Damage detection using the Lipschitz exponent estimated by the wavelet transform: applications to vibration modes of a beam

Damage detection by the wavelet transform of the fundamental vibration mode receives much attention recently. Many investigations report successful applications of the wavelet transform in damage detection,but most of them appear to lack theoretical justifications. The objective of this contribution is to show the effectiveness of the wavelet transform by means of its capability to estimate the Lipschitz exponent. It is also addressed that the magnitude of the Lipschitz exponent can be used as a useful indicator of the damage extent. As a specific example,damaged beams are investigated both numerically and experimentally. The continuous wavelet transform (CWT) by a Mexican hat wavelet having two vanishing moments is utilized for the estimation of the Lipschitz exponent. The analysis by the CWT also gives a guideline to choose appropriate discrete wavelet transforms