Bayesian parameter updating in linear structural dynamics with frequency transformed data using rational surrogate models

The identification of parameters of structural models through measurements of the system's response is of interest in many contexts. In Bayesian system identification the underlying inverse problem is formulated in a probabilistic setting, and Bayes’ rule is applied to update a prior conjecture on the parameters. We apply the Bayesian framework to identify the parameters of structural systems using dynamic measurement data. The likelihood function is formulated in terms of the misfit of the frequency transformed data and the model frequency response function. We introduce a novel formulation that accounts for the correlation of the model error in both spatial and frequency domain. The proposed formulation is able to handle dense data sets in the frequency domain without need to manually select data points. Due to the high computational demands of sampling-based approaches for solving the Bayesian updating problem with expensive structural dynamics models, we resort to surrogate models. We apply a recently introduced rational surrogate model that approximates the complex frequency response as a rational of two polynomials with complex coefficients. Samples of the posterior distribution of the model parameters are then obtained through an adaptive sequential sampling approach using the surrogate instead of the original dynamic model. The proposed method is successfully applied to identify the orthotropic stiffness and damping parameters of a finite element model of a cross laminated timber plate.