OPTIMIZATION BASED ON EVOLUTIONARY ALGORITHMS FOR AERONAUTICS

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