Abstract Summary
Sequential Bayesian estimators are often employed in structural dynamics to estimate unknown probability density functions using incoming measurements and a mathematical process model. In the simplest case, where all variables of interest are normally distributed and the transitions are linear, the Bayesian estimator becomes equal to the Kalman filter. For more complex cases, a wide variety of nonlinear alternatives and algorithms able to deal with non-Gaussian distributions has been proposed. These sequential estimators rely on (possibly erroneous) mathematical state and observation equations, and by far the majority of them assume that the errors between the true and modelled states and observations can be modelled as Gaussian white noise. It is well-known, however, that for structural systems this assumption is questionable in the least, and mostly false. This could for instance be due to biases stemming from wrongfully modelled dynamic properties, or specific noise colour generated by the measurement equipment. In this contribution, we systematically characterize the process noise typically found in state-space formulations of structural systems, based on commonly encountered modelling discrepancies: damping errors, offsets in natural frequencies, and mode shape errors. The characterization is a first step towards more focused attempts at identifying or developing algorithms able to deal with different types and distributions of noise.
