1. Multilevel Distributed
Structure Optimization
Welcome everyone, my name is Jorg Entzinger
The next 15 to 20 minutes, I will be talking to you about a project I did for Airbus Industries on multilevel distributed structure optimization.
In this project I worked with other students at the university of twente to develop an optimization tool for aircraft structures
We had some support and supervision from the university, Airbus and the Duch Aerospace Laboratory NLR
Jorg Entzinger
Roberto Spallino
Wout Ruijter

2. Outline Introduction Problem description Program design
Tests & results
Conclusion
Outline
Introduction
Problem description
Program design
Tests and test results
Conclusion
My presentation is set up as following:
I will start with a short introduction about the goal of the project
Then we will take a look at the optimization problem
After that I will show our optimization strategy
Then I show some testresults
Finally I will draw some conclusions
After my presentation there will be time for your questions

3. Problem Formulation Develop a design tool to minimize the weight
Intro
Problem description
Program design
Tests & results
Conclusion
Problem Formulation
Develop a design tool to
minimize the weight
of an aircraft substructure
subjected to static loadcases.
New design features must be analyzed
in an autonomous, overnight run.
As I said earlier, this project was initiated by Airbus.
And as we all know, weight minimization is one of the most important things in Aircraft design – together with safety –
The goal of this project is to develop a design tool to minimize the weight of an aircraft substructure.
To make a practical tool, it is important that different options and the influence of new design constraints can be analysed fast and autonomous to save time and manpower, besides kilos

4. Vertical Tail Plane . Intro Problem description Program design
Tests & results
Conclusion
Vertical Tail Plane .
The substructure we are investigating is the centerbox of the vertical tail plane (or VTP), however the presented setup could very well be used for other parts, and is not at all restricted to the aircraft industry.

5. Vertical Tail Plane . Intro Problem description Program design
Tests & results
Conclusion
Vertical Tail Plane .
As you probably know, the tailplane of an aircraft consists of Ribs (horizontal panels), Skins (on the sides) and Spars (front and rear).
Although the spars are actually two big laminate panels, in calculations we assume the whole spar can be divided into panels located between two ribs. In the same way skins are divided in panels between two ribs.
In the optimization we make a distinction between the global structure and the (more or less similar) components
During the component optimization the panels are considered mutually independent
This means for instance that each spar is optimized without considering the other panels surrounding it.

6. Spar Panel Configurations
Intro
Problem description
Program design
Tests & results
Conclusion
Spar Panel Configurations
For these panels we defined different lay-outs, containing different combinations of access holes and stiffeners
Here you see the configurations we defined for the SPAR panels
All configurations are rotated 90 degrees compared to their orientation in the VTP
You can see all configurations are symmetric, both left/right and top/bottom
These different types are available to be chosen for each panel in the optimized design, and thus form a discrete optimization parameter.

7. Finite Element Models Linear static analyses FEM models are parametric
Intro
Problem description
Program design
Tests & results
Conclusion
Finite Element Models
Linear static analyses
buckling multiplier
maximum strain
FEM models are parametric
About 8000 nodes quadratic 3D shell (48000 DOF)
To be sure that the panels won’t fail in operation, we need to know their maximum strain under the applied loads and their buckling loads
Therefore we developed a parametric finite element model which can handle all the configurations i showed you on the previous slide.
This means a ‘standard plate’, longitudinal and transversal stiffeners and holes are available as a geometry and are put together forming a surface which is automatically meshed and solved.
Ofcourse also all other design variables are taken into account here like plate thickness, exact distances between holes and stringers and also non-optimized variables like length, width and material type
Depending on the complexity of the panel about 8000 nodes are used, which takes about 1-5 minutes to do a static analysis, depending on the speed of the pc

