1. Efficient Design & Analysis of Variable-Fidelity Experiments for High Dimensional Aerodynamic Data Space Design & Analysis of Variable-Fidelity Multi-Objective Experiments for High Dimensional A 1 Airbus-UPM (AIRUP) Marie-Curie ESR, PhD Student; yondo.raul@upm.es, guy-raoul.yondo-mine@airbus.com http://www.airup-itn.eu/fellows/yondo-mine-guy-raoul Raul Yondo 1 UPM Madrid 30.10.2015 Introduction Background, Rationale &Scope Brief introduction to DoEs & SUMOs Releases & Research Trends Closing remarks

2. Airbus - UPM European Industrial Doctorate in Mathematical Methods Applied to Aircraft Design Introduction Background, Rationale &Scope Brief introduction to DoEs & SUMOs Releases & Research Trends Closing remarks UPM Introduction RAUL YONDO raul.yondo@upm.es guy-raul.yondo.mine@airbus.com http://www.airup-itn.eu/fellows/yondo-mine-guy-raul SUPERVISORS Prof. Eusebio Valero Dr. Esther Andrés Dr. Lars Hansen BACKGROUND MSc. Aeronautical Eng. MSc. CFD BSc. Mechanical Eng. BSc. Mathematics 3 years in Aero industry Madrid 30.10.2015

3. UPM Background, Rationale & Scope Introduction Background, Rationale & Scope Brief introduction to DoEs & SUMOs Releases & Research Trends Closing remarks Madrid 30.10.2015

4. UPM Brief introduction to DoEs & SUMOs DoE SIMULATION Evaluation at sample points, Snapshots (computer code,…) Introduction Background, Rationale &Scope Brief introduction to DoEs & SUMOs Releases & Research Trends Closing remarks Madrid 30.10.2015

5. A Comprehensive review (A joint paper with K. Bobrowski, E. Andrés & E. Valero) A Review of Surrogate Modeling Techniques for Aerodynamic Analysis and Optimization: Current Limitations and Future Challenges in Industry – EUROGEN 2015 Proceedings Paper contents:  Classical & Modern Design of Experiments  Surrogate Models –Data fits (QI, MARS, GPR a.k.a Kriging, SVR, RBF, ANN…) –Variable-Fidelity Models (a.k.a Multi-Fidelity or Multi-Complexity Models) –Reduced Order Models (POD, Manifold Learning…) –Hybrid Models  Global & Local Surrogate-Based Optimization - SBO (Sequential sampling, validation metrics, sensitivity analysis, constraints handling, …)  Surrogates in Aircraft Aerodynamic Industries: Use, Limitations & Future Challenges UPM Releases Smart sampling LSQ-ROM & CBA Introduction Background, Rationale &Scope Brief introduction to DoEs & SUMOs Releases & Research Trends Closing remarks Madrid 30.10.2015

6. Smart sampling  investigate the influence of a priori sampling on surrogates accuracy There are hands-on approaches when one think of smart sampling, among which:  Starting with quite good ‘space-filling’ approaches at the a priori design stage   Taking advantage of some a priori knowledge of the problem physics to sample specific areas of the design space   Using schemes like EA, PSO, SA, etc to optimally sample the design space where necessary during the sequential sampling process, starting with very few training points at the a priori design stage.   Research trends:  Use of space-filling design ‘uniformity’ metrics  Proper analytical test cases + Data fit surrogate models  Model accuracy metrics to assess the results: IMSE, (R)MSE, MAE, UQ, Execution time…  Possible extension: real aerodynamic cases, constrained test cases, sequential sampling… UPM Expensive with complex industrial aerodynamic problems Introduction Background, Rationale &Scope Brief introduction to DoEs & SUMOs Releases & Research Trends Closing remarks Releases Smart sampling LSQ-ROM & CBA Madrid 30.10.2015

7. Efficient ‘Physics-Based’ Reduced-Order Model Variable-Fidelity Surrogate  Fidelity  degree to which a model captures the physics of a phenomenon of interest.  VFM = LF MODEL + CORRECTION (THROUGH BRIDGE/CALIBRATION… WITH HF)  VFM & HF need to be sufficiently well correlated (especially for nonlinear problems)  LFM needs to capture the governing physics of the HFM.  LFM in aerodynamics are mainly developed based on one or the combination of the following:  Simplified physics, Coarse discretization, Relaxed convergence criteria. UPM Madrid 30.10.2015 Increasing Fidelity Empirical Methods Panel/VL Methods Euler/NS WTT Flight Test AERODYNAMICS Introduction Background, Rationale &Scope Brief introduction to DoEs & SUMOs Releases & Research Trends Closing remarks Releases Smart sampling LSQ-ROM & CBA

8. UPM Madrid 30.10.2015 An optimization problemDR & Snapshots reconstruction L 2 Norm Introduction Background, Rationale &Scope Brief introduction to DoEs & SUMOs Releases & Research Trends Closing remarks Releases Smart sampling LSQ-ROM & CBA

9. UPM Madrid 30.10.2015 Introduction Background, Rationale &Scope Brief introduction to DoEs & SUMOs Releases & Research Trends Closing remarks Releases Smart sampling LSQ-ROM & CBA

10. UPM Madrid 30.10.2015 Introduction Background, Rationale &Scope Brief introduction to DoEs & SUMOs Releases & Research Trends Closing remarks Releases Smart sampling LSQ-ROM & CBA @Courtesy of Ralf Zimmermann

11. UPM Madrid 30.10.2015 Introduction Background, Rationale &Scope Brief introduction to DoEs & SUMOs Releases & Research Trends Closing remarks Releases Smart sampling LSQ-ROM & CBA CLCL CDCD TAU-CFD 0.7380.0722316.6-0.0203-32.95 LSQ-ROM 0.726 (-1.63%) 0.0720 (-0.275%) 313.1 (-1.11%) -0.0188 (-7.45%) -33.49 (+1.65%)

12. Research Trends:  Use of inequality constraints in the Nonlinear LSQ optimization problem  Use of GEK (Co-Kriging) to improved the prediction of the constraint bounds  Develop methods to restrict the POD coefficients to a 'physically reasonable' range  Optimal snapshots prediction for LSQ-ROM predictions using GEK  Automated detection of the correlation between the high and low fidelities  CBA as a stopping criteria UPM Madrid 30.10.2015 Introduction Background, Rationale &Scope Brief introduction to DoEs & SUMOs Releases & Research Trends Closing remarks Releases Smart sampling LSQ-ROM & CBA

13. Closing remarks UPM Madrid 30.10.2015 Thanks for listening! Remarks or Questions? Introduction Background, Rationale &Scope Brief introduction to DoEs & SUMOs Releases & Research Trends Closing remarks