The paper investigates a robust optimisation for detail design of active shock control bump on a transonic Natural Laminar Flow (NLF) aerofoil using a Multi-Objective Evolutionary Algorithm (MOEA) coupled to Computational Fluid Dynamics (CFD) software. For MOEA, Robust Multi-objective Optimisation Platform (RMOP) developed in CIMNE is used. For the active shock control bump design, two different optimisation methods are considered; the first method is a Pareto- Game based Genetic Algorithm in RMOP (denoted as RMOGA). The second method uses a Hybridised RMOGA with Game-Strategies and a parallel computation for high performance computation. The paper not only shows how a shock control bump approach coupled to CFD improves aerodynamic performance of original transonic aerofoil but also it shows how high performance computation with applying Hybrid- Game and parallel computation increase the efficiency of optimisation in terms of computational cost and result accuracy.Postprint (published version

Bugeda Castelltort, Gabriel

Lee, Dong Seop

Oñate Ibáñez de Navarra, Eugenio

Periaux, Jacques Francis

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Robust Active Shock Control Bump Design Optimisation usingParallel Hybrid-MOGAD.S. Lee∗, G. Bugeda∗,∗∗, J. Periaux∗,∗∗ and E. Onate∗,∗∗Corresponding author: dslee@cimne.upc.edu∗ International Center for Numerical Methods in Engineering (CIMNE), Barcelona, Spain.∗∗ Universitat Politecnica de Catalunya, Barcelona, Spain.Abstract: The paper investigates a robust optimisation for detail design of activeshock control bump on a transonic Natural Laminar Flow (NLF) aerofoil using aMulti-Objective Evolutionary Algorithm (MOEA) coupled to Computational FluidDynamics (CFD) software. For MOEA, Robust Multi-objective Optimisation Plat-form (RMOP) developed in CIMNE is used. For the active shock control bump de-sign, two different optimisation methods are considered; the first method is a Pareto-Game based Genetic Algorithm in RMOP (denoted as RMOGA). The second methoduses a Hybridised RMOGA with Game-Strategies and a parallel computation forhigh performance computation. The paper not only shows how a shock control bumpapproach coupled to CFD improves aerodynamic performance of original transonicaerofoil but also it shows how high performance computation with applying Hybrid-Game and parallel computation increase the efficiency of optimisation in terms ofcomputational cost and result accuracy.Keywords: Parallelization, Computational Fluid Dynamics, Shock Control Bump,Multi-Objective Evolutionary Algorithms, Game Strategies.1 IntroductionComputational Fluid Dynamics (CFD) has become an important tool in optimisation and has seen suc-cess in many real world applications. Most important among these is in the optimisation of aerodynamicsurfaces. Most of these have been carried out for a given set of input parameters such as free streamMach number and angle of attack. One cannot ignore the fact that Multi-Objective (MO) and Multidis-ciplinary Design Optimisations (MDO) in aerospace engineering frequently often deal with situationswhere the design input parameters and flight/flow conditions have some amount of uncertainty attachedto them. This challenge can be solved by using a robust/uncertainty design approach which can producehigh quality solutions in terms of magnitude of performance and its sensitivity at a variable uncertaintydesign parameters [1, 2, 3]. However, one major drawback of using robust design method is extensivecomputational cost. Therefore it is inevitable to conduct the optimisation in high performance (parallel)computation while innovating the optimisation techniques.This paper develops a methodology for robust multi-objective design optimisation. The methodol-ogy couples CFD software, robust/uncertainty design strategy, and a parallelised hybrid evolutionaryoptimiser, to produce a set of reliable optimal designs which have higher performance and lower sensi-tivity. In this paper, an Active Flow Control (AFC) device design is considered as a robust optimisation1application.One of important