Sparse Bayesian rational approximation for uncertainty quantification of structural dynamic models

Surrogate models enable efficient propagation of uncertainties in computationally demanding models of physical systems. We employ surrogate models that draw upon polynomial bases to model the stochastic response of structural dynamics systems. In linear structural dynamics, the system response can be described by the frequency response function. Recently, the authors proposed a rational approximation that expresses the system frequency response in terms of random input parameters as a rational of two polynomials with complex coefficients. In order to extend the applicability of the proposed surrogate model to higher dimensional problems, we introduce a sparse Bayesian learning approach with a hierarchical prior construction that retains only the polynomial terms that contribute significantly to the predictability of the surrogate. The proposed surrogate model is applied to predict the stochastic response of a frame structure with parameter uncertainties.