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Developments in Evolutionary Algorithms and Multi Disciplinary Optimisation

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## Developments in Evolutionary Algorithms and Multi Disciplinary Optimisation

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**Developments in**Evolutionary Algorithms and Multi Disciplinary Optimisation A University of Sydney Perspective**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**Overview**General aspects of the program K. Srinivas Discussion of specific examples Mr. Luis Felipe Gonzalez**Multi Disciplinary**Motivation Search Space – Large Multimodal Non-Convex Discontinuous Traditional Methods- Trade off between Conflicting Requirements**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.**Multi-Objective Optimisation**Maximise/ Minimise Subjected to constraints**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**Our Contribution**Parallel Computing Asynchronous Evaluation Hierarchical Population Topology Hierarchical Asynchronous Parallel Evolutionary Algorithms (HAPEA)**DifferentSpeeds**1 individual EvolutionAlgorithm Asynchronous Evaluator 1individual Parallel Computing and Asynchronous Evaluation**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**Pareto Tournament Selection**Create a tournament WhereBis the selection buffer. If the new individual xis not dominated any other in the tournament(Q),then it is immediately accepted and inserted into the main population according to the replacement rules.**Model 1**precise model Exploitation (small mutation span) Model 2 intermediate model Exploration (large mutation span) Model 3 approximate model Hierarchical Population Topology**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 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).**NASA and US Air force and EAs**• [1] N. Madavan, Turbomachinary airfoil Design Optimization using Differential Evolution, • [2] Thomas A. Zang and Lawrence L. Green, Multidisciplinary Design Optimisation Techniques: Implications and opportunities for Fluid Dynamics Research. • [3] Illinois Genetic Algorithms Laboratory, U.S. Air Force Office of Scientific Research, F49620-97-1-0050..**Optimisation of Analytical Test Functions**• Ackley • MOEAs Examples • Asynchronous Test Case – Sphere Function**Test Functions: Ackley**Increasing number of variables**Asynchronous Test Case – Sphere Function**• 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**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 on : • Evolved Aerofoils • Evolved Wings (in progress) • Evolved Aircrafts (in progress)**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).**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**Technical Resources Analysis Tools**• CAD • Solid Works, Autocad • Aircraft Design • FLight Optimisation System (FLOPS) NASA Langley • AAA (DART corporation) • ADS (In House) 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**Four Representative Examples**• Three Element Aerofoil Euler Reconstruction. • Aerofoil Optimisation • Multidisciplinary UAV Design Optimisation • Multidisciplinary Wing 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 n x 2500 Hierarchical Asynchronous Parallel EA (HAPEA)**Example of Convergence History.**A better solution in lower computing time**Aerofoil Optimisation**• Problem Definition: • Find the Pareto set of aerofoils for minimum total drag at two design points, • Compare to Nadarajah and RAE 2822.**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.**Exploitation**Population size = 30 Intermediate Population size = 20 Exploration Population size = 15 Implementation Hierarchical Asynchronous Parallel EA (HAPEA) 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**Pareto Front Transonic Aerofoil Design Problem**Flight Condition 1 Compromise Flight Condition 1**Aerofoil Optimisation Results**• 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. • [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.**UAV Conceptual DesignOptimisation 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**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