Damage identification method for cantilever beam based on multifractal spectrum of multi-scale reconstructed attractor

Abstract

A damage identification method for a cantilever beam based on a multifractal spectrum of a multi-scale reconstructed attractor includes: acquiring an original acceleration signal of the cantilever beam by a dynamic measurement system, performing stationary wavelet decomposition on a pretreated acceleration signal to obtain multi-scale sub-signals, selecting the multi-scale sub-signal that can represent main vibration characteristics of the cantilever beam for phase space reconstruction and normalization to obtain a normalized multi-scale reconstructed attractor, constructing the multifractal spectrum of the multi-scale reconstructed attractor, establishing a damage index based on a singularity index of the multifractal spectrum, and identifying and locating damage of the cantilever beam according to a relative numerical value of the damage index. The method can quantify structural damage characteristics in multi-scale phase space domain from the perspective of multifractal, and provide the simple, rapid and accurate damage identification method for cantilever beam.