Uncertainty quantification in Volterra series analysis of a nonlinear beam considering the noise effect

Luis Gustavo Giacon Villani (1) , Samuel da Silva (1) , Americo Cunha Jr (2)

1 UNESP - Universidade Estadual Paulista Júlio de Mesquita Filho = São Paulo State University
2 UERJ - Universidade do Estado do Rio de Janeiro [Brasil] = Rio de Janeiro State University [Brazil] = Université d'État de Rio de Janeiro [Brésil]

Many mechanical systems can operate with strong nonlinear behavior, making the negligence of such effects a source of errors in the prediction of the system response. A methodology, that has been successfully used, to predict the behavior of such systems is based on the identification of Volterra kernels. However, this technique is subject to uncertainties that are induced by the measurements noise. This work presents a study that assesses the influence of these uncertainties in the Volterra kernels, expanded with Kautz functions, and their propagation through the nonlinear dynamic system. The proposed method is applied to a nonlinear beam. Monte-Carlo simulations are used to compute the propagation of uncertainties in Volterra kernels. The results have been shown that the kernels are greatly influenced by the presence of uncertainties and confidence limits for the system responses can be established.

Mots clés: Nonlinear dynamics; Volterra series; Uncertainties quantification

Domaines: Vibrations [physics.class-ph]; Probabilités [math.PR]; Statistiques [math.ST]; Mécanique des structures [physics.class-ph]; Mécanique des solides [physics.class-ph]; Génie mécanique [physics.class-ph]

Luis Gustavo Giacon Villani, Samuel da Silva, Americo Cunha Jr. Uncertainty quantification in Volterra series analysis of a nonlinear beam considering the noise effect. XVII International Symposium on Dynamic Problems of Mechanics (Diname 2017), Mar 2017, São Sebastião, Brazil. ⟨hal-01487344⟩