Mueller

Question 1

What is an Adjoint Solution?

Answer 1

One which expresses the sensitivity of a single cost function w.r.t. many design variables.

Question 2

What are Surface Sensitivities?

Answer 2

Sensitivity of a given change to the surface geometry w.r.t. many design variables.

Question 3

What is the difference between multivariate and univariate optimization problems?

Answer 3

Univariate - only one design variable

Multivariate - more than one design variable

Question 4

Draw the Gradient-Based design loop.

Answer 4

.

Question 5

How does the Gradient-Based design loop vary from the manual and numerical optimization design loops?

Answer 5

vs manual:

• Includes the calculation of variables
• Includes update of design variables before the pre-processing step.
• No design parametrization step before pre-processing

vs numerical opt:

• Includes the calculation of variables

Question 6

What does the optimization “Model” include?

Answer 6

CAD geometry, Simulation methods and types, Evaluation of the cost function.

Question 7

What is Parametrization?

Answer 7

Definition of how the design variables affect the model

Question 8

What is the Design Space?

Answer 8

The full range of shapes/topologies that can be produced by parameter variation

Question 9

What is the Cost-Function?

Answer 9

The function to be minimized.

Question 10

What is an optimization Algorithm?

Answer 10

The method of varying the design variables after each iteration.

Question 11

Define Uni- and Multi-variate Problems.

Answer 11

Uni-Variate - One design variable

Multi-Variate - Multiple design variables

We often try to reduce Multi- to Uni-

Question 12

Define Single- and Multi-Disciplinary Problems.

Answer 12

Single-Disciplinary - Only one discipline required e.g. Aerodynamics

Multi-Disciplinary - Multiple disciplines involved e.g. Structural and Aerodynamics

Question 13

Describe Linear and Non-Linear problems

Answer 13

The degree of the cost function w.r.t. the design variables (is it a linear function or not?) Typically, relevant industrial problems are non-linear.

Question 14

Describe Constrained and Non-Constrained problems

Answer 14

Whether or not an additional constraint(s) must be satisfied as well as the minimization of the cost function .

Question 15

Describe Local vs Global optimization problems.

Answer 15

Local - Finding a local minimum relativeto some starting point.

Global - Finding the global max of the entire design space.

In most industrial applications we seek an
improvement of an existing solution (local), not the best
solution in the entire design space.

Question 16

Describe Continuous vs Discrete optimization problems.

Answer 16

Continuous - Variables can take on any value between two limits (e.g. wing span)

Discrete - Variables can only take on specific values (e.g. number of engines)