Optimization of Structure Positions in an Acoustic Cavity Using XFEM, Reduced Models and a Gradient-Based Surrogate Model Approach

International audienceNoise reduction for passengers comfort in transport industry, or more generally in an acoustic cavity, is now an important constraint to be taken into account during the design process. The optimization of internal structures positioned according to acoustic of the cavity can lead to the study of several configurations and thus may become prohibitive in terms of computational time. The aim of this work is to be able to efficiently optimize the position of structures in an acoustic cavity. The first idea is to use XFEM in order to take into account the embedded structures, such as seats in a plane cabin [Legay 2013]. These structures are immersed arbitrarily within the acoustic mesh allowing to always use the same acoustic mesh, the acoustic pressure is enriched by a Heaviside function. This makes the parametric study easier since it does not involve a meshing process anymore. The second idea of the proposed approach is to use a surrogate-based optimization in order to furthermore reduce the computational time of the whole optimization process. It is based on the Efficient Global Optimization [Jones 1998]. At least, the use of the XFEM approach enables to easily compute the gradient of the pressure field with respect to the design variables which governed the position of the structure in the cavity. Moreover, a reduced basis [Legay 2015] is used to compute the solution as well as the gradient. Many operators remain indeed independent of the design variables and the main effort consists only of building gradients of the XFEM enrichment operators. These gradients enable to build a more accurate surrogate model [Laurent 2019]. This strategy enable to divide the CPU time by a factor from 2 to 10, depending of the problem complexity. The whole strategy is applied on some 2D and 3D cavities on which the position of a wall is determined in order to minimize the mean quadratic pressure in a control volume. - A. Legay. An extended finite element method approach for structural-acoustic problems involving immersed structures at arbitrary positions. International Journal for Numerical Methods in Engineering, 93(4):376-399. 2013 - A. Legay. The extended finite element method combined with a modal synthesis approach for vibro-acoustic problems. International Journal for Numerical Methods in Engineering, 101(5):329-350. 2015 - L. Laurent, R. Le Riche, B. Soulier and P.-A. Boucard. An Overview of Gradient-Enhanced Metamodels with Applications. Archives of Computational Methods in Engineering, 26(1):61-106. 201