CAESES / FRIENDSHIP-Framework Users‘ Meeting and Conference 2013

Identifying the Right Parameters Adjoint-parametric sensitivities and visualization

• Usually, a high number of parameters defines a parametric model (about 30-50 for a

typical FRIENDSHIP-Framework model)

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

How to select the most suitable ones 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

Optimization with a Parametric Model

Users‘ Meeting and Conference 2013 | Best Practices and Anniversary | 2

• Comparison to direct gradient-based method:

J: objective function, α: parameter

What is Adjoint Analysis?

Users‘ Meeting and Conference 2013 | Best Practices and Anniversary | 3

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

11

optn J ,,,, 321

Result: sensitivity (change in objective function

due to change in parameter value)

• In shape optimization: shape sensitivity (change of

objective function 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

What is Adjoint Analysis?

kn

J

© Volkswagen

Users‘ Meeting and Conference 2013 | Best Practices and Anniversary | 4

• 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

Solution: connect shape sensitivities to CAD parameters

• Parametric sensitivity

How to use the Adjoint Sensitivities

n

k

kn

n

n

JJ

Adjoint shape

sensitivity

Normal displacement of model boundary due to

CAD parameter changes: „design velocity“

Users‘ Meeting and Conference 2013 | Best Practices and Anniversary | 5

• Normal displacement of the boundary due to change of CAD parameter value

• Determine by perturbing the parameters and measuring the normal displacement of given

positions on the model boundary (tessellation nodes of surfaces or trimeshes)

Sensitivity Computation

• Input: model boundary as surfaces or trimeshes

• 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

Design Velocity

Users‘ Meeting and Conference 2013 | Best Practices and Anniversary | 6

• Also computed by Sensitivity Computation

• Adjoint 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

• Adjoint sensitivities are multiplied with the design velocities for each parameter

• Result: one scalar parametric sensitivity for each parameter

Parametric Sensitivities

Users‘ Meeting and Conference 2013 | Best Practices and Anniversary | 7

• Parameter with small influence

Parametric Sensitivities

Users‘ Meeting and Conference 2013 | Best Practices and Anniversary | 8

• Parameter with large influence

Parametric Sensitivities

Users‘ Meeting and Conference 2013 | Best Practices and Anniversary | 9

• From the list of parametric sensitivities select the parameters with the biggest influence on

the objective function 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

• …?

Parametric Sensitivities

Users‘ Meeting and Conference 2013 | Best Practices and Anniversary | 10

• Largest possible design space can be considered

• All parameters in the model can be used for 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

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

Also:

• Apart from the connection to adjoint analysis, the sensitivity computation can be used to

understand the effect of the parameters on the model

Discussion

Users‘ Meeting and Conference 2013 | Best Practices and Anniversary | 11