Novel approximate waveform capacity dimension for damage identification of beam-type structures

摘要

Fractal as a novel mathematical tool has a great potential to deal with transit events in a complex waveform. In this paper, fractal is introduced to detect irregularity of vibration mode shapes without using a baseline requirement. Different from the popular Katz's waveform fractal dimension (KWD), a novel approximate waveform capacity dimension (AWCD) specialized in irregularity detection in vibration mode shapes is introduced, from which an AWCD-based modal abnormality algorithm (AWCD-MAA) is established. The fundamental characteristics of AWCD-MAA, such as crack location identification and size quantification, are investigated using an analytical crack model of cantilever beams. An experimental modal shape evaluation of a cracked composite cantilever beam using smart piezoelectric sensors/actuators (i.e., Piezoelectric lead-zirconate-titanate (PZT) and polyvinylidene fluoride (PVDF)) is conducted to confirm the feasibility of the proposed algorithm. The proposed AWCD-MAA is capable of locating and quantifying the crack in a beam-type structure without prior requirement of baseline reference data.