditional optimisation methods will fail to find the real answer in many real engineering applications, (Noise, complex functions). • Commercial solvers are essentially inaccessible from a modification point of view (they are black-boxes). • Question- High Fidelity model? Or a thorough search with a Low Fidelity Model?
Why Evolution? • Evolution Algorithms can explore large variations in designs. • Robust towards noise and local minima and easy to to parallelise, reducing computation time. • Provide optimal solutions for single and multi-objective problems or calculating a robust Nash game • EAs successively map multiple populations of points, allowing solution diversity.
Evolution Algorithms What are EAs. • Based on the Darwinian theory of evolution Populations of individuals evolve and reproduce by means of mutation and crossover operators and compete in a set environment for survival of the fittest. Evolution Crossover Mutation Fittest • Computers can be adapted to perform this evolution process.
Introduction to Multi-Objective Optimisation (1) • Aeronautical design problems normally require a simultaneous optimisation of conflicting objectives and associated number of constraints. They occur when two or more objectives that cannot be combined rationally. For example: • Drag at two different values of lift. • Drag and thickness. • Pitching moment and maximum lift. • Best to let the designer choose after the optimisation phase.
Introduction to Multi-Objective Optimisation (2) Maximise/ Minimise Subjected to constraints • objective functions, output (e.g. cruise efficiency). • x: vector of design variables, inputs (e.g. aircraft geometry ) with upper and lower bounds; • g(x) equality constraints and h(x) inequality constraints: (e.g. element von Mises stresses); in general these are nonlinear functions of the design variables.
Pareto Optimal Set • A set of solutions that are non-dominated w.r.t all others points in the search space, or that they dominate every other solution in the search space except fellow members of the Pareto optimal set.
Our Approach: • Parallel Computing and Asynchronous Evaluation • Pareto Tournament Selection • Hierarchical Population Topology Hierarchical Asynchronous Parallel Evolutionary Algorithms (HAPEA)
Parallel Computing and Asynchronous Evaluation DifferentSpeeds 1 individual EvolutionAlgorithm Asynchronous Evaluator 1individual
Asynchronous Evaluation Why asynchronous Methods of solutions to MO and MDO -> variable time to complete. Time to solve non-linear PDE - > Depends upon geometry How: 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
Asynchronous Evaluation Methods of solutions to MO and MDO -> variable time to complete. Time TO SOLVE NON-linear pfF - > DEPENDS UPON GEOMETRY Traditional EAs -> create an unnecessary bottleneck when used on parallel computers; -> i.e processors that have already completed their solutions will remain idle until all processors have completed their work.
Pareto Tournament Selection • The selection operator is a novel approach to determine whether an individual x is to be accepted into the main population Population Asynchronous Buffer • Create a tournament Tournament Q Evaluate x x If x not dominated Where B is the selection buffer.
Hierarchical Population Topology Exploitation (small mutation span) Model 1 precise model Exploration (large mutation span) Model 2 intermediate model Model 3 approximate model
Optimisation of Analytical Test Functions • Ackley • MOEAs Examples
Test Functions: Ackley Increasing number of variables
MOEA Examples • 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 • Again, we solve a two objective problem with two design variables however now the optimal Pareto front contains four discontinuous regions
Results So Far… • The new technique is approximately three times faster than other similar EA methods. • A testbench for single and multiobjective problems has been developed and tested • 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)
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.
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.
Applications So Far… (3) • Transonic wing design Two Objectives • UAV Wing Design • Wind Tunnel Test : • Evolved Aerofoils • Evolved Wings • Evolved Aircrafts (in progress)
Two Representative Examples • Three Element Aerofoil Euler Reconstruction. • Multidisciplinary UAV Design Optimisation
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
Multi-element aerofoil reconstruction problem Design variables The design variables are the position And rotation of the slat and flap Upper and lower bounds of position and rotation are and respectively Fitness Function The fitness function is the RMS error of the surface pressure coefficients on all the three elements
Implementation Single Population EA (EA SP) Population size: 40 Grid nbv 2500 Hierarchical Asynchronous Parallel EA (HAPEA)
Example of Convergence History. A better solution in lower computing time
UAV Conceptual DesignOptimisation Problem Minimise two objectives: Gross weight min(WG) Endurance min (1/E) Subject to: Takeoff distance <1000 ft, Alt Cr > 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
Design Variables In total we have 29 design variables 13 Configuration Design variables Camber Wing Twist
Design Variables Camber Tail Twist Fuselage
Design Variables: Bounding Envelope of the Aerofoil Search Space 16 Design variables for the aerofoil Two Bezier curves representation: Six control points on the mean line. • Constraints: • Thickness > 12% x/c • Pitching moment > -0.065 • Ten control points on the thickness distribution.
