Evolutionary Algorithms for Aeronautics Optimization

1. With support of the Walloon Region and European Structural Funds ERSF, ESF Rajan FILOMENO COELHO OPTIMIZATION BASED ON EVOLUTIONARY ALGORITHMS FOR AERONAUTICS

2. Outline • I. Introduction • II. Brief overview of CENAERO activities • III. Optimization algorithms • IV. New trends in structural optimization for aeronautics • V. Conclusions

3. I. Introduction I. Introduction • Since the sixties: • outgrow of numerical methods for structural mechanics, fluid dynamics, etc. (e.g. finite element, boundary element, finite volume methods, …) • parallely, development of novel and efficient optimization algorithms →structural optimization: “collection of methods designed to optimize (mechanical) structures, by means of optimization algorithms & numerical models” • In aeronautics: • mostly: shape optimization (e.g. wing design optimization) • several physics are involved ( multidisciplinary) • expensive simulations (CFD, CSM, …)

4. I. Introduction I. Introduction • Multi-disciplinary shape optimization • objectives: optimal aerodynamic performances • constraints: mechanical integrity, … • State of the art: • expert designers with know-how and trial / error procedure • numerical optimization starts to be used in the real design process, but in general: • limited number of design variables • one physic at a time • the uncomputable functions must be tackled • robustness of the whole design process • link / access to the CAD systems • efficient shape parameterization

5. II. CENAERO • Private Non-Profit Research Centre • 3 universities (ULB, UCL, ULg) • 1 research center (VKI) • 50 industry members • incorporated in 2002 in Gosselies • 35 employees • Activities & Competences • development of simulation softwares for multidisciplinary problems in aeronautics • R&D in supercomputing, advanced numerical methods, parallel computing • advanced engineering studies for the industry • High Performance Computing (HPC) center II. Cenaero

6. II. CENAERO • Four R&D groups: • Virtual manufacturing • Multiscale Material Modelling • CFD-multiphysics • Multidisciplinary Optimization II. Cenaero Electron beam welding Crack propagation Aeroelasticity Optimization

7. II. CENAERO • Virtual Manufacturing • Welding (Friction Stir, Laser, Electron Beam) • Metal forming, Machining, Hot forging • Multiscale Material Modelling • Fatigue analysis • Micro-macro • Composites • CFD-multiphysics • Simulation of large scale turbulent unsteady flows • Aeroacoustics • Heat pipes modelling • Numerical methods and Optimization • Multidisciplinary optimization • Parallelization II. Cenaero

8. x : vector of the variables • f: objective function(s) • g : inequality constraints • h : equality constraints III. Optimization algorithms • Optimization problems can be written as follows: f(x)T = { f1(x) f2 (x) … fm (x)} g(x)T = { g1 (x) g2 (x) … gk (x)} h(x)T = { h1 (x) h2 (x) … hl (x)} xT = { x1 x2 … xn } X min { f(x) } s.t.: g(x)  0 h(x) = 0 III. Optimization algorithms • Once an optimization problem is correctly formulated, a suitable optimization algorithm has to be chosen

9. III. Optimization algorithms • Optimization problems are classified following … • the nature of the variables : • continuous: e.g. geometrical dimensions • discrete: e.g. sections from a catalogue • integer : e.g. number of holes in a plate • mixed variables • the differentiability (or not) of the functions • the presence of explicit or implicit functions (with respect to the variables) • the size of the problem • the analytical properties of the functions (linearity, convexity, …) • one or several objectives ( single- or multi-objective optimization) III. Optimization algorithms

10. III. Optimization algorithms • Characteristics of optimization problems in aeronautics: • global optimum • multiple objectives and constraints • robust • multi-physics implies at least • no access to objective function derivatives • need of a generic optimization method • high CAE computational time (> 1h) • must be parallelized • uncomputable functions have to be tackled • several type of design variables: real, integer, … • non-differentiable objectives and constraints • noisy objective functions III. Optimization algorithms

