Development of an algorithm for the detection of discontinuities in a design of experiments: application to nonlinear systems with contact interfaces

Abstract

The drive towards reducing aircraft engines' aerodynamic losses has led engineers to reduce the clearances between blade tips and their surrounding casing, thereby increasing the risk of blade/casing contact interactions. Tools to accurately predict subsequent nonlinear dynamics are thus essential at design stage. Design of Experiments and the construction of surrogate models are very effective in studying complex and costly experimental blade/casing devices. Nonetheless, the convergence of surrogate models is linked to the smoothness of the response, evidencing the requirement of new approximation approaches for discontinuous responses. In this context, this report proposes a methodology to localize discontinuities in a 2D Design of Experiments inputs space in order to apply approximation methods on the smooth subdomains subsequently. First, a mesh is constructed on the inputs parameter space using a Delaunay triangulation and gradient-based indicators along with polynomial annihilation are then used as refinement indicators. The proposed methodology makes use of the Support Vector Machine to create a smooth approximation of the discontinuity location. Local improvement of the solution is finally completed. The applicability and the robustness of the proposed discontinuity localization tool are then tested on a variety of analytical models. The test cases have demonstrated satisfactory localization of closed discontinuities, multiple discontinuities in the same model, and discontinuities running partially through the domain. The numerically costly engineering model of blade/casing contact interactions is then considered and the proposed methodology is used to localize a jump in the response.