A new damage detection approach for beam-type structures based on the combination of continuous and discrete wavelet transforms

In this work, a new wavelet-based damage detection approach has been proposed. The method is based on the assumption that a damaged mode shape of a beam is approximately composed of an undamaged mode and other contributors such as measurement- and local damage-induced variations. Then, a proper approximation function (AF) to be used as undamaged mode can be extracted from the damaged one by the discrete wavelet transform (DWT), provided a suitable wavelet and a decomposition level (DL) are determined. By this way, a reliable damage index can be defined taking the difference of the continuous wavelet transform (CWT) coefficients of the damaged mode and those of the AF. It is demonstrated that the AF which is well-correlated with the numerical undamaged mode of beam can be obtained at the DL after which the approximation energy ratio (Ea) drops significantly, if a suitable wavelet having sufficient number of vanishing moments (NVM) is selected. In order to test the method, the first two numerically obtained modes of a damaged beam as well as the first two experimental modes of another damaged beam are employed. Although the physical properties and damage features of these two beams are quite different, it is concluded that the AFs which are derived from these modes by the proposed method can be conveniently used as baseline data for damage detection purpose.

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