Interval-oriented eigensystem realization algorithm and its modification for structural modal parameter identification with bounded uncertainties

Abstract

Structural modal parameter identification is the initial step in modeling, monitoring and controlling dynamic systems, which can determine the accuracy of dynamics and control research. However, the uncertainty of dynamic systems is difficult to quantify, which will lead to deviations in structural modal parameter identification. Aiming to identify modal parameters under the influence of structural uncertainty parameters, this study proposed a novel interval-oriented eigensystem realization algorithm (ERA) and its modification with bounded uncertainties, which is particularly suitable for the case where structural uncertainty samples are scarce. The uncertain structures are quantified as interval uncertain parameters, which can reduce the need for quantification of uncertainty parameters without loss of accuracy. The first and second-order interval-oriented singular value decomposition (SVD) is developed, which is regarded as an important tool to solve the interval Hankel matrix. The conventional modal parameter identification method of ERA and ERA/DC are extended into the interval framework using first and second-order interval perturbation with a detailed derivation process, and the identified bounds of frequency and damping ratio can be accurately estimated using both interval-oriented ERA and ERA/DC in conjunction with first and second-order interval perturbation SVD. Finally, two numerical examples and one experimental verification are used to assess the proposed method.