Damage detection using covariance functions or a series of Hankel matrices

Damage in a structure can be detected from changes in its dynamic characteristics. Useful information must be extracted from vibration response measurements for this indirect method. This study investigates the effectiveness of covariance functions in damage detection. Covariance functions are attractive features, because they can be easily estimated, and they include all necessary information about the dynamic properties of the structure. Moreover, they are spatiotemporally correlated yielding data redundancy, which can be utilized by applying subspace-based methods. Covariance functions can be organized separately or in a Hankel matrix. Hankel matrix is always larger than the covariance function matrix, but its dimensionality is lower. This study compares their efficiencies in damage detection. An automatic algorithm was proposed to detect damage by applying whitening transformation. The advantage is that the subspace dimensions need not be determined. Instead, dimensionality can be reduced by selecting the first principal component only. Numerical and experimental data were used to validate the proposed method. The results demonstrate the potential of covariance functions for early warning using only a moderate number of sensors.