1. INFLUENCE OF GEOMETRY PARAMETERIZATION IN AERODYNAMIC SHAPE DESIGN OF AERONAUTICAL CONFIGURATIONS BY EVOLUTIONARY ALGORITHMS Daniel González Juárez Esther Andrés Pérez Mario Jaime Martin Burgos Fluid Dynamics Branch INTA/ISDEFE Email: gonzalezjd@inta.es eandres@isdefe.es martinbj@inta.es Leopoldo Carro Calvo Sancho Salcedo Sanz Dep. Signal Theory and Communications University of Alcalá Email: leopoldo.carro@uah.es sancho.salcedo@uah.es 1/22 ETSIAE,UPM 10th of October, 2015

2.  What’s new?  Motivation – Why SBGO? - GARTEUR AG52 - Why EA+SVMs?  Approach overview  Test cases definition  Surrogate model construction & validation  Aerodynamic shape optimization  Next steps & Conclusions Outline 2/22

3. What’s new? 3/23 INTA's Fluid Dynamics Branch have been working on aerodynamic shape optimization for years How sensitive to the number of design variables this approach is?  Non-Uniform Rational B-Splines aerodynamic shape parameterization  Surrogate-Based Global Optimization  Evolutionary Algorithms & Support Vector Machines  GARTEUR AD/AG 52

4. 4/23 Motivation (1/5) Why SBGO? SVM-assisted evolutionary aerodynamic shape design ﺤ Support Vector Machines (SVMs) as metamodels to predict the aerodynamic coefficients and substitute expensive CFD ﺤ Application of evolutionary algorithms (EAs) in the aerodynamic design of aeronautical configurations SBGO methods in aerodynamic shape design: ﺤ broad design space exploration ﺤ high potential to find the global optimum ﺤ inherent parallelization ﺤ independence from initial configuration  may allow to reach innovative aircraft shapes Main drawbacks and challenges: ﺤ require a vast number of evaluations (with CFD can be time prohibitive) ﺤ may be inefficient when large number of design variables, “curse of dimensionality” ﺤ reduction of the design space ﺤ use multiple fidelity models ﺤ efficient constraints handling Non-conventional configurations This work is part of the GARTEUR Action Group AD/AG52 Source: http://adg.stanford.edu/aa241/intro/futureac.html (based on a presentation by Ilan Kroo entitled, Reinventing the Airplane: New Concepts for Flight in the 21st Century, 2005)

5. GARTEUR AD/AG52  GARTEUR (Group for Aeronautical Research and Technology in EURope, www.garteur.org)www.garteur.org  Multinational organization that performs collaborative research in the field of aeronautics to improve technological competence of the European Aerospace Industry.  Action Group on Surrogate-based global aerodynamic design optimization  Objectives: ﺤ Exploit the capability to perform a broad exploration of the design space ﺤ Evaluation of different global optimization strategies and their feasibility for shape design ﺤ Evaluation of different surrogate modeling techniques for fast evaluation ﺤ Demonstration of the applicability and CPU time savings by the use of surrogate-based global optimization.  Participants: ﺤ 2 industries (AIRBUS Military, SAAB) ﺤ 4 research establishments (INTA, CIRA, FOI, ONERA) ﺤ 3 universities (UAH, UNIS, VUT)  Expected duration: 2013-2016 Task 1: Basic configurations EG67-TC1.1RAE2822 RANS airfoil EG67-TC1.2DPW1 EULER wing Task 2: Industry-relevant configurations EG67-TC2.1DPW1 RANS wing Task 3: Best-practice guidelines To give a clear statement about the possibilities and restrictions in using SBGO methods. To facilitate their use in aeronautic industries Task 2 Industrial-relevant configurations Task 1 Basic configurations Task 3 “Best Practice” Guidelines To make comparatively studies of partners’ simulations to highlight the benefits and drawbacks of different SBGO methods To validate the experience gained from T1 in designing industrial-relevant configurations T1.1 Surrogate validation T1.2 Optimization comparison Motivation (2/5) GARTEUR AD/AG52 5/23

6. Motivation (3/5) GARTEUR AD/AG52 www.ag52.blogspot.com 6/23

7. 7/23 SVM EA Evolutionary Algorithm (EA) EA Robust search on noisy functions. No need for gradient computation. Global optimization method Handle non-continuos functions Efficient exploration of multimodal functions Motivation (4/5) Why EA+SVM?

