Efficient flexibility identification method using structured target rank approximation and extended Prony's method

Abstract

An accurate estimation of the structural flexibility is crucial in applications such as deflection prediction, damage detection, and finite element model updating. By introducing a unit impulsive response function (UIRF) matrix estimated from noisy input and output signals collected through impact testing, this paper proposes a new method for estimating the structural flexibility matrix from a noisy UIRF. The advantages lie in the way the noise and decoupling modes of the impulse response signal are handled in the time domain. The proposed method consists of three steps: (1) Constructing an enhanced unit impulse response function (EUIRF) from the UIRF by utilizing the orthogonality of the displacement mode shapes for mode decoupling, (2) Noise removal from the constructed EUIRF to obtain a filtered one by implementing the improved Cadzow's algorithm for the structured target rank approximation (STRA) of the Hankel matrix constructed from the EUIRF, and (3) Structural flexibility identification from the EUIRF using the extended Prony's method to identify the basic modal parameters and modal scaling factors for a single-mode impulse response function with one degree of freedom. To validate the applicability of the proposed method, numerical and laboratory case studies were performed. A noisy impact test was simulated for a three-span continuous beam bridge, and the identified modal parameters and structural flexibility matrix were found to be accurate. Moreover, an impact test was conducted on a simply supported beam in a laboratory, and the results showed that the deformation predicted from the identified flexibility matrix and the one measured from the static load test are in good agreement.