8. Optimization Problem Optimize Variables Loads Constraints VTP
Intro
Problem description
Program design
Tests & results
Conclusion
Optimization Problem
Optimize
Variables
Loads
Constraints
VTP
Center Box
Configuration
Stiffener height
Hole position
Stiffener position
Panel thickness
Etc.
Manoeuvre
Rudder
Crash
Maintenance
Assembly
Feasibility
Strain
Buckling
The optimization problem can be described like this:
We can tune some variables like the configurations we saw before
There are some loadcases the structure must withstand
And some constraints that must be met.
For constraints on Maintenance and assembly one could think of pre-defined places for holes because of accessability or hydrolics

9. Multilevel Implementation
Intro
Problem description
Program design
Tests & results
Conclusion
Multilevel Implementation
Level
Variables
Loads
Constraints
Structure -
Manoeuvre
Rudder
Crash
Maintenance
Assembly
Component
Configuration
Stringer height
Hole position
Stringer position
Panel thickness
Etc.
Shear
Bending
Compression
Strain
Buckling
I will show you how the tool we developed works
We split the optimization into a global structure level and a local level where the components are optimized.
The structurel level does not contain a real optimization, it only translates the global loadcases to shear, bending and compression on the component level
This process can be depicted as following 

10. Structure Level Optimization
Intro
Problem description
Program design
Tests & results
Conclusion
Structure Level Optimization
Initialize structure
Calculate component loadings and BCs
Converged?
Postprocess
First a CAD model and the vertical positions of the ribs are loaded, all components are extracted, their dimensions are set and each component gets an unique ID
In the next step the global loadcases are applied to the structure to obtain the loading for each component
When these loadings are obtained, they are compared to the loadings derived in the previous iteration. When they have changed more than a certain treshold, all components are optimized.
This optimization can be done in parallel, because all panels are considered mutually independent on the local level.
After optimization, the optimized components are placed back into the structure model and new loads are calculated.
When loads don’t change much, postprocessing can be done, else the panels are optimized again, with the updated loads
-> if we zoom in on one of the component optimizations, we see the following structure 
Optimize component 1
Optimize component N
......

11. Component Level Optimization
Intro
Problem description
Program design
Tests & results
Conclusion
Component Level Optimization
Population
Set of possible solutions
Calculation of pseudo objective (objective + penalties)
Ranking based on pseudo objective
Interchange of parameter values
Random change of param. values
FE solver
Selection
Crossover
On the previous slide we saw the boxes ‘optimize component N’
The optimization is carried out by a genetic algorithm
Genetic Algorithms are guided random search techniques
A population is a group of individuals, or points in the solution space.
Compared to conventional optimization methods this means we use several starting points
For each individual, we need to know how well it solves our problem, so we perform some calculations to obtain it’s weight and check whether strain and buckling and constraints are violated. This way we calculate a pseudo objective, called fitness in GA terms
Based on this fitness the better solutions get a higher chance to be selected for reproduction
Now crossover and mutation are applied, to generate new individuals, based on the parameter values of the currently existing ones
these new individuals are analysed etc etc.
Finally the solutions in the population converge to an optimum
Mutation
Converged?
Optimum

12. Component Level Optimization
Intro
Problem description
Program design
Tests & results
Conclusion
Component Level Optimization
Population
FE solver
Selection
Crossover
Because the GA is an iterative process, and we maintain a population with several `starting points’, a lot of FE calculations have to be done, which all takes 1-5 minutes each, which is much to long to wait for.
Mutation
Converged?
Optimum

13. Component Level Optimization
Intro
Problem description
Program design
Tests & results
Conclusion
Component Level Optimization
Population
Training data set
Neural Networks
FE solver
Selection
Crossover
This is why use a neural network to estimate the FE outcomes
The NN can be seen as a response surface. It is trained with a set of FE calculations to reproduce the outputs given the parameter inputs.
for each configuration a separate NN is trained
The NN can be evaluated in a few miliseconds, making it very useful in this setup with the GA
However NNs are are not exact, but provide an approximation.
The accuracy of the NN was not very good and the initial trainingset was very large (about 300 FE calculations)
Mutation
Converged?
Optimum

