MULTI-OBJECTIVE OPTIMISATION IN MODEFRONTIER FOR AERONAUTIC APPLICATIONS

Transcription

1 EVOLUTIONARY METHODS FOR DESIGN, OPTIMIZATION AND CONTROL P. Neittaanmäki, J. Périaux and T. Tuovinen (Eds.) CIMNE, Barcelona, Spain 2007 MULTI-OBJECTIVE OPTIMISATION IN MODEFRONTIER FOR AERONAUTIC APPLICATIONS Alberto Clarich * ESTECO srl Area Science Park Padriciano 99, Trieste, Italy clarich@esteco.it web page: Carlo Poloni Department of Energetics University of Trieste Via Valerio 10, Trieste, Italy poloni@units.it web page: Abstract. This paper shows how the optimisation environment modefrontier is applied to solve multi objective problems in aeronautic field. These problems include solution robustness on uncertain definition of parameters, and automatic and distributed communication between parametric CAD and simulation software. Two application cases are presented: first, a 3D wing defined and parameterised in CATIA V5, is to be optimised for two different mission points, clean wing in cruise transonic regime and opened high-lift devices for subsonic take-off, following aerodynamic criteria and constraints. Second, the shape of a transonic airfoil is to be optimised under uncertainties of flight conditions, in order to optimise not only the design point, but to keep efficiency as well after operating condition fluctuations. Key words: Multi objective optimisation, Robustness analysis, CAD/CAE distributed environment, Game Theory, Metamodels, Evolutionary Algorithms, Aeronautic applications 1 INTRODUCTION Multi objective optimisation, including solution robustness on uncertain definition of parameters, in an automatic and distributed environment that allows direct communication between parametric CAD and simulation software, is becoming continuously a key factor in aeronautic industries and not only. This paper shows how the optimisation environment modefrontier allows to implement practically this methodology, whatever software is used in the simulation phase; two different applications will be illustrated. modefrontier [3] is a multi-objective design environment software that allows the integration of any commercial or built-in house computational code (CAD, FEM, CFD, etc..) into a common environment, in order to run automatically a series of designs, scheduled by the available optimisation algorithms, until the defined objectives are satisfied.

2 A. CLARICH, C.POLONI/ Multi-objective aeronautic optimization with modefrontier In this modular environment, each component of the optimisation, including input variables, input files, scripts to run the commercial software, output files, output variables and objectives, is defined as a node to be connected to the other components. In this way, the complete logic flow from CAD parameterisation to performances evaluation is defined by the user, that can select among several available optimisation algorithms, accordingly to the defined objectives; they include Genetic Algorithms, Evolutionary Algorithms, Game Strategies [1], Gradient-based Methodologies, Robust Design Optimisation as well as main DOE (Design Of Experiments) algorithms (Sobol, Factorials, Latin Square, Montecarlo, D-Optimal, etc.). These algorithms drive automatic series of simulations, allowing when available distributed and parallel computations to fully exploit the computational resources, until the objectives are met. In addition, the influence of all the parameters in the process can be analysed in detail by the use of statistical analysis (correlation matrix, t-student, etc. ) and response surface methods (Kriging, Neural Networks, Radial Basis Functions, SVD, Parametric, Gaussian, etc.), that can be also used to reduce the number of computations required in the optimisation, allowing an extrapolation of the results. In particular, Game Strategies and Response Surface Methodologies are used to reduce the global number of design evaluations required by a Robust Design Analysis (design under uncertainties or fluctuations of input parameters), as it will be illustrated in the second application of this paper. 2 3D WING MULTI-POINT OPTIMISATION 2.1 Problem definition In fig.1 below we can see a representation of the two design points of the optimisation problem. The original wing is defined by three main sections derived by the RAE-16 airfoil, and the geometry of these sections should be modified in order to minimise the drag of the smooth configuration (a) for a fixed angle of attack (2 ) and transonic Mach number (0.7), and to maximise the efficiency (lift/drag ratio) of the three-element deployed configuration (b) that corresponds to the take-off mission point for another fixed angle of attack (17.12 ) and Mach number(0.12; Re= for both configurations). a) b) Figure 1 Smooth transonic design point (a) and three-element deployed design point (b) There is an aerodynamic constraint on the lift coefficient for the transonic point, since it should be kept greater than the original one (0.18), another constraint on the lift

3 EVOLUTIONARY METHODS FOR DESIGN, OPTIMIZATION AND CONTROL (EUROGEN 2007) coefficient for the subsonic point (0.78) and also a geometric constraint on the maximum thickness that should be greater than the original one (16% of the chord length). 2.2 CAD Parameterisation The whole geometry model is defined inside Catia V5 CAD system; in particular, the geometry of the two mission points is controlled by two set of variables: the first 30 ones control the three main section shapes, while the further 26 ones define the internal shape and the position of the aerodynamic flaps deployed from the smooth wing. About the first set of 30 variables, there are 10 parameters for each of the three main sections (root, kink, tip). For each one of the three sections, the 10 parameters controls the control points co-ordinates of four NURBS curves [1], that define the upper and lower side of the profile. Z1 Z2 X345 Z6 Z7 Z1d Z2d Zmax Z6d Z7d Figure 2 : Airfoil section: it is defined by 4 NURBS, the second one is represented here About the second set of 26 variables, 13 ones of them parameterise the aerodynamic elements located between the root and kink sections, while the other 13 ones are relative to the elements located between the kink and tip sections. X1s Xc X1f Dx_slat alfa_slat X2s Dz_slat Dx_flap X2f alfa_flap Figure 3 : Parameterisation of shape and position of the flaps deployed from the smooth section Dz_flap For each subset of 13 variables, five of them define the shape of the flap and slat that are detached during the subsonic mission point (fig.3, left), in order to increment the lift coefficient, while the other 6 ones define respectively the position (translation and rotation) of the same aerodynamic elements (fig.3, right).

