Multi-element polynomial chaos with automatic discontinuity detection for nonlinear systems

Juliette Dréau (1) , Benoit Magnain (2) , Alain Batailly (1)

1 EPM - École Polytechnique de Montréal
2 DivS - Dynamique interactions vibrations Structures

Generalized Polynomial Chaos expansion (gPC) is a well-known method for uncertainty quantification of stochastic systems, in particular for smooth responses [1]. In the case of nonlinear systems exhibiting discontinuities in their surface response, it has been demonstrated that multi-element generalized polynomial chaos (ME-gPC)—which is based on an element decomposition of random space—provides accurate results. However, the definition of the elements, a key step of ME-gPC, is usually based on a tensor structure and the number of elements increases dramatically at high stochastic dimension [2]. In this study, the focus is made on the decomposition of the random space for nonlinear mechanical systems in order to efficiently apply gPC with a limited number of elements. More specifically, this decomposition relies on an automated detection procedure of the surface response discontinuities (referred to as edges) represented by cubic-spline curves. The proposed edge tracking detection is first detailed and validated on analytical test cases. Then, a specific implementation of ME-gPC is presented so that it may be efficiently applied on elements whose frontiers are defined by four cubic-splines in order to maximize the versatility of the random space decomposition. Finally, the proposed methodology is applied to the analysis of an academic Duffing system and an industrial compressor blade, NASA rotor 37, featuring blade-tip/casing contacts [3]. It is shown that the proposed developments yield accurate results both for the discontinuity detection and the response approximation in comparison to the reference Monte-Carlo simulations

Mots clés: Polynomial Chaos; Multi-element; Discontinuity Detection; Polynomial Annihilation; Support Vector Machines; Uncertainty quantification

Domaines: Génie mécanique [physics.class-ph]

Juliette Dréau, Benoit Magnain, Alain Batailly. Multi-element polynomial chaos with automatic discontinuity detection for nonlinear systems. 15th World Congress on Computational Mechanics, Jul 2022, Yokohama, Japan. ⟨hal-03736522⟩