On the Use of Singular Vectors for the Flexibility‐Based Damage Detection under the Assumption of Unknown Structural Masses

Abstract

The main purpose of this work is to investigate the usability of easily obtainable parameters instead of the modal traditional ones, in the context of a flexibility-based damage detection procedure, under the assumption of unknown structural masses. To this aim, a comparison is made between two different approaches: the first involves the calculation of the flexibility matrix by using traditional modal parameters, such as natural frequencies and modal vectors, normalized to unitary values, while the second involves the use of singular vectors, obtained through a simple matrix factorization. The modal parameters and the singular vectors necessary for the implementation of the damage detection procedure are evaluated through two different techniques: the Eigensystem Realization Algorithm and a wavelet-based procedure, for which a variant is proposed by introducing the energy reassignment concept into the original algorithm. Through the latter approach, in particular, it is possible to obtain a high number of singular vectors even in the case of reduced availability of sensors. The study is performed under the assumption of nonstationary excitation, in order to achieve general results, and the effectiveness of the procedures is evaluated through simulated tests regarding different structural schemes.

Passive single-station techniques applied for dynamic characterization of reinforced concrete buildings

“…In structural assessments, a seismometer is generally used to detect acceleration, speed, or displacements depending on time, whose operation is based on sensors, amplifiers, and analog or digital recording instruments [6]. Typically, structural surveys are based on the use of accelerometers [7][8][9]. Under operation (or passive) modal analysis, it is assumed that the background noise is a white function.…”

An FDD-based modal parameter-less proportional flexibility-resembling matrix for response-only damage detection

“…As shown in [17], the higher the number of identified modes, the more accurate are the obtained estimates. In [23] the mode shapes, to be used for assembling the modal flexibility matrix, are estimated as the singular vectors computed from the decomposition of the acceleration response matrix measured for the considered structural system. Damage detection techniques based on the use of the modal flexibility are also applicable starting from dynamic strain measurements, as shown, for example, in [24][25][26].…”