Model Order Reduction based on Proper Generalized Decomposition for the Propagation of Uncertainties in Structural Dynamics

Mathilde Chevreuil (1) , Anthony Nouy (1)

1 GeM - Institut de Recherche en Génie Civil et Mécanique

A priori model reduction methods based on separated representations are introduced for the prediction of the low frequency response of uncertain structures within a parametric stochastic framework. The Proper Generalized Decomposition method is used to construct a quasi-optimal separated representation of the random solution at some frequency samples. At each frequency, an accurate representation of the solution is obtained on reduced bases of spatial functions and stochastic functions. An extraction of the deterministic bases allows for the generation of a global reduced basis yielding a reduced order model of the uncertain structure which appears to be accurate on the whole frequency band under study and for all values of input random parameters. This strategy can be seen as an alternative to traditional constructions of reduced order models in structural dynamics in the presence of parametric uncertainties. This reduced order model can then be used for further analyses such as the computation of the response at unresolved frequencies or the computation of more accurate stochastic approximations at some frequencies of interest. The dynamic response being highly nonlinear with respect to the input random parameters, a second level of separation of variables is introduced for the representation of functions of multiple random parameters, thus allowing the introduction of very fine approximations in each parametric dimension even when dealing with high parametric dimension.

Mots clés: Uncertainty propagation; Spectral stochastic methods; Structural dynamics; Model reduction; Proper Generalized Decomposition; Tensor product approximation; Separated representations

Domaines: Mécanique [physics.med-ph]; Analyse numérique [math.NA]

Mathilde Chevreuil, Anthony Nouy. Model Order Reduction based on Proper Generalized Decomposition for the Propagation of Uncertainties in Structural Dynamics. International Journal for Numerical Methods in Engineering, 2012, 89, pp.241--268. ⟨10.1002/nme.3249⟩. ⟨hal-00603342⟩