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This paper presents a methodology for constrained efficient global optimization (EGO) using support vector machines (SVMs). While the objective function is approximated using Kriging, as in the original EGO formulation, the boundary of the feasible domain is approximated explicitly as a function of the design variables using an SVM. Because SVM is a classification approach and does not involve response approximations, this approach alleviates issues due to discontinuous or binary responses. More importantly, several constraints, even correlated, can be represented using one unique SVM, thus considerably simplifying constrained problems. In order to account for constraints, this paper introduces an SVM-based "probability of feasibility" using a new Probabilistic SVM model. The proposed optimization scheme is constituted of two levels. In a first stage, a global search for the optimal solution is performed based on the "expected improvement" of the objective function and the probability of feasibility. In a second stage, the SVM boundary is locally refined using an adaptive sampling scheme. An unconstrained and a constrained formulation of the optimization problem are presented and compared. Several analytical examples are used to test the formulations. In particular, a problem with 99 constraints and an aeroelasticity problem with binary A. Basudhar · C. Dribusch · S. Lacaze · S. Missoum (B) Aerospace and Mechanical Engineering Department, output are presented. Overall, the results indicate that the constrained formulation is more robust and efficient.

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This paper introduces a methodology for the reliability-based design optimization of systems with nonlinear aeroelastic constraints. The approach is based on the construction of explicit flutter and subcritical limit cycle oscillation boundaries in terms of deterministic and random design variables. The boundaries are constructed using a support vector machine that provides a way to efficiently evaluate probabilities of failure and solve the reliabilitybased design optimization problem. Another major advantage of the approach is that it efficiently manages the discontinuities that might appear during subcritical limit cycle oscillations. The proposed approach is applied to the construction of flutter and subcritical limit cycle oscillation boundaries for a two-degree-of-freedom airfoil with nonlinear stiffnesses. The solution of a reliability-based design optimization problem with a constraint on the probability of subcritical limit cycle oscillation is also provided.

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International audienceSingle-reed instruments can produce multiphonic sounds when they generate quasi-periodic oscillations. The aim of this article is to identify a minimal model of a single reed-instrument producing quasi-periodic oscillations. To better understand the influence of model parameters on the production of quasi-periodic regimes, the mapping between parameters and quasi-periodic regimes is explicitly identified using a support vector machine (SVM) classifier. SVMs enable the construction of boundaries between quasi-periodic and periodic regimes that are explicitly defined in terms of the parameters. Results and conclusions obtained from the numerical model are compared to published experiments related to the the production of quasi-periodic oscillations with an alto saxophone. This qualitative comparison highlights the influence of key parameters on the production of multiphonic sounds