Design Tools pMOEA (HAPEA) Optimisation FLOPS (Modified to accept user computed aerodynamic data) Aircraft design and analysis A compromise on fidelity models Vortex induced drag: VLMpc Viscous drag: friction Aerofoil Design Xfoil Aerodynamics Structural & weight analysis FLOPS
Pareto optimal region Objective 1 optimal Compromise Objective 2 optimal
Sample of Pareto Optimal configurations Pareto Member 16 Pareto Member 0 Pareto Member 14 Pareto Member 19
Conclusions • The results indicate that aircraft design optimisation and shape optimisation problem can be resolved with an evolutionary approach using a hierarchical topology. • The new method contributes to the development of numerical tools required for the complex task of MDO and aircraft design. • A practical design of a long endurance high altitude UAV was studied and realistic designs were obtained. • No problem specific knowledge is required The method appears to be broadly applicable to different analysis codes • A family of Pareto optimal configurations was obtained giving the designer a restricted search space to proceed into more details phases of design.
Acknowledgements • The authors would like to thank Arnie McCullers at NASA LARC for providing the FLOPS code. • 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 Professor M. Drela for providing the MSES code • Also to Professor K. Deb for discussions on developments and applications of MOEA during his visit to The University of Sydney in 2003.
CFD Solver • Flow is treated as two dimensional, inviscid and is calculated using B. Mohammadi code NSC2ke • The solver uses unstructured mesh which are generated using Bamg. • The computations stop when the 2-norm of the residual falls below a prescribed limit, in this case
Optimization Methods • Guess /Intuition: decreases as the increasing dimensionality. • Nonlinear simplex: simple and robust but inefficient for more than a few design variables. • Grid or random search: the cost of searching the design space increases rapidly with the number of design variables. • Gradient-based: it is most efficient for a large number of design variables; assumes the objective function is “well-behaved”. • Evolution algorithms: good for discrete design variables and very robust; but infeasible when using a large number of design variables.
Asynchronous Evaluation (1) Different Speeds 1 individual EvolutionAlgorithm Asynchronous Evaluator 1individual • Ignores the concept of generation-based solution. • Fitness functions are computed asynchronously. • Only one candidate solution is generated at a time, and only one individual is incorporated at a time rather than an entire population at every generation as is traditional EAs. • Solutions can be generated and returned out of order.
Asynchronous Evaluation (2) Different Speeds 1 individual EvolutionAlgorithm Asynchronous Evaluator 1individual • No need for synchronicity no possible wait-time bottleneck. • No need for the different processors to be of similar speed. • Processors can be added or deleted dynamically during the execution. • There is no practical upper limit on the number of processors we can use. • All desktop computers in an organisation are fair game.
Need for Asynchronous Evaluation cases used in engineering today may take different times to complete their operations Time taken for solutions of non-linear partial differential equations will strongly depend upon the geometry. Generation –based approach used by evolutionary algorithm, traditional genetic algorithms and evolution strategy create an unnecessary bottleneck when used on parallel computers , i.e., the processors that have already completed their solutions will remain idle until all processors have completed their work
Methods of solutions to MO and MDO -> VARIABLE TIME TO COMPLETE. Time TO SOLVE NON-linear pfF - > DEPENDS UPON GEOMETRY Traditional EAs -> create an unnecessary bottleneck when used on parallel computers; -> I.E processors that have already completed their solutions will remain idle until all processors have completed their work.