Application of response surface methodology to stiffened panel optimization

In a multilevel optimization frame, the use of surrogate models to approximate optimization constraints allows great time saving. Among available metamodelling techniques we chose to use Neural Networks to perform regression of static mechanical criteria, namely buckling and collapse reserve factors of a stiffened panel, which are constraints of our subsystem optimization problem. Due to the highly non linear behaviour of these functions with respect to loading and design variables, we encountered some difficulties to obtain an approximation of sufficient quality on the whole design space. In particular, variations of the approximated function can be very different according to the value of loading variables. We show how a prior knowledge of the influence of the variables allows us to build an efficient Mixture of Expert model, leading to a good approximation of constraints. Optimization benchmark processes are computed to measure time saving, effects on optimum feasibility and objective value due to the use of the surrogate models as constraints. Finally we see that, while efficient, this mixture of expert model could be still improved by some additional learning techniques

Modèles réduits en optimisation multiniveau de structures aéronautiques

Le dimensionnement de grandes structures aéronautiques s’appuie sur des heuristiques qui garantissent l’admissibilité de la structure par rapport aux contraintes de tenue mais pas nécessairement l’optimalité en masse. On se propose ici de formaliser le problème d’optimisation de structures en l’incluant dans la catégorie des problèmes d’optimisation multiniveau. On montre comment l’utilisation de modèles réduits peut simplifier et améliorer les méthodes directes. On présente les premiers résultats obtenus sur un cas test pour les différentes méthodes

Application des modèles réduits à l'optimisation multiniveaux d'une structure aéronautique

TOULOUSE-ISAE (315552318) / SudocSudocFranceF

Lagrange-Kuhn-Tucker coordination for multilevel optimization of aeronautical structures

In this paper, we propose a Lagrange-Kuhn-Tucker based coordination scheme to deal with level coupling. First, we give a precise definition of several multilevel decomposition schemes, namely the StiffOpt -industrial- approach, and the minMass approach which keeps a mass minimization as objective of local optimisations. Then, we introduce a new decomposition strategy using dual variables. Last section is dedicated to numerical results and comparison of these approaches on the classical ten bar truss problem benchmark

Multilevel optimization with local mass minimization

In this study, we propose a new multilevel optimisation process which responds to these requirements. The original optimization problem is decomposed into a system level and several element levels, aiming at the minimization of element weight under inequality constraints. Bounds of these constraints are given by the system level optimisation. In order to speed up the process and avoid local minima–which is met in most multilevel optimisation schemes- we replace the system constraints by a surrogate model. Last, a penalty term added in the "element level" objective allows us to force the equality of some design variables among all elements. The surrogate is incrementally built along system/element level loops from local optimisation results. For this reason, we choose to use Support Vector Regression methodology, which is more suitable to incremental training and data compression than more classical non-linear regression schemes such as neural networks are. The proposed multilevel strategy is tested on the classical ten bar truss problem; the benchmark structure is subject to several load cases and its weight is minimized under both mechanical and geometrical (equality in detailed variables) constraints. We obtain good results in terms of objective value, convergence time and detailed variables continuity. The implementation of our scheme on a full-size industrial problem: dimensioning of stiffened panels of a fuselage is under development