Bayesian inference; Model updating; Modeling errors; Nonlinear normal modes; Nonlinear system identification
Abstract :
[en] This paper presents a Bayesian model updating methodology for dynamical systems with geometric nonlinearities based on their nonlinear normal modes (NNMs) extracted from broadband vibration data. Model parameters are calibrated by minimizing selected metrics between identified and model-predicted NNMs. In the first approach, a deterministic formulation is adopted, and parameters are updated by minimizing a nonlinear least-squares objective function. A probabilistic approach based on Bayesian inference is next investigated, where a Transitional Markov Chain Monte Carlo is implemented to sample the joint posterior probability distribution of the nonlinear model parameters. Bayesian model calibration has the advantage to quantify parameter uncertainty and to provide an estimation of model evidence for model class selection. The two formulations are evaluated when applied to a numerical cantilever beam with geometrical nonlinearity. The NNMs of the beam are derived from simulated broadband data through nonlinear subspace identification and numerical continuation. Accuracy of model updating results is studied with respect to the level of measurement noise, the number of available datasets, and modeling errors.
Disciplines :
Aerospace & aeronautics engineering
Author, co-author :
Song, Mingming; Department of Civil and Environmental Engineering, Tufts University, Medford, MA, United States
Renson, Ludovic; Bristol University
Noël, Jean-Philippe ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Département d'aérospatiale et mécanique
Moaveni, Babak; Department of Civil and Environmental Engineering, Tufts University, Medford, MA, United States
Kerschen, Gaëtan ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux
Language :
English
Title :
Bayesian model updating of nonlinear systems using nonlinear normal modes
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