OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is a publisher-deposited version published in: http://oatao. Any correspondence concerning this service should be sent to the repository administrator:staff-oatao@inp-toulouse.fr Surrogate modeling approximation using a mixture of experts based on EM joint estimation Dimitri Bettebghor · Nathalie Bartoli · Stéphane Grihon · Joseph Morlier · Manuel Samuelides Abstract An automatic method to combine several local surrogate models is presented. This method is intended to build accurate and smooth approximation of discontinuous functions that are to be used in structural optimization problems. It strongly relies on the Expectation−Maximization (EM) algorithm for Gaussian mixture models (GMM). To the end of regression, the inputs are clustered together with their output values by means of parameter estimation of the joint distribution. A local expert is then built (linear, quadratic, artificial neural network, moving least squares) on each cluster. Lastly, the local experts are combined using the Gaussian mixture model parameters found by the EM algorithm to obtain a global model. This method is tested over both mathematical test cases and an engineering optimization problem from aeronautics and is found to improve the accuracy of the approximation.
In this paper, topology optimization is used to design aircraft pylons. Original results for two Airbus pylons are first presented. An innovative bi-level optimization scheme is then proposed, which combines topology and geometric optimizations. At the first level, the dimension of the design domain, that is the envelope of the structure, and the location of the fixations are variables. At the second level, topology optimization is used to determine the optimal lay-out for given geometric parameters. This bi-level scheme is used to solve the aero-structural optimization of a pylon.
-Structure optimization at airframe level is mainly focused on sizing design variables detailing the thin-walled properties of aircraft structures. Typical design variables are cross sectional dimensions for 1D and 2D elements with an additional complexity brought by composite materials with their directional and multi-layer aspects. Even if the scope of these design variables is clear and well understood, the vision of the structure behaviour is multi-criteria and encompasses various fidelity levels. Its design requires several stages from the future project to the detailed definition of structural parts using various analysis tools from different disciplines. These several stages require adequate structural optimization processes to offer the best response with the right level of details to answer questions being sought at each maturity level of the design. A review of methods & tools developed and applied at AIRBUS to deliver automated sizing for aircraft structures along their development will be presented. Ways forward and major stakes for the future will be discussed.
Advanced nonlinear analyses developed for estimating structural responses for recent applications for the aerospace industry lead to expensive computational times. However optimization procedures are necessary to quickly provide optimal designs. Several possible optimization methods are available in the literature, based on either local or global approximations, which may or may not include sensitivities (gradient computations), and which may or may not be able to resort to parallelism facilities. In this paper Sequential Convex Programming (SCP), Derivative Free Optimization techniques (DFO), Surrogate Based Optimization (SBO) and Genetic Algorithm (GA) approaches are compared in the design of stiffened aircraft panels with respect to local and global instabilities (buckling and collapse). The computations are carried out with software developed for the European aeronautical industry. The specificities of each optimization method, the results obtained, computational time considerations and their adequacy to the studied problems are discussed.
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