Measurement of high-frequency vibration modes using event cameras and low-rank tensor completion

Various optical methods have been developed to visualize and measure dynamic structural behaviors, such as vibration modes and frequency spectra, for detecting fastener loosening and crack propagation. However, capturing high-frequency vibration modes typically requires high-speed cameras, which involve substantial power consumption, data volume, and cost. This study addresses these challenges by introducing a vibration measurement method based on an event camera, which records only logarithmic changes in luminance, combined with rectangular tracking and low-rank tensor completion for displacement reconstruction. The proposed method was experimentally validated through vibration measurements of a 630-mm-long polyvinyl chloride pipe and a coil spring. The results demonstrated that the method can quantitatively measure displacement waveforms under single-frequency, multi-frequency, and band-limited noise excitation conditions. For the pipe vibration tests, the normalized mean squared error (MSE) of the measured displacement waveform was less than 3% at relatively large displacement amplitudes of approximately 0.5 pixels, corresponding to 0.25 mm. Even at smaller amplitudes of approximately 0.1 pixels, corresponding to 0.05 mm, the MSE remained below 25%, demonstrating that the proposed method can quantitatively measure subpixel vibrations. The vibration modes exhibited a modal assurance criterion ≥ 0.9 under all test conditions, demonstrating excellent agreement with finite-element method results. Additionally, the proposed approach successfully detected changes in vibration modes caused by loosened bolted joints. The upper frequency measurement limit was assessed using an ultrasonic transducer experiment, achieving quantitative displacement spectrum measurements at a vibration frequency of 19.75 kHz and amplitudes of 30.1–37.6 μm. The mean MSE was below 10% for frequencies above 1 kHz. However, since ultrasonic vibrations are extremely subtle, it is necessary to zoom in significantly to capture them, and we have not yet been able to measure the vibration modes; this will be a topic for future research.