Shape Optimization by Mapping Adjoint Sensitivities to CAD Model Parameters

DNV GL © 2014 SAFER, SMARTER, GREENER DNV GL © 2014

Efficient Optimization of Flow-Exposed Geometries

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by mapping adjoint shape sensitivities to CAD model parameters

Mattia Brenner, Andre Zimmer, Sebastian Weickgenannt

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Optimization Task

Rear wing of a hyper sports car should be

optimized with respect to the objectives

drag and downforce

iconCFD is used for adjoint CFD

computations

CAESES is used for parametric

modeling, mapping of the

adjoint sensitivities to the

CAD model parameters

and subsequent

geometry modification

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With kind permission of: Koenigsegg Automotive AB

www.koenigsegg.com

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CAESES

Specifically geared for automated CFD-driven design

Focus on complex free-form surfaces and shapes, difficult to parameterize

Models defined and varied according to “smart parametric” descriptions

Reduced degrees-of-freedom; constraints can be built in to the description

Complex models and their variants maintain high-fidelity and fairness

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Profile defined using specialized curve types and controlled by user-defined parameters

Initial profile is transformed along a specified path, and its parameters are varied based on functional distributions

Proprietary meta-surface technology creates complex surfaces with intelligent parameterization and high quality

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Parametric Model

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Parametric Model

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Parametric Model

19 design variables control the shape with the help of spanwise distributions of

profile parameters

Geometry constraints regarding span and chord length are automatically met

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Optimization with a Parametric Model

Usually, a high number of parameters defines a parametric model (in this case 19,

often 30-50 for a typical CAESES model)

Way too much effort to involve all of them in a conventional optimization

process…

How to select the most suitable parameters for the optimization task at hand?

Normally, the designer selects or specifically creates a small number of

parameters based on experience and engineering judgment

– This reduces the design space for the optimization

– The designer might not have enough experience to make a good selection

– Especially difficult if the model was created by someone else

Solution: adjoint analysis

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What is Adjoint Analysis?

Comparison to direct gradient-based method:

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Adjoint method

Question: what changes to the design parameters are

necessary to get an optimal product performance?

1 primal + 1 adjoint simulation run for each objective

necessary

Direct method

Question: how do changes of the design parameters influence the product‘s

performance?

n+1 simulation runs necessary

nn J

J

J

J

33

22

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optn J ,,,, 321

J: objective function, α: parameter

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Adjoint Analysis Results

In shape optimization: shape

sensitivity (change of objective

function J due to normal displacement

of cells on the design boundary)

A positive shape sensitivity means that

the boundary should be moved in

positive normal direction

A negative shape sensitivity calls for

boundary movement in negative

normal direction

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kn

J


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Push inwards Pull outwards

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How to Use the Adjoint Sensitivities

Adjoint shape sensitivity values can be used to displace the surface cells directly

and to morph the shape, e.g. in a CAD independent approach

Downside is that the shape changes cannot easily be fed back into the design

workflow, geometry constraints may be violated

Solution: map shape sensitivities to CAD model parameters

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.avg

k

k n

k

kn A

An

n

JJ

Adjoint shape sensitivity

Normal displacement of model boundary due to CAD parameter change: „design velocity“

Relative local cell size

Parametric sensitivity

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Design Velocities

Normal displacement of the boundary due to changes of CAD parameter values

Determined by perturbing the parameters and measuring the normal

displacement of given positions on the model boundary (surface tessellation

nodes)

CAESES Sensitivity Computation

Input: model boundary as surface geometry

Automatically determines all design variables

that are suppliers to the boundary

User can deselect design variables and set

individual deltas

Result: design velocity maps for all selected

parameters

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Parametric Sensitivities

Also computed by Sensitivity Computation in CAESES

Adjoint shape sensitivities are mapped to the positions on the boundary used to

determine the normal displacement (tessellation nodes) by probing the result

data set of the adjoint computation

For each parameter adjoint sensitivities are locally multiplied with the design

velocities and summed up, weighted with the relative area of the local element

Result: one scalar parametric sensitivity for

each parameter

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Parametric Sensitivities

From the list of parametric sensitivities select the parameters with the biggest

influence on the objective function manually change values or follow up with

conventional optimization

or

Multiply the vector of the parametric sensitivities with a step size factor and add

to the parameter values determine the right step size with 1-dimensional

search using primal CFD computations

or

…?

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CFD Setup

Mesh size: 18 Mill. cells

Spalart-Allmaras turbulence model

Primal run: 6000 iterations, ~7h on 64 CPUs

Adjoint run: 6000 iterations, ~5h on 64 CPUs

Adjoints computed for drag and downforce

Inlet velocity: 40m/s

turbulence intensity: 0.005

turbulence length scale: 0.01

Wheels with rotating wall

Incompressible, rho=1.204, nu= 1.436877e-05

Three radiators modeled as porous media

Frozen adjoint turbulence

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www.koenigsegg.com

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Design Velocity Results

Thickness_pressCenter

– Rank 1 for drag

– Rank 2 for downforce

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Adjoint Sensitivities (drag)

Adjoint Sensitivities (downforce)

Design Velocity

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StepPos_yShift

– Rank 2 for drag


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Design Velocity

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Camber_pressCenter

– Rank 5 for drag


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Design Velocity

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Thickness_pressTip


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Design Velocity

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Thickness_sucCenter

– Rank 3 for drag


19



Design Velocity

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Thickness_sucInner

– Rank 4 for drag

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Design Velocity

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Parametric Sensitivity Results

Top 5 of most influential parameters

for drag and downforce

Most of these parameters point in

opposite direction for the two

objectives

Three modified geometries were

generated

1. Based on the top 5 parametric

sensitivities for drag

2. Based on the top 5 parametric

sensitivities for downforce

3. Changing all parameters that primarily

affect one objective while having little

influence on the other, in an effort to

improve both objectives

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Optimization Results

Baseline geometry

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www.koenigsegg.com

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Drag optimized geometry

-0.96% drag

-3.75% downforce

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www.koenigsegg.com

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Downforce optimized geometry

-0.03% drag

+3.86% downforce

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www.koenigsegg.com

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Combined optimized geometry

-10.58% drag

+2.94% downforce

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www.koenigsegg.com

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Discussion

Adjoint sensitivities can be mapped to the CAD geometry parameters to allow for

feasible shape modifications

Largest possible design space can be considered

All parameters in the model can be involved in the optimization, without the need

for the user to understand the effect of each parameter

The effort does not scale with the number of parameters

Parametric sensitivities for all parameters in the model can be computer more

quickly than for a small set using the direct approach

Separate adjoint solutions may be used to perform a multi-objective optimization

But:

Predictions based on sensitivities are only valid for small changes in shape

In practice iterative process: new sensitivities should be computed for modified

shape

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SAFER, SMARTER, GREENER

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CAESES , Your Upfront CAE System for Shape Optimization

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Dipl.-Ing. Mattia Brenner

[email protected]

+49 331 96 766 0

Design Solve Optimize