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

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

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

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.

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.

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.

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

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

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 

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 ......

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 1 .... 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

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

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

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

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

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.

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

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

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

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.

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

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 workstations @400 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

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

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

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.

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.

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

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.

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

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 PCs @ 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

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

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

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

Spar Panel Parametrization

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

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

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

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, 16 E = 3, 10, 120, 18 5, 8, 120, 18 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, 20 E = 8, 6, 140, 20 11, 10, 40, 14 F = 11, 10, 100, 14

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