challenges in aeronautical engineering is to control flow over a transonic aero-foil/wing to reduce drag while increasing aerodynamic performance (L/D). The drag reduction can savemission operating cost, condense critical aircraft emissions and increase the performance envelope ofthe aircraft. Such drag reduction can be achieved by implementing a type of AFC called Shock ControlBump (SCB) [4, 5] without the need to design a new aerofoil or wing planform shape.The approach is demonstrated on its application; robust design optimisation of SCB on the suctionside of Natural Laminar Flow (NLF) aerofoil; RAE 5243 to minimise the total transonic drag at thevariable Boundary Layer Transition (BLT) positions and lift coefficients (250 samples obtained by LatinHypercube Sampling [9]). This design problem is solved by using two different Multi-Objective Evolu-tionary Algorithms (MOEAs); the first is the Genetic Algorithm (GA) [6, 7] in Robust Multi-objectiveOptimisation Platform (RMOP) (denoted as RMOGA). The second method uses a hybridised GA withNash-Game [8] and parallel computation [10] (denoted as HPRMOGA). The paper will show;• how to control the design quality under considering uncertain design parameters,• how to control the transonic flow on a current aerofoil using a SCB,• how to improve the optimisation efficiency using Hybrid-Game coupled to parallel computation.The rest of paper is organised as follows; Section 2 considers robust design optimisation of detaileddesign of Active Shock Control Bump using RMOGA and HPRMOGA.2 Robust optimisation for detailed design of Shock Control BumpProblem De f initionThe problem considers a detailed robust design optimisation of shock control bump under consideringuncertainty parameters including Boundary Layer Transition (BLT) positions and lift coefficients (250samples in total) using RMOGA and HPRMOGA. The number of CPUs usage for RMOGA (Pareto-Game) and HPRMOGA (Pareto and Nash games) are one and ten CPUs respectively in Dell PowerEdge6850 (Intel(R) Xeon(TM) CPU 16 × 3.20GHz and 32GB RAM) machine. The objectives are to min-imise the total drag and to minimise its sensitivity as shown Equations (1) and (2); HPRMOGA employsthree players; Pareto-Player (considering fitness functions 1 and 2 at 250 samples for uncertainty), Nash-Player1 (considering fitness function 1 at 25 samples for uncertainty) and Nash-Player 2 (consideringfitness function 2: 25 samples for uncertainty). The stopping criterion is based on the predefined elapsedtime; RMOGA and HPRMOGA are stopped after 50 and 25 hours respectively.f1 = min(µCd) =1N×MN∑iM∑jCdi j (1)f2 = min(σCd) =1N×M−1N∑iM∑j(Cdi j−µCd)2(2)Stopping Criterion;ElapsedTimeRMOGA ≤ 50Hours, ElapsedTimeHPRMOGA ≤ 25Hoursat uncertainty conditions; Boundary Layer Transition positions (BLT) and lift coefficients (Cl)µBLT = 0.3782 and σBLT = 0.0802 at a range of BLT = [0.25 : 0.50]µCl = 0.7462 and σCl = 0.0398 at a range of BLT = [0.67 : 0.82]where N and M are number of samples for Boundary Layer Transition positions and lift coefficients (Cl)respectively i.e. N = 10 and M = 25.Numerical ResultsResulting Pareto front obtained by RMOGA and HPRMOGA are compared to the baseline design asshown in Figure 1. Both RMOGA and HPRMOGA produce a set of solutions which have lower meantotal drag and sensitivity at variable BLT andCl conditions when compared to the baseline design. Eventhough the computational cost of HPRMOGA is only half of RMOGA, Pareto member 1 (the best solu-tion for objective 1) obtained by HPRMOGA produces lower mean total drag when compared to Paretomember 1 obtained by RMOGA. The convergence history obtained by RMOGA and HPRMOGA areplotted to compare the computational efficiency as shown in Figure 2 where x-axis is normalised by eachtotal function evaluation. It can be seen that HPMOGA saves upto 75% of RMOGA computational costwhile producing lower converged value for fitness function 1.Figure 1: Pareto optimal front. Figure 2: Computational cost comparison.Pareto member 1 obtained by RMOGA (denoted as RMOGA PM1), and Pareto members 1 and2 obtained by HPRMOGA (denoted as HPRMOGA PM1 and PM2) are selected as a compromisedsolution to proceed more detailed statistical analysis. The mean and standard deviations of total dragobtained by compromised solutions are compared using Cumulative Distribution Function (CDF) andProbability Density Function (PDF) as shown in Figures 3 and 4. It can be seen that all solutionsobtained by RMOGA and HPRMOGA have lower mean total drag when compared to the baselinedesign. In addition, all optimal solutions obtained by RMOGA and HPRMOGA produce lower dragsensitivity when compared to the baseline design as shown in Figure 4.Figure 5 compares the pressure contour obtained by Pareto member 1 from both RMOGA andHPRMOGA at the mean BLT and Cl i.e. µBLT = 0.3782, µCl = 0.7462. It can be seen that the optimalsolution obtained by HPRMOGA reduces the total drag by 26% while improving L/D by 34.2%.References[1] G. Taguchi and S. Chowdhury. Robust Engineering. McGraw-Hill, New York, 2000.[2] D. S. Lee, L. F. Gonzalez, K. Srinivas and J. Periaux. Robust Design Optimisation using Multi-Objective Evolutionary Algorithms International Journal Computers and Fluids, Vol 37. Issue 5,pages 565-583, ISSN 0045-7930. 2008.Figure 3: Pareto optimal front. Figure 4: Computational cost comparison.Figure 5: Cp contour comparison.[3] D. S. Lee, L. F. Gonzalez, K. Srinivas and J. Periaux. Robust Evolutionary Algorithms forUAV/UCAV Aerodynamic and RCS Design Optimisation International Journal Computers andFluids, Vol 37. Issue 5, pages 547-564, ISSN 0045-7930. 2008.[4] P. R. Ashill, L. J. Fulker and A. Shires. A novel technique for controlling shock strength of laminar-flow aerofoil sections. Proceedings 1st Europian Forum on Laminar Flow Technology, pp. 175-183,Hamburg, Germany, DGLR, AAAF, RAeS, March 16-18 1992.[5] N. Qin, Y. Zhu and S. T. Shaw. Numerical Study of Active Shock Control for Transonic aerody-namics International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 14 No. 4, pp444-466, 2004.[6] Z. Michalewicz. Genetic Algorithms + Data Structures = Evolution Programs, Artificial Intelli-gence, Springer-Verlag, 1992.[7] K. Deb. Multi-objective genetic algorithms: Problem difficulties and construction of test problemsEvolutionary Computation Journal, Vol. 7 (3), pages 205-230, 1999.[8] D. S. Lee, J. Periaux and L. F. Gonzalez. UAS Mission Path Planning System (MPPS) UsingHybrid-Game Coupled to Multi-Objective Design Optimizer Journal of Dynamic System, Mea-surement and Control, Transactions of ASME, ISSN 00220434, Vol. 132, Iss. 4. 041005-1 -11,July 2010.[9] R. L. Iman, J. M. Davenport and D. K. Zigler. Latin Hypercube Sampling (Program UserâA˘Z´sGuide), Dept. of Energy, Sandia Laboratories, Albuquerque (N.M.), Jan., 1980.[10] R. van der Pas. An Overview of OpenMP 3.0. Tutorial - International Workshop on OpenMP 2009(IWOMP), Dresden, German, June 3, 2009.

Robust active shock control bump design optimisation using parallel hybrid-MOGA

The paper investigates a robust optimisation for detail design of active shock control bump on a transonic Natural Laminar Flow (NLF) aerofoil using a Multi-Objective Evolutionary Algorithm (MOEA) coupled to Computational Fluid Dynamics (CFD) software. For MOEA, Robust Multi-objective Optimisation Platform (RMOP) developed in CIMNE is used. For the active shock control bump design, two different optimisation methods are considered; the first method is a Pareto- Game based Genetic Algorithm in RMOP (denoted as RMOGA). The second method uses a Hybridised RMOGA with Game-Strategies and a parallel computation for high performance computation. The paper not only shows how a shock control bump approach coupled to CFD improves aerodynamic performance of original transonic aerofoil but also it shows how high performance computation with applying Hybrid- Game and parallel computation increase the efficiency of optimisation in terms of computational cost and result accuracy

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Robust active shock control bump design optimisation using parallel hybrid-MOGA

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