Damage detection in composite structures using vibration response under stochastic excitation

The investigations in damage detection methods based on vibration response are reviewed according to two categories, i.e. model-based damage detection method (MBDDM) and non-model-based damage detection method (NMBDDM). Then a new concept of inner product vector (IPV) is introduced using the cross correlation function of the measured vibration responses of the structure, and the corresponding damage detection method is proposed based on this vector. It is theoretically proved that the elements in IPV of a structure is the inner product of the time domain vibration responses of corresponding measurement points, and this vector can be directly calculated using the measured time domain vibration responses. Under white noise excitation the IPV of a structure is a weighted summation of mode shapes of the structure, and the weighted factors of the summation only depend on modal parameters of the structure. The effect of measurement noise on IPV is also considered, and the effect can be eliminated by the definition of IPV and an interpolation technique. The difference of IPVs between the intact and damaged structure is adopted as the damage index, and damage location is determined by the abrupt change in the difference of IPV. In order to distinguish the abrupt change caused by structural damage and measurement noise, two thresholds are proposed to classify the damaged and intact structures. Numerical simulation results of damage detection of single-location and multi-location delamination in a composite laminate beam demonstrate the effectiveness and veracity of the proposed method, even though measurement noise is considered in the vibration responses.