Fatigue cracks can cause nonlinearities in the vibration responses of cracked structural components. Nevertheless, it is difficult to extract crack-induced weak dynamic nonlinearities, leading to a noticeable barrier to evaluating the severities of the fatigue cracks. To overcome this barrier, this study proposes a nonlinear vibration-based approach for quantitatively evaluating fatigue cracks. The singular spectrum analysis (SSA) is utilized to process structural vibration responses, by which crack-induced dynamic nonlinearities are extracted and embodied in the status features (SFs). In the status space, the dispersed distributions of the SF clusters can visually characterize different crack statuses. In addition, the 3D probability density functions of the SFs are formed, based on which a status probability index is established to quantify the relative probabilities of different known crack statuses. Hereby, the fatigue cracks can be quantitatively evaluated in a probabilistic manner. The approach is experimentally validated on a steel cantilever beam with a fatigue crack. The beam is excited by an electromagnetic shaker, steady-state velocity responses of which are acquired from its free end through noncontact measurement using a Doppler laser vibrometer. The open extents of the fatigue crack are controlled by the excitation amplitudes. The results prove that the approach can visually characterize the crack statuses corresponding to different open extents and quantify their relative probabilities.

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