11. III. Optimization algorithms • To handle those requirements, evolutionary algorithms combined with approximation methods have been selected • Main instances of EAs: • Genetic algorithms, genetic programming, evolution strategies • Principle: • a. Creation of a random population of potential designs • b. Selection of the best individuals (through a fitness fct.) • c. Recombination of the individuals (by crossover and mutation) in order to generate new ones • d. Go back to step b and repeat the procedure until a convergence criterion is reached III. Optimization algorithms

12. III. Optimization algorithms initial population initial population Illustration of a standard GA (2-variable design space) selection of the best crossover mutation III. Optimization algorithms Termination criterion reached ? no yes STOP

13. III. Optimization algorithms • Example of design optimization with EAs • aero-engine liner optimization: Approach Condition M∞= 0.21 Noise Frequency = 2500 Hz III. Optimization algorithms Liners [Credits: Dr. Paul Ploumhans (FFT)]

14. III. Optimization algorithms • Problem definition • Design Variables • Liner 1 Impedance Z • 1 < Re(Z) / (0c0) < 4 • -2 < Im(Z) / (0c0) < 0.5 • Liner 2 Impedance Z • 1 < Re(Z) / (0c0) < 4 • -2 < Im(Z) / (0c0) < 0.5 • Design Objectives • Minimize acoustic pressure • Simulation • Actran – FFT • Simulation time: 1 h III. Optimization algorithms

15. III. Optimization algorithms • Reduction of the noise for both liners III. Optimization algorithms

16. III. Optimization algorithms • In CENAERO, MAX optimization software is developed (C++ object-oriented code) • Properties of the optimization algorithms in MAX: • based on evolutionary algorithms with advanced genetic operators • multiobjective optimization • optimization combined with meta-models • “in-house” tools to perform multidisciplinary optimization and allow access to CAD design geometries • Future developments considered: • robust optimization III. Optimization algorithms

17. IV. New trends in structural optimization • Advanced optimization strategies in aeronautics involve: • Multiobjective optimization • Optimization combined with meta-models • Multidisciplinary optimization • Robust optimization • Collaborative design & optimization IV. New trends in structural optimization

18. IV. New trends in structural optimization • Multiobjective optimization: • ex.: optimizing a heat pipe for satellite • objectives: 1. maximize the power 2. minimize the room occupied IV. New trends in structural optimization

19. D IV. New trends in structural optimization • definition of the multiobjective problem: Design Variables • D = internal diameter [5, 30 mm] • G = groove count [5, 20] • d = hydraulic diameter [0.8, 2.5 mm] Objectives • maximize power • minimize external diameter IV. New trends in structural optimization Dext Credits: S. Rossomme & C. Goffaux

20. IV. New trends in structural optimization IV. New trends in structural optimization

21. IV. New trends in structural optimization  Concept of Pareto solution: « if fi : m criteria to be minimized;x is a Pareto (or non- dominated solution if there exists no other solution x* such that fi (x) fi (x*)  i and i | fi (x)> fi (x*)  » IV. New trends in structural optimization

22. 3 approches are available [Horn, 1997]: • a posteriori methods: 1 run of the algorithm  overview of the front de Pareto (PF)  so far: lack of reliable convergence criterion  difficulty to visualize the Pareto front when the number of criteria exceeds 3 • a priori methods:  interesting for more than 3 criteria, because the search is directly oriented towards a specific region of the Pareto front  only one point for each run of the algorithm what is the exact interpretation of the weights given to each objective ? IV. New trends in structural optimization IV. New trends in structural optimization

23. interactive methods: the choice of a solution is guided by an interaction with the user  usually : only one point by run of the algorithm  requires from the user a good knowledge of the problem most common approach in aeronautics: - use an a posteriori method to find the Pareto front - use a multicriteria decision aid method to choose a solution (or a set of solutions)  a posteriori multiobjective algorithms: often based on evolutionary algorithms (based on a population)  in MAX: Strength-Pareto Evolutionary Algorithms 2 (SPEA2) due to Zitzler & Thiele IV. New trends in structural optimization IV. New trends in structural optimization

