Fatigue cracks often occur in structural components due to dynamic loadings acting on them, such as wind loads and ground motion. If the static deflection due to dead loads is smaller than the vibration amplitude caused by dynamic loadings, these fatigue cracks alternately open and close with time, exhibiting a breathing-like behavior. This type of crack leads to a smaller change in structural dynamic characteristics than open cracks, and thus it is more difficult to be detected. If undetected timely, these fatigue cracks may lead to a catastrophic failure of the overall structure. Considering that breathing cracks introduce bilinearity into the structure, the present authors first developed a simple and efficient system identification method for bilinear systems by separating the global responses into two parts and performing Fourier transform on each set of separated data [1]. By applying this method, the natural frequency of each stiffness region can be identified. Then, breathing fatigue cracks can be detected by looking for the difference in the identified natural frequency between stiffness regions [1]. That approach is only applicable to the cases where the intact structure is linear. This study is to extend the approach in [1] to the cases when the intact structure is nonlinear, e.g., a structure with large displacements (geometrical nonlinearity). Once breathing cracks occur, there will exist both bilinearity (caused by breathing cracks) and cubic nonlinearity (caused by large displacements). To detect fatigue cracks in this case, Hilbert transform is proposed to be employed to process the separated data, instead of employing Fourier transform as in [1]. This approach has been successfully validated by numerical simulations.

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