Keywords: neural networks, genetic algorithms, panel buckling, composites, optimisation.

This paper presents an approach for the design of weight-minimal aircraft components made of composite materials by application of Genetic Algorithms (GA) and Neural Networks (NN). The approach is designed within a research effort aimed at optimising a structural assembly of multiple components, typically the vertical tail plane box of a commercial aircraft. The procedure basically consist of the following steps:

1. Evaluate a global model of the structure
2. Retrieve component loading and sizing, checking whether the component withstands given loads
3. Optimise all components to minimal weight considering buckling and local strain constraints
4. Re-evaluate the global structural model with optimised design
5. Update the load distribution in the structure and return to 3 until convergence.

This paper is focussed on the implementation of the component optimisation routine mentioned in step 3. The use of Feedforward Backpropagation Neural Networks as an approximate solver (or Response Surface) is evaluated to replace a large part of the Finite Element (FE) analyses required for the optimisation of a component when considering the full range of design variables. This routine contains the following steps:

• Create an initial set of NN training patterns using FE analysis of components on a partial coarse grid in the design space
• Train NNs for all topologically distinct design configurations
• Use a GA to find the optimum solution within the approximated space made up by all NNs
• Check the obtained optimal solution with FE
• Feedback pass; when the error (with and the solutions of NN and FE, respectively) is above a threshold value the solution is added to the training set and the NN is trained again

Each Neural Network takes an input vector made up of global parameters like length, width and applied loading and local optimisation parameters such as the number of plies in a laminate, location and number of holes and stringers. The output vector of the network consists of the linear buckling load and local strain level.

The aim of implementing the feedback pass is twofold. First, the possible output of a non-realistic optimal solution is eliminated (this was a problem in a previous attempt with the NN-GA set-up by the authors as described in [1]). Secondly, the selection of the initial data set is assumed to be less critical because no full coverage of the space is demanded (fewer FE evaluations are needed).

The results are obtained using the Matlab Neural Network toolbox, a Matlab implemented GA by Houck et. al. [2] is used and parametric FE models are constructed using the commercial finite element package ANSYS.

Results are presented for the problem posed by the optimisation of stiffened composite panels with access holes as used in the Vertical Tail Plane of commercial passenger aircraft under variable global sizing and loading.

The method proved to be convergent in terms of accuracy on the test problem. This convergence was achieved in relatively few feedback passes. Application of the algorithm to the test problem and comparison of the results with a reference design shows that weight reduction can be achieved using the presented algorithm.

1

Ruijter, W., Spallino, R., "Optimization of composite panels using neural networks and genetic algorithms", in "Proceedings of the Second MIT conference on Computational Fluid and Solid Mechanics". Boston: 2003. (In Press) doi:10.1016/B978-008044046-0.50580-7

2

Houck, C.R., Joines, J.A., Kay, M.G., "A Genetic Algorithm for Function Optimization: A MATLAB Implementation. GAOTv5 Manual (Genetic Algorithm Optimization Toolbox)", 1998.

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