Rajan FILOMENO COELHO OPTIMIZATION BASED ON EVOLUTIONARY ALGORITHMS FOR AERONAUTICS With support of...

Rajan FILOMENO COELHO

OPTIMIZATION BASED ON EVOLUTIONARY ALGORITHMS

FOR AERONAUTICS

With support of the Walloon Region and European Structural Funds ERSF, ESF

Rajan Filomeno Coelho – Optimization based on EAs for Aeronautics 2

I. Introduction

III. Optimization algorithms

V. Conclusions

II. Cenaero

IV. New trends in structural optimization

I. Introduction

II. Brief overview of CENAERO activities


IV. New trends in structural optimization for

aeronautics

V. Conclusions

Outline


I. Introduction


V. Conclusions

II. Cenaero


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, …)

I. Introduction


I. Introduction


V. Conclusions

II. Cenaero


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

I. Introduction


I. Introduction


V. Conclusions

II. Cenaero


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


I. Introduction


V. Conclusions

II. Cenaero


II. CENAERO Four R&D groups:

– Virtual manufacturing– Multiscale Material Modelling– CFD-multiphysics– Multidisciplinary Optimization

II. Cenaero

Electron beam welding

Crack propagation

Aeroelasticity Optimization


I. Introduction


V. Conclusions

II. Cenaero


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


I. Introduction


V. Conclusions

II. Cenaero



Optimization problems can be written as follows:

min { f(x) }

s.t.: g(x) 0h(x) = 0

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

– x : vector of the variables– f : objective function(s)– g : inequality constraints– h : equality constraints

Once an optimization problem is correctly formulated, a suitable optimization algorithm has to be chosen



I. Introduction


V. Conclusions

II. Cenaero


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)




I. Introduction


V. Conclusions

II. Cenaero


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




I. Introduction


V. Conclusions

II. Cenaero


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




I. Introduction


V. Conclusions

II. Cenaero


III. Optimization algorithmsinitial population

selection of the best crossover mutation

initial population

Termination criterion

reached ?

STOPyes

no

Illustration of a standard GA

(2-variable design space)



I. Introduction


V. Conclusions

II. Cenaero


Example of design optimization with EAs

– aero-engine liner optimization:

LinersLiners

Approach Condition

M∞= 0.21

Noise Frequency = 2500 Hz

[Credits: Dr. Paul Ploumhans (FFT)]




I. Introduction


V. Conclusions

II. Cenaero


Problem definition

• Design VariablesDesign 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 ObjectivesDesign Objectives– Minimize acoustic pressure

• SimulationSimulation– Actran – FFT– Simulation time: 1 h




I. Introduction


V. Conclusions

II. Cenaero


Reduction of the noise for both liners




I. Introduction


V. Conclusions

II. Cenaero


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




I. Introduction


V. Conclusions

II. Cenaero



Advanced optimization strategies in aeronautics

involve:

– Multiobjective optimization– Optimization combined

with meta-models– Multidisciplinary optimization– Robust optimization– Collaborative design

& optimizationIV. New trends in structural optimization


I. Introduction


V. Conclusions

II. Cenaero


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



I. Introduction


V. Conclusions

II. Cenaero



– definition of the multiobjective problem:

Design VariablesDesign Variables

– D = internal diameter [5, 30 mm]

– G = groove count [5, 20]

– d = hydraulic diameter [0.8, 2.5 mm]

D

ObjectivesObjectives– maximize power– minimize external diameter

Dext

Credits: S. Rossomme & C. Goffaux



I. Introduction


V. Conclusions

II. Cenaero





I. Introduction


V. Conclusions

II. Cenaero



« 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*) »

Concept of Pareto solution:



I. Introduction


V. Conclusions

II. Cenaero



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 ?



I. Introduction


V. Conclusions

II. Cenaero



• 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



I. Introduction


V. Conclusions

II. Cenaero



Optimization combined with meta-models– MAX software developed at CENAERO combines

evolutionary algorithms with approximation models



I. Introduction


V. Conclusions

II. Cenaero



– 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



I. Introduction


V. Conclusions

II. Cenaero



– 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



I. Introduction


V. Conclusions

II. Cenaero


initial design control points


– 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:

y-coordinates of 16 control points



I. Introduction


V. Conclusions

II. Cenaero



– 2. Constructing the viscous mesh (TRAF)

– 3. Computing the flow (TRAF quasi-3D analysis)

– For the optimizer, the objective is defined as follows ...

• for each operating point, the loss coefficient is to be minimized

• practically, a weighted sum approach is followed minimize

2op1 +

2op2

– ... and the constraint:

• the outlet flow angle must remain between -74.8° and -74.7°

– 4. Post-processing: for each operating point, the loss coefficient

2 is computed:



I. Introduction


V. Conclusions

II. Cenaero



– density for the initial design:



I. Introduction


V. Conclusions

II. Cenaero



– convergence history (200 design cycles):

iteration

loss

coe

ffic

ient

sum



I. Introduction


V. Conclusions

II. Cenaero



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)



I. Introduction


V. Conclusions

II. Cenaero



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-disciplinary optimization (on multiple operating points)



I. Introduction


V. Conclusions

II. Cenaero


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)



I. Introduction


V. Conclusions

II. Cenaero



– 3D representation of the optimized blade design:



I. Introduction


V. Conclusions

II. Cenaero



Advantage of multidisciplinary optimization

– multidisciplinary = different physics are taken into accountsimultaneously 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 (onCENAERO Linux cluster)

– the use of meta-models enables a reduction of the CPUtime by a factor ~10



I. Introduction


V. Conclusions

II. Cenaero


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

Rajan FILOMENO COELHO OPTIMIZATION BASED ON EVOLUTIONARY ALGORITHMS FOR AERONAUTICS With support of...

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