Bayesian time-domain semi-analytical method for dynamic parameter identification based on filtering technology

This study proposes a time-domain methodology for identifying dynamic parameters within target frequency bands based on a filtering technique and a Bayesian framework. For linear time-invariant systems, owing to the commutative property of convolution, the filtering sequences of the system input and output are interchangeable. The semi-analytical formulation of the state transition matrix is derived via Eigen decomposition, establishing explicit expressions of the modal responses with respect to the natural frequencies and damping ratios. An optimization objective function dependent solely on the natural frequency and damping ratio is formulated using Bayesian inference and the theory of functional extrema. An improved grey wolf optimizer is then employed to solve this function. The proposed method is used to identify the dynamic parameters of a pantograph in a numerical example, with uncertainties quantified by the coefficient of variation. Finally, the effects of data truncation, filter bandwidth, noise level and optimization algorithms are studied.