4 A. CLARICH, C.POLONI/ Multi-objective aeronautic optimization with modefrontier 2.3 modefrontier optimization workflow Direct CATIA node Link each optimisation variable to a parameter defined in the CATIA model Batch script to run mesher Figure 4 : modefrontier optimisation workflow Figure 4 above illustrates how modefrontier can, in its modular workflow, drive this optimization problem. Two applications chains are defined, from top to bottom, in parallel: they are relative to the simulation of the two mission points (cruise at left and take-off at right) for each design proposed during the optimization. The input variables are defined in an opportune subsystem, and they are linked directly to the two CATIA model nodes, that are updated automatically for each design. The output file in IGES format is sent by a relative transfer node to the following application, a UNIX batch command that run the mesher code, ICEM, that rebuild the mesh over the IGES file, following instructions recorded in a macro file (during the creation of the original model mesh). In a similar way, the output file, an.inp file, is transferred to the following application, a script that run in batch StarCD for the CFD evaluations. Output variables to evaluate the design fitness, drag coefficient in cruise condition and efficiency in take-off conditions, are automatically extracted from the StarCD output file accordingly to the specified pattern. Once the modular workflow is built, the DOE and optimisation algorithm can be chosen and the optimisation automatically run. 2.4 Optimisation results: MOGT + GA strategy In this application, a combined strategy using the algorithms available in modefrontier has been used. First, MOGT (Multi-Objective Game Theory) algorithm has been run [1]. The philosophy of this algorithm is that two players divide the objectives and the search space. Each player tries to optimise his own objective applying an efficient and fast mono-objective algorithm, Downhill Simplex [1], sharing

5 EVOLUTIONARY METHODS FOR DESIGN, OPTIMIZATION AND CONTROL (EUROGEN 2007) in several steps the best variables found, and influencing in this way the search of the other player. During the optimisation, the decomposition of the variable space is updated accordingly to the statistical significance of the variable to the objective, in such a way that if a variable is not significant for one objective, it is given to another player. The solution is an equilibrium point, that represent the best compromise for the two objectives. After 300 designs, the (Nash) equilibrium pint has been found, but in order to extend the results into a wider Pareto frontier, or set of not-dominated designs, the best results from MOGT optimisation phase have been used to initialize a MOGA (Multi-Objective Genetic Algorithm) algorithm of other 200 designs (4 generations of 50 designs). The results are reported in table below. Since a cluster of 8 CPUs has used and 1 analysis takes 2 hs, about 5 days have been spent to obtain the results. Pareto front Nash point Original point original Nash/Simplex best Transonic drag (-4%) Subsonic lift/drag (+18%) Figure 5 : optimisation results (transonic drag in abscissa, subsonic efficiency in ordinate) 3 ROBUST DESIGN OF TRANSONIC AIRFOIL 3.1 Problem definition The objective of this test case is the robust design optimisation [2] of the RAE2822 airfoil under uncertainties of free stream Mach number and angle of attack, regarding drag reduction, with constraints on lift and momentum coefficients. The design point is defined by Mach=0.73 and angle of attack α=2 while, due to the not deterministic events (like gusts of wind, atmospheric turbulence, instable conditions of flight, manoeuvre inaccuracy, etc...), the range of operating conditions is fixed to α=2±0.5 and Mach=0.73±0.05 (Re= ) In order to evaluate the robustness of each candidate solution proposed by the optimisation algorithm, we need to compute a set of sampling point around the nominal design, varying the values of Mach and angle of attack accordingly to stochastic definition of uncertainty (Montecarlo sampling): from the samples, mean and standard deviation of the output variables will be computed. 3.2 modefrontier workflow Also in this case modefrontier allows the definition of a modular workflow, of the Robust Design sampling policy and the definition of optimisation algorithms. Using the Kriging RSM, modefrontier create a metamodel that can approximate the response of the sampling points for each design: only 10 points for each design are necessary for the training.

6 A. CLARICH, C.POLONI/ Multi-objective aeronautic optimization with modefrontier Figure 6 : modefrontier optimisation workflow Figure 6 above shows the modular workflow of modefrontier: the input variables are relative to Bezier control points ordinates (9 for each side) that modify the airfoil shape; a script reads these points, modify the airfoil shape, update the mesh and run the Navier Stokes solver based on Johnson-Coakley turbulence model. From output file, aerodynamic performances are read for each sample, whereas the objectives and constraints are defined on mean and standard deviation values of the sampling distribution computed for each configuration design. 3.3 Optimisation results The algorithm used is also in this case MOGT, and 250 designs were needed to obtain the equilibrium point (these correpsonds, thanks to the application of Kriging RSM, to a total of 2500 CFD computations). Table in fig.7 reports the comparison of the best configuration with the original one, regarding mean and standard deviation of aerodynamic coefficients (objectives and constraints are distincted). MeanCd (obj) σcd (obj) MeanCl >original σcl <original MeanCm <original σcm <original original best RAE e-2 7.6e e e-3 BEST 1.18e e e e-3 Figure 7 : optimisation results 11 REFERENCES [1] A.Clarich, J.Periaux, C.Poloni, Combining Game Strategies And Evolutionary Algorithms for CAD Parameterisation and Multi-Point Optimisation of Complex Aeronautic Systems, EUROGEN 2003, Barcelona, September 2003 [2] Clarich A., Padovan L., Pediroda V., Periaux J., Poloni C., Application of game strategy in multi-objective robust design optimisation implementing self-adaptive search space decomposition by statistical analysis, ECCOMAS2004, Jyvaskila [3]