8. 8/23 SVM EA Support Vector Machines (SVM) Prediction Regression method Machine learning method. Tools for: Training methods. Robust models. Automatic parameter search. Machine learning method. Tools for: Training methods. Robust models. Automatic parameter search. SVM Motivation (5/5) Why EA+SVM? Estimation SVMs as metamodels: ﺤ Have demonstrated high accuracy for a large number of tests in the literature ﺤ Black-box approach  no physics-based modelling ﺤ Flexibility (SVMs can be adapted to every problem by little adjustment, kernel and hyper-parameters ) But: ﺤ The time for training the SVM model can be high (selection of proper hyper-parameters)  efficient search algorithms ﺤ Efficiency is problem-dependent  Motivation: Test the performance of EA+SVM for aerodynamic shape design

9. 9/23 EA SVM CFD Aerodynamic shape design INTA Fluid Dynamics Branch Experience in applying fluid dynamics mainly to aeronautical configurations. ﺤDevelopment and application of CFD tools. ﺤAerodynamic load calculation. ﺤDesign for optimization of aerodynamics loads. ﺤAnalysis and design of wind energy generators: aerodynamic computation on wind turbines and blades. ﺤAir safety studies: effects of adverse weather conditions (heavy rain, ice accretion). ﺤSupport for wind tunnel test. ﺤSupport for the certification of civil and military aircraft. ﺤImplementation of transition and turbulence models. ﺤAerodynamic support to INTA UAV designs. GHEODE Research Group Dep. Signal Theory & Communications ﺤ Artificial Intelligence ﺤ Soft-Computing techniques: evolutionary computing, harmony search, particle swarm, neural computing algorithms (neural networks, support vector machines, extreme learning machines…) ﺤ Applications in many problems in Science and Engineering: Renewable energy, environment (predicting the wind, temperature, precipitation), prediction and optimization problems in insurance, communications network design, aerodynamic coefficient prediction and design ﺤ Dr. Leopoldo Carro and Dr. Sancho Salcedo Approach overview (1/4) Multi-disciplinary research team

10. Approach overview (2/4) Method Flowchart 10/23 Proposed method: The Intelligent Estimation Search with Sequential Learning (IES-SL) Adaptive sampling directly focused on the optimization search Two steps-method: 1-) Initial surrogate model construction: ﺤ A priori sampling of the design space ﺤ CFD simulation of the selected samples ﺤ Training the SVMs network with the database ﺤ Construction of a first surrogate model 2-) Model enrichment and optimization: ﺤ The optimization algorithm searches for the optimum with the surrogate model  estimation for the real optimum position. ﺤ The estimated optimum is then evaluated with the CFD solver, obtaining a new pair (design, high fidelity performance) that will enrich the database. ﺤ The surrogate is updated by adjusting it to the complete database and the cycle is finished, starting again the search for the new sample

11. Proposed method: The Intelligent Estimation Search with Sequential Learning (IES-SL) Approach overview (3/4) Method Flowchart – Specific tools 11/23 Optimizer (Evolutionary Algorithm) Optimizer (Evolutionary Algorithm) Optimized geometry Surrogate model (SVM network - libSVM) Surrogate model (SVM network - libSVM) CFD solver (DLR TAU) CFD solver (DLR TAU) Training dataset Limit of CFDs? Initial geometry + 4 random initial points Initial geometry + 4 random initial points Yes No Estimated optimum

12. Approach overview (4/4) Considerations on the EA and SVM 12/23 Evolutionary algorithm: ﺤ Solution coding: ﺤ Solutions are coded as a vector of real values from 0-1. ﺤ Each element represents the value of a normalized design parameter. ﺤ Selection operator: ﺤ Those individuals with fitness function lower than the mean population fitness are discarded. ﺤ Crossover operator: A new individual is generated from the values of two parents randomly selected from the survival population: the value of one of the parents (with probability 0.5) is applied. ﺤ Mutation operation: The values of each new individual are mutated with probability 1/Np (Np is the number of parameters to be optimized). The operator changes the initial individual by using the formula: SVM: ﺤ A radial basis function has been used as the kernel function ﺤ Improved hyper-parameters search algorithm ( based on search space reductions, Ortiz et al., Neurocomputing 2009) ﺤ libSVM (L1-SVR, ɛ -insensitive loss function) gk: fitness of the kth individual ξ: number of individuals in the population Vi: represents one of the paremeters to optimize U: uniform noise [0,1] α: is a value which represents the mutation level (1 (strong change), 0.1, 0.01 (small change) with probability 1/3)

13. Test cases definition (1/2) 2D RAE2822 airfoil & 3D DPW-W1 wing 13/23 #Design variables Flow conditions DP1 Flow conditions DP2 Objective function(OF) Aerodynamics constraints and penalties Geometric constraints RAE 2822 Airfoil 6,8,10, 12,14,16, 18 M=0.734 Re=6.5 x 10 6 AoA=2.8 o SA M=0.754 Re=6.2 x 10 6 AoA=2.12 o SST Limit: +/- 20% of the initial control points values DPW-W1 wing 12,18,24, 30, 36 M=0.8 AoA=0 0 Euler - ﺤ A total budget of 100 CFD computations for RAE 2822 airfoil and 300 CFD computations for DPW-W1 wing was defined