14. Component Level Optimization
Intro
Problem description
Program design
Tests & results
Conclusion
Component Level Optimization
Population
Training data set
Neural Networks
FE solver
Selection
Crossover
That is why we added a finite element check of the optimum found by the GA.
When the properties of the panel estimated by the NN differ too much from the outcomes of the FE check, the parameters and the FE outcomes are added to the trainingset and the NNs are retrained, so they will be (locally) more accurate
After all NNs are updated, the panels are optimized again, using the old loading conditions, but the new NNs
When all found optima are accurate, a reliable optimum is found and the program swiches back to the structure level to update the component loads
This method of feeding back preliminary optima trains the neural network better in places where the GA expects an optimum, it also allows starting with a much smaller initial training set.
Mutation
Accuracy check (FE)
Converged?
Optimum

15. Algorithm Overview Finite Element Models (Analysis)
Intro
Problem description
Program design
Tests & results
Conclusion
Algorithm Overview
Finite Element Models (Analysis)
Neural Networks (Response Surface)
Genetic Algorithm (Optimization)
Distributed Computing (for Speeding up)
A short overview of the used algorithms:
finite element models are used on the structure level to derive component loading
And at the component level to determine the maximum strain and buckling loads
This response surface is needed because FE calculations take too much time in the optimization
And is implemented using NNs
A GA optimizes all components, which are considered independent during this optimization
All tasks: FE Analyses, NN training and component optimization are independent tasks
And can therefore well be distributed over several computers

16. Algorithm Features Accuracy because of Network retraining
Intro
Problem description
Program design
Tests & results
Conclusion
Algorithm Features
Accuracy because of Network retraining
Robustness by the Genetic Algorithm
FE knowledge is preserved in the Neural Network
Neural Networks can be pre-trained offline
Fast optimization
Applicable in an industrial environment
Feedback of inaccurately estimated solutions improves the accuracy of the response surface
Genetic algorithms are very robust and can therefor handle almost any optimization problem without getting stuck in local optima.
The knowledge obtained from FE calculations is stored in the NN, so for instance in case of load changes accurate networks can be re-used
Also the pre-training can be done offline
Using these neural networks as a response surface and a distributed computing algorithm to spread the computational load over several computers, the algorithm should work quite fast
Which is essential for a practical tool in an industrial environment.

17. Tests Box test Convergence tests Tests with series of Spar Panels
Intro
Problem description
Program design
Tests & results
Conclusion
Tests
Box test
Convergence tests
Tests with series of Spar Panels
Half VTP tests
Full VTP tests
Of course it is nice to have the routine as proposed, but to it means nothing if it isn’t put to the test
Therefore we made a JAVA implementation and
in 2 years of work the program has grown from nothing into a fully functioning tool
First we did a test with a box consisting of 6 components. A symmetric loadcase was applied, and the program found a symmetric optimum. This may seem an academic problem, but it is an easy check and shows robustness.
This makes the proposed method very promising, so we did some more testing of which I will show some results

18. Convergence Intro Problem description Program design Tests & results
Conclusion
Convergence
Here we see the convergence plots for two parameters of a certain component.
The upper one is the relative stiffener location
The lower one is the relative hole location
As we see both parameters change a lot at first, but stabilize nicely later

19. Neural Network Accuracy
Intro
Problem description
Program design
Tests & results
Conclusion
Neural Network Accuracy
The accuracy of the Neural Network approximation also shows good convergence
Especially when one recognises that the relative error between the FE checking calculation and the NN is plot on a LOGARITHMIC scale here

20. Spar Optimization Series of spar panels
Intro
Problem description
Program design
Tests & results
Conclusion
Spar Optimization
Series of spar panels
Multiple runs with different design considerations
Different laminate stackings
Different hole placement throughout the structure
Different variables (such as variable stiffener height)
New configurations
First I will show you a test with just a series of components, thus ommitting the structure and the structure loop
Because there are different design considerations affecting the structure as a whole, we did several optimizations, so for each run an optimum is found which can be compared to the other optima with different decicions
An interesting point to mention here is that we can include the stiffener height in the optimization, something that is virtually impossible to do when optimizing by hand.

