Variational Filter for Predictive Modeling of Structural Systems

Abstract

AbstractBayesian inference offers a distinct advantage in predictive structural modeling as it quantifies the inherent epistemic uncertainties that arise due to observations of the system which are both finite in length and limited in representative behavioral information. Current research interest in the field of predictive structural modeling has emphasized analytical and sampling approaches to Bayesian inference, which have the respective advantages of either computational speed or inference accuracy. Recent work in optimization-based inference approaches have created new opportunities to balance these advantages and generate flexible, efficient, and scalable filters for joint parameter-state identification of complex nonlinear structural systems. These techniques, commonly referred to as variational inference, infer the hidden states of a system by attempting to match the true posterior and to a parameterized distribution. In this study we build on the theory of automatic differentiation variational inference to introduce a novel approach to variational filtering for the identification of complex structural systems. We evaluate our method using experimental observations from a nonlinear energy sink device subject to base excitation. Comparison between identification performed using our approach and the unscented Kalman filter reveals the utility of the variational filtering technique in terms of both flexibility in the stochastic model and robustness of the method to poor specification of prior uncertainty.KeywordsSystem identificationNonlinear energy sinkBayesian inferenceUnscented Kalman filterVariational inference