Damage detection by modal curvatures: numerical issues

This work is concerned with modal curvature-based damage detection in slender beam-like structures, whereby the modal curvatures are computed by numerical differentiation of noisy mode shapes sampled at a finite number of measurement points. Within this framework, most common techniques greatly amplify the measurement errors and their application leads to unreliable outcomes, especially when a large set of measurement points is considered. Preliminary signal processing, even if beneficial for reducing the noise level, does not solve the problem in that neither the detection of damaged zones nor the reduction of false alarms exhibit significant improvements. In a comparative fashion, we herein demonstrate that a modified Savitzky–Golay filter and the cubic smoothing spline method can provide a more affordable way for detecting damages when using numerically obtained modal curvatures. In doing so, the robustness against the measurement errors and the role of the adopted formulation for the modal curvature-based damage index are considered. A simple statistical procedure that can further improve the detection of damaged regions together with the identification of possible false positives is also presented.