14. Test cases definition (2/2) NURBS-based geometry parameterization 14/23 Design variables are the vertical displacements (z axis) of the control points. Non-Uniform Rational B-Splines (NURBS) ﺤFlexible enough to represent a large family of geometries providing a global parameterization with a smooth surface while still maintaining the locality in the deformation (each control point has a zone of influence) ﺤStandard (Easier integration, the optimized surface at the end of the optimization process has the correct format to feed directly the CAD and grid generation applications)

15. Surrogate model construction & validation MSE values 15/23 ﺤA 10-fold cross validation strategy has been applied to measure its prediction capabilities. ﺤAs the choice of the sampling fold decomposition is crucial for error estimation, the validation procedure was repeated 5 times using different decompositions (the MSE values are provided) ﺤThe proposed sampling method is compared to a Latin Hypercube Sampling (LHS) method, showing that at this stage, there are not significant differences in accuracy. ﺤThe surrogate model has been built to predict the corresponding objective function (Min Cd/Cl), which was normalized with its initial value. ﺤThe maximum number of CFD runs allowable for model construction is: RAE2822  100 CFD runs DPW  300 CFD runs Sampling method ProblemObjective C L constraint C M constraint MSE EA-SVMRAE 2822min (C D / C L )No 0.0766 EA-SVMRAE 2822min (C D / C L )NoYes0.0599 EA-SVMRAE 2822min (C D / C L )Yes 0.2089 EA-SVMDPW-W1min (C D / C L )Yes 0.0072 LHSDPW-W1min (C D / C L )Yes 0.0078 EA-SVMDPW-W1min (C D / C L )YesNo0.0075 LHSDPW-W1min (C D / C L )YesNo0.0075

16. Aerodynamic shape optimization (1/5) RAE2822 airfoil 16/23 ﺤResults show an optimum within 10 DV, reaching an improvement by ~40%, while fulfilling the constraints imposed to C L and C M. #dv OF baseline1 60.7481 80.6113 100.6048 120.6077 140.6051 160.6323 180.66511

17. Aerodynamic shape optimization (2/5) RAE2822 airfoil 17/23

18. Aerodynamic shape optimization (3/5) DPW wing 18/23 ﺤResults show an optimum within 30 DV, reaching an improvement by ~30%, while fulfilling the constraints imposed to C L and C M. #dvOF baseline1 12 dv0.7373 18 dv0.7069 24 dv0.6964 30 dv0.6962 36 dv0.7361

19. Aerodynamic shape optimization (4/5) DPW wing 19/23

20. 20/23 The following formula approximates the computational time required by the proposed approach as a combination of the simulation time, the training time and the optimization time: Execution time considerations on a Linux x86_64 computational cluster Aerodynamic shape optimization (5/5) Execution time considerations The most time-consuming step in the optimization process is the simulation (CFD solver). The current implementation is parallel in each CFD simulation (domain decomposition), but the inherent parallelism of EA methods is not yet fully employed (only one sample is simulated by CFD in each optimization cycle). RAE2822 (RANS, 27k points) DPW-W1 (Euler, 427k points) Training time~ 10 s. Optimization time~ 60 s. Simulation time30 s.+150 s. (8 processors)300 s. (8 processors) TOTAL APPROX6.8 hours30.7 hours

21. EA+SVMs aerodynamic shape design:  This work presented an EA+SVMs global optimization strategy using “The Intelligent Estimation Search with Sequential Learning (IES-SL)”  The aim of this work is to provide a comprehensive study about how sensitive this approach is to the number of control points  The proposed approach has been tested on the optimization of a RA2822 airfoil and a DPW wing, showing promising results.  RAE2822: An optimum within 10-14 DV reaching an improvement by ~40% on OF  DPW-W1: An optimum within 18-30 DV reaching an improvement by ~30% on OF Future work within GARTEUR AD/AG52:  Control points location sensitivity. (on progress)  DPW-W1 in viscous flow conditions (EUROGEN 2015) √  Optimization of a 2D circle, in order to test the capability of this method to reach innovative shapes, when considering different objective functions. (on progress) Conclusions Cylinder (Mach=0.3, Re=1000, 14 DVs, OF: Minimize Cd with constant volume) DVs can move +/- 95% of their initial value (x and z movements of the control points) 21/22

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23. INFLUENCE OF GEOMETRY PARAMETERIZATION IN AERODYNAMIC SHAPE DESIGN OF AERONAUTICAL CONFIGURATIONS BY EVOLUTIONARY ALGORITHMS Daniel González Juárez Esther Andrés Pérez Mario Jaime Martin Burgos Fluid Dynamics Branch INTA/ISDEFE Email: gonzalezjd@inta.es eandres@isdefe.es martinbj@inta.es Leopoldo Carro Calvo Sancho Salcedo Sanz Dep. Signal Theory and Communications University of Alcalá Email: leopoldo.carro@uah.es sancho.salcedo@uah.es 23/23