21. Spar Panel Series Test 36 Components
Intro
Problem description
Program design
Tests & results
Conclusion
Spar Panel Series Test
36 Components
No access holes demanded in the 6 lowest panels (for both front and rear spar)
Combined shear & bending loads
Realistic loadcases
I will highlight one of these runs
The front and rear spar combined have 36 components
Access holes are demande in all spar panels, except the lowest 6 ones
Realistic loads were used for all panels
With 7 400MHz HP unix machines this took about 18 hours

22. Spar Panel Series Test 36 Components
Intro
Problem description
Program design
Tests & results
Conclusion
Spar Panel Series Test
36 Components
No access holes demanded in the 6 lowest panels (for both front and rear spar)
Combined shear & bending loads
Realistic loadcases
7 HP-UX MHz
Runtime: ca. 18 hours
I will highlight one of these runs
The front and rear spar combined have 36 components
Access holes are demande in all spar panels, except the lowest 6 ones
Realistic loads were used for all panels
With 7 400MHz HP unix machines this took about 18 hours

23. Front Spar Panels Intro Problem description Program design
Tests & results
Conclusion
Front Spar Panels
Here you see the panels of the front spar (I cut it in half so it fits on the slide)
As we can see in all panels, holes surrounded by stiffeners are the best option when a hole is required

24. Intro
Problem description
Program design
Tests & results
Conclusion
Front Spar Panels
Many stiffeners in lower spar panels (to prevent buckling)
The lower spar panels have a lot of stiffeners, which is quite logic, because they have to withstand very high loads

25. Intro
Problem description
Program design
Tests & results
Conclusion
Front Spar Panels
Many stiffeners in lower spar panels (to prevent buckling)
Holes found where not demanded
However we also see some holes where they were not demanded. This is a surprising result which probably no engineer would have come up with. Apparently the hole (surrounded by stiffeners) does not affect the mechanical properties of these panels to a critical level, and thus it only saves weight.

26. Intro
Problem description
Program design
Tests & results
Conclusion
Front Spar Panels
Many stiffeners in lower spar panels (to prevent buckling)
Holes found where not demanded
More stiffeners in upper spar panels might be beneficial
The upper spar panels are relatively long and holes are required here. A configuration with more stiffeners might be better, but was not available in the set of possible configurations. Such a new configuration could easily be added.

27. Rear Spar Panels Intro Problem description Program design
Tests & results
Conclusion
Rear Spar Panels
Let’s have a look at the rear spar
Here we see about the same as in the front spar:
A lot of stiffeners in the lower part
A lot of holes surrounded by stiffeners

28. Intro
Problem description
Program design
Tests & results
Conclusion
Rear Spar Panels
More longitudinal stiffeners might me beneficial (compare with front spar!)
Conclusion:
add configurations
But now the upper panels have more stiffeners
When we compare this with the situation in the front spar, adding configurations with more stiffeners surrounding one hole could be a very interresting option
Compared to a manual optimization the results are sensible and promising.
And the optimization is of course much faster.
These are results obtained at Airbus, so I’m not allowed to be more specific.

29. Full VTP Test 90 components Non-realistic global loadcase
Intro
Problem description
Program design
Tests & results
Conclusion
Full VTP Test
90 components
Non-realistic global loadcase
Limited set of configurations
No holes required in upper 4 panels
Another test I want to show you is this one,
Here you see fully optimized VTP structure consisting of 90 panels (36 sp, 18 r, 36 sk)
The global loadcase was not realistic,
but this optimization shows that
With 27 quite fast PCs a complete structure
Can be optimized overnight

30. Full VTP Test 90 components Non-realistic global loadcase
Intro
Problem description
Program design
Tests & results
Conclusion
Full VTP Test
90 components
Non-realistic global loadcase
Limited set of configurations
No holes required in upper 4 panels
27 Win-XP 2.6GHz
3 structure iterations
Runtime: ca. 9 hours.
Another test I want to show you is this one,
Here you see fully optimized VTP structure consisting of 90 panels (36 sp, 18 r, 36 sk)
The global loadcase was not realistic,
but this optimization shows that
With 27 quite fast PCs a complete structure
Can be optimized overnight

