Time-Varying Motion Filtering for Vision-Based Nonstationary Vibration Measurement

In the field of vibration measurement, the vision-based approach can achieve high spatial resolution compared to traditional accelerometers and lasers and thus has attracted much attention during the past decades. A recently developed phase-based video motion magnification (PVMM) technique to estimate subtle motions from videos is only suitable for stationary vibration measurement, because it is limited to analyze the well-separated vibration modes. In this article, a time-varying motion filtering (TVMF) method is presented to endow the PVMM technique with the ability to decompose nonstationary vibrations and visualize the time-dependent mode shapes of nonstationary systems. Specifically, we first build a parameterized mathematical model for the video motions and then extract each vibration mode by optimizing a set of parameters. After modulating each mode with an amplification factor, the time-varying characteristics of the vibration mode shapes can be visualized to naked eyes. Compared to the traditional PVMM technique, the merit of the proposed TVMF is verified to be able to produce less noise and fewer artifacts in nonstationary vibration measurement. The performance of TVMF is demonstrated on both a simulated experiment and a real nonstationary moving mass system.