Abstract Summary
Surrogate models enable the 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 problems, the system response can be described by the frequency response function. In [1] we proposed a rational approximation that expresses the system frequency response as a rational of two polynomials with complex coefficients. We showed that the proposed model is able to capture accurately the highly nonlinear nature of the frequency response function, even for structures with low damping. To estimate the coefficients of the approximation, a non-intrusive regression approach was employed that can be coupled easily with existing deterministic solvers. Recently, a sparse Bayesian learning approach was proposed in [2] in which only the polynomial terms that significantly contribute to the predictability of the surrogate are retained. The proposed approaches are based on global, static experimental designs. Especially in applications, where the relevant region in the input space is not known a-priori, e.g., Bayesian parameter updating, reliability analysis or optimization, using a static experimental design can lead to significant errors. In such cases it is beneficial to resort to active learning approaches, in which the experimental design is adaptively enriched during the training process. A so-called learning or acquisition function is employed as a means to choose further experimental design points. Often, the formulation of the acquisition function is based on the availability of the uncertainty in the surrogate model prediction. In the context of linear, Gaussian surrogate models, such as Gaussian processes, the predictive covariance can be obtained analytically. For non-linear models, such as the rational approximation, the predictive covariance is seldom available in closed-form. In this contribution we assess simulation- and approximation-based approaches to active learning using rational surrogate models. We specifically focus on Bayesian updating problems in which we are interested in learning the posterior distribution of a set of system parameters based on measured frequency response data. Furthermore, we demonstrate the applicability of the presented methods on different dynamic models. [1] F. Schneider, I. Papaioannou, M. Ehre and D. Straub, Polynomial chaos based rational approximation in linear structural dynamics with parameter uncertainties. Computers & Structures 233 (2020): 106223. [2] F. Schneider, I. Papaioannou and G. Müller, Sparse Bayesian Learning for Complex-Valued Rational Approximations, https://arxiv.org/abs/2206.02523, 2022
