Keywords: industrial optimisation, metamodel, polynomial chaos expansion, sensitivity analysis, particle swarm optimisation, dimensionality reduction.

The application of uncertainty management techniques to the aircraft design process is currently a high profile research area and of key strategic interest within aerospace industry. Within the aircraft design process there is always a difficult balance between non specific and specific design steps for configuration and design maturity versus the overall project lead time. This leads to either an immature design that causes delays of the entry into service or significant re-design loops within the aircraft development project again resulting in a significant cost penalty. The ability to quantify uncertainties in the design enables the application of more robust optimisation approaches to balance the quantitative risks of design evolution against the aircraft performance implications (e.g. aircraft weight) and specific design lead time.

Although the application of stochastic analysis is a powerful way of making informed design decisions, its integration into the standard design process requires the generation of deterministic design data which achieve the design targets from an uncertainty approach.

In this paper the problem of retrieving deterministic design data from a collection of responses provided by aircraft structural computer models is addressed. Firstly, a framework that enables metamodel generation and dimensionality reduction is presented. The framework relies on polynomial chaos expansion (PCE) for metamodel generation [1]. The technique was chosen for its ability to ease the sensitivity analysis process, as sensitivity information in the form of Sobol indices can be extracted analytically from the PCE metamodels. Secondly, a search algorithm that can be used to explore the metamodels generated by PCE is presented. The algorithm, based on the particle swarm optimisation (PSO) paradigm [2], was developed specifically to be used in constrained search problems: it performs a search of the design configurations that produces a specified target response level. Constraints can also be defined using additional metamodels.

The framework and the search algorithm have been validated on an aircraft structural analysis problem. The accuracy of the results and the reduced computational cost of the entire process make the presented methodology a valuable tool for uncertainty and sensitivity analysis in the aerospace industry.

1

M.S. Eldred, C.G. Webster, P.G. Constantine, "Evaluation of non-intrusive approaches for Wiener-Askey generalized polynomial chaos", Proceedings of the 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, AIAA, Schaumburg, IL, USA, 2008.

2

J. Kennedy, R. Eberhart, "Particle swarm optimization", Proceedings of the IEEE International Conference on Neural Networks, 4, 1942-1948, IEEE, 1995.

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