24. IV. New trends in structural optimization • Optimization combined with meta-models • MAX software developed at CENAERO combines evolutionary algorithms with approximation models IV. New trends in structural optimization

25. IV. New trends in structural optimization • initial accurate points are used to build the first approximated model • the optimization is executed on this approximated model • the optimized point is computed with the accurate model IV. New trends in structural optimization

26. IV. New trends in structural optimization • the new accurate point is added to the initial database and a new approximated model is built • the process is repeated until a convergence criterion is reached IV. New trends in structural optimization

27. initial design control points IV. New trends in structural optimization • example: design optimization of a blade from VKI-LS89 highly loaded transonic turbine – 1. Building the blade design geometry:  the algorithm generates points in order to minimize the distance between the points created and the initial design • these points play the role of the control points of B-splines  the variables are: IV. New trends in structural optimization y-coordinates of 16 control points

28. IV. New trends in structural optimization – 2. Constructing the viscous mesh (TRAF) – 3. Computing the flow (TRAF quasi-3D analysis) – 4. Post-processing: for each operating point, the loss coefficient z2 is computed: – For the optimizer, the objective is defined as follows ... • for each operating point, the loss coefficient z2 is to be minimized • practically, a weighted sum approach is followed  minimize 2op1 + 2op2 – ... and the constraint: • the outlet flow angle a must remain between -74.8° and -74.7° IV. New trends in structural optimization

29. IV. New trends in structural optimization • density r for the initial design: IV. New trends in structural optimization

30. loss coefficient sum iteration IV. New trends in structural optimization • convergence history (200 design cycles): IV. New trends in structural optimization

31. IV. New trends in structural optimization • Multidisciplinary optimization: application to boosters • commercial aircraft turbofan engines are complex systems involving several engineering sciences • the compression system of the turbofan is generally composed of three elements: • a fan • a multistage low pressure compressor (LPC = booster) • a multistage high pressure compressor (HPC) IV. New trends in structural optimization

32. IV. New trends in structural optimization • The design of a LPC (booster) is a challenging task: • from a mechanical point of view: • ensuring the static viability of the compressor • preventing any dangerous dynamical modes from aerodynamical and mechanical excitations • from an aerodynamical point of view: • satisfy a set of critical performances in terms of mass • flow rate, total pressure ratio and efficiency • typical LPC maps show wide variations of mass flow and rotational speed during their operating lines: • these large variations influence significantly the blade inlet conditions (Mach number, airflow incidence)  the design of LPC turbomachinery blades requires multi-disciplinaryoptimization (on multiple operating points) IV. New trends in structural optimization

33. IV. New trends in structural optimization • The methodology followed to optimize turbomachinery blade design is described schematically: • CFD code: TRAF (A. Arnone, University of Florence) • FEM Structural Analysis code: SAMCEF (Samtech) IV. New trends in structural optimization

34. IV. New trends in structural optimization • 3D representation of the optimized blade design: IV. New trends in structural optimization

35. IV. New trends in structural optimization • Advantage of multidisciplinary optimization • multidisciplinary = different physics are taken into account simultaneously  enhanced reliability of the solution • but : problematic of coupling of physics (theoretical – numerical – softwares) • Interest of using meta-models • each simulation run takes ~1h40 on 1 processor (on CENAERO Linux cluster) • the use of meta-models enables a reduction of the CPU time by a factor ~10 IV. New trends in structural optimization

36. V. Conclusions • Why optimize structures in aeronautics ? • optimization more and more important, to decrease time dedicated to design and dimensioning, and increase the quality of the product • optimization algorithms and simulation tools are now mature enough to be used in several aeronautical applications • for the engineer: gain of knowledge about the problem (influence of the parameters on a design, …)  improvement of expertise V. Conclusions