Baseline-free structural damage detection using PCA- Hilbert transform with limited sensors

Conventional vibration-based damage identification methods need a large number of sensors on the bridge to identify the structural modal information and rely on the response data of bridges under a non-damage state for comparison, which restricts their implementations in the health monitoring of bridge structures in service. This paper proposes a baseline-free structural damage detection method based on limited sensor information. The proposed method uses the Hilbert transform combined with principal component analysis (PCA) to locate the damage. Firstly, PCA is performed on the displacement response data matrix of the bridge under a moving load to obtain the principal component matrix. According to the physical interpretation of PCA of the responses of a beam-like bridge under a moving load, each column of the principal component matrix, namely the principal component, composes of a mode shape and the dynamic information at this modal frequency of the bridge. The dynamic information of the modal frequency is indirectly obtained by filtering out the mode shape by low pass filter. Then the Hilbert transform is used to process the dynamic component information to receive the instantaneous frequency which is regarded as the damage index. When the structure is damaged, the first instantaneous frequency at the damaged location changes abruptly. To demonstrate the effectiveness and performance of the proposed method, numerical simulations and experimental validations on beam bridge models are conducted. The results show that the method is free from the requirement of the information of bridges under the undamaged state, and only limited sensors are needed to locate the damage.