3rd European Workshop on Automatic Differentiation

http://www.amorg.co.uk/AD/EuroADWorkshops/OxfordJune06

Thursday June 1st, 2006

Oxford University Computing Laboratory
Wolfson Building

Parks Road

Oxford

UK

M.S. Campobasso, P. Fantini, M.D. Guenov (CU, School of Engineering)

Robust Optimization of Aircraft Conceptual Design supported by MATLAB AD

Abstract:   The life cycle of complex products such as civil aircrafts consists of a number of stages ranging from conceptual to advanced design. These two phases are both inherently multidisciplinary, and the main difference between them is that conceptual design usually considers a large collection of disciplines modeled by relatively simple functions (J. Su and J.E. Renaud, Automatic Differentiation in Robust Optimization, AIAA Journal, Vol.35, No. 6, June 1997.), whereas advanced design considers fewer disciplines modeled by sophisticated high-fidelity simulation codes (J.J. Alonso, J,R,R,A Martins, J.J. Reuther, R. Haimes, C. Crawford, High-fidelity aero-structural design using a parametric CAD-based model, RAIAA paper 2003-3429.). The accuracy of both conceptual and advance design analyses may be affected by various sources of uncertainty, but the kind and level of uncertainty is substantially different in the two cases. An extreme example is that of the geometry of an aircraft wing: the source of stochastic error in advanced design may be the geometry uncertainty due to manufacturing tolerances,whereas in conceptual design the overall geometry may be uncertain because design variables such as span and dihedral angle may change at a later design stage.

This presentation deals with some computational issues encountered in the robust optimization of aircraft conceptual design. Unlike deterministic design optimization, robust design considers not only the optimization of one or more objectives, but also that of their variance due to the probabilistic nature of some input variables. In our approach, the estimate of such variance is based on sensitivity derivatives, and these latter can be accurately and efficiently determined by using Automatic Differentiation tools. The test case we consider reproduces the main features of a typical industrial environment: it consists of a relatively large set of given MATLAB functions, and the prescribed solution schedule requires solving subsets of equations by means of MATLAB optimization functions. The MATLAB AD package MAD (S.A. Forth, An efficient overloaded implementation of forward mode Automatic Differentiation in MATLAB, ACM Transactions of Mathematical Software, Vol. 19, No. 2, pp. 250--259, 2003.) is used to obtain the derivatives appearing in the variance of the robust objective function (ROF). Previous studies on aircraft conceptual design typically considered the use of fixed-point iterations to solve strongly coupled subsets of equations, and the automatic differentiation of this process has already been addressed in the past. By contrast, the main difficulty of the problem we consider is that the calculation of the ROF at each step of the optimization requires propagating derivatives automatically through the MATLAB optimization functions yielding the solution of coupled subsets of equations. The presentation will highlight how these pitfalls have been overcome by using recent extensions of the MAD package.

Slides: CampobassoJune06.pdf