Tracking the variation of complex mode shapes for damage quantification and localization in structural systems

Abstract

Real structures' mode shapes estimated by modal analysis techniques have a common feature: in most cases they are complex, and this complexity can derive from nonproportional damping, nonlinearities, mass loading effects, high modal density and localized damage, among others.Starting from the contributions available in the literature, the present paper investigates, from a numerical and experimental point of view, the correlation existing between localized damage and variation of global modal complexity indices conventionally employed to quantify the nonproportionality of damping in structural systems. Finally, driven by the inferences made through numerical and experimental test cases by tracking the variation of complex modes over multiple and progressive damage scenarios, a new index for damage localization and quantification is formulated and validated against real data.

Dynamic Behaviour of the Carillon Tower in Castel San Pietro Terme, Italy

“…(iv) Tere are no signifcant changes in mode shapes, with the MAC values being greater than or equal to 0.97. (v) Tere are no signifcant variations in the MPC values [25].…”

Ai-Driven Blind Source Separation for Fast Operational Modal Analysis of Structures

“…Note that, in general, the modal matrix is complex-valued when the damping matrix 𝐂 is non-classical. In large-scale civil engineering structures, complex mode shapes can arise for various reasons [43], including the existence of nonproportional and non-viscous damping, gyroscopic effects, asynchronous sampling, non-linearities, or limitations in the identification of low-excited modes.…”

Damage Identification in Cement-Based Structures: A Method Based on Modal Curvatures and Continuous Wavelet Transform

“…Indeed, wavelets have been demonstrated to be sensitive to the presence of damages (e.g., Haar and Gabor wavelets for crack detection [46]) and represent a powerful tool to be exploited in this context, along with numerical methods. Masciotta and Pellegrini [47] proposed an index based on the imaginary component of mode shapes in different damage conditions; in particular, they considered the difference in the imaginary part (normalized with respect to the initial average imaginary content) and multiplied it by the ratio between natural frequency in damaged and undamaged conditions, evidencing the higher sensitivity to damage occurrence with respect to the real component. Bayissa et al [48] exploited continuous wavelet transform (CWT) to derive the energy distribution in the time-frequency domain and transform the wavelet coefficients into damage identification parameters.…”

“…Then, the cuspid caused by the damage occurrence was evidenced through CWTbased analysis; curvatures were interpolated considering 200 points and Equation ( 4) was used to extract the real part of the mode shape curvature, being the real part of mode shape more informative [47]. Given the noise typical of experimental data, plus the discrete measurement points, at first, data were oversampled (i.e., the number of points in the signal was increased, with an oversampling factor of ×5 used to increase the original sample rate) in order to have more points on for the computation of modal curvature (since experimental data are acquired on discrete points and the error increases with the distance between two consecutive points [45]).…”

“…Then, the cuspid caused by the damage occurrence was evidenced through CWTbased analysis; curvatures were interpolated considering 200 points and Equation ( 4) was used to extract the real part of the mode shape curvature, being the real part of mode shape more informative [47].…”