Development of a noise reduction approach for vibration-based damage detection involving high-order derivatives

To enhance the sensitivity of vibration-based identification techniques to damage of relatively small dimension, it is a common practice to explore higher-order derivatives of a captured vibration signal. However the measurement noise and uncertainties, inevitably contained in a vibration signal, can be fairly exacerbated during the differentiation process towards higher-order derivatives, masking damage-associated signal features and posing difficulty in signal interpretation. The objective of the present work is to examine variations of random measurement noise in such a differentiation process. A quantitative description of the noise influence, subject to various mathematic factors during the differentiation including differential intervals and initial noise level, was derived. A signal processing method based on low-pass wavenumber filtering was developed, to facilitate the de-noising treatment. As proof-of-concept validation, the proposed approach was employed 10 reduce measurement noise in vibration signals during detection of damage in a structural beam component. Thanks to the diversity of de-noising options, enhanced identification precision and accuracy over traditional de-noising endeavors was obtained.