31. Conclusions Powerful tool to evaluate the potential of a design
Intro
Problem description
Program design
Tests & results
Conclusion
Conclusions
Powerful tool to evaluate the potential of a design
Flexible in component optimization
Tests show good optimization results
Overnight runs possible with sufficient computers
In the end we developed a powerfull concept tool
The component optimization is very flexible, new optimization variables or new configurations can easily be added.
The tests give sensible results compared to optimization done by hand, and are much faster than optimization by hand
And can even do overnight optimizations
Because time consuming tasks are spread over a number of PCs

32. Prospects Handle constraints on structure level
Intro
Problem description
Program design
Tests & results
Conclusion
Prospects
Handle constraints on structure level
Apply for other (aircraft) structures
Enable interaction with other calculations (Flutter)
Apply in other fields (acoustics, dynamics)
The project has oficially finished, but the different partners in the project have some ideas to go on with parts of the program
What could be done is implementing a true multilevel optimization with an extra constrained optimization on the structure level.
The tool could be applied for optimization of different aircraft structures, such as the wings or fuselage
On the structure level interaction with aerodynamics could be added to develop more accurate loadcases and constraints to prevent flutter
The tool could be applied in different fields, like acoustics and dynamics

33. Questions? Jorg Entzinger Roberto Spallino Wout Ruijter
I’ve reached the end of my presentation
Thank you very much
If there are any questions, please don’t hasitate to ask them
Jorg Entzinger
Roberto Spallino
Wout Ruijter

35. Spar Panel Parametrization

36. Spar Panel Parametrization
Optimized parameters:
Configuration
Panel thickness
Stringer height
Stringer positions
Hole positions
Fixed parameters:
Length
Width
Loading

37. Half VTP Test 45 panels Non-realistic global loadcase
Ansys FE analyses
Limited set of configurations
No holes required
20 Win-XP 2.6GHz
2 structure iterations
Runtime: ca. 8 hours.
Watch the diverging stringers in the rear spar

38. Neural Network Training
Network Simulation (Evaluation) h1
1 2
in = 2 3
3 4 i1 h2 o1
Error (tar - output) i2 h3 o2 i3 h4
3 5
5 7 h5
tar =
Neurons are grouped in layers, neurons in successive layers are interconnected, each interconnection has a weight multiplication
Each neuron has a transfer function (here: tansig, hyperbolic tangent) for the middle (hidden) layer
Biasses are used to implement an offset for all neuron inputs
Interconnection weights and biasses are updated with an iterative (training) algorithm until the outputs closely match the targets b1 b2
Error Backpropagation
 w11
 w21 
 w12
 w22
 w13

39. Genetic Algorithms Population Parametrization Fitness calculation
FA = 55
FB = 40
FC = 43
FD = 47
A = 3, 10, 100, 16
B = 11, 6, 140, 20
C = 5, 8, 120, 18
D = 11, 10, 40, 14
Parametrization
Fitness
calculation
Crossover (A,C)
3, 10, 100, E = 3, 10, 120, 18
5, 8, 120, F = 5, 8, 100, 16
3, 10, 100, 16
5, 8, 120, 18 or
E = 4, 9, 110, 17
See also sheet 9 (component level)
The population consists of a number of possible solutions or a single component in the structure (individuals)
The solutions are parametrized, the vector of parameter values is the gene of the individual
The fitness is calculated using for instanc a parametric FE calculation or a NN evaluation
The fitness shows to what extent each solution fullfills the design wishes and constraints
The solutions with the best fitnesses are selected, the others are thrown away
With the “better” solutions new solutions are made using crossover and mutation
Crossover is the exchange of genetic material to converge to an optimum
Mutation is a random change to make sure the algorithm doesn’t get stuck in a local optimum
Mutation (B & D)
11, 6, 140, E = 8, 6, 140, 20
11, 10, 40, F = 11, 10, 100, 14

40. Screenshot Wizard

41. Screenshot Master