Modal Identification Using Vibration Signals Sampled at Sub-Nyquist Rates

Abstract

This paper presents an extensive experimental conducted to verify the performance of a previously proposed vibration transducer framework, which is capable of capturing vibration motions with high frequency contents relative to the sampling rate of the vibration signal. The transducer consists of a primary sensor, which consists of multiple single-degree-of-freedom systems (SDOF) and a secondary sensor- a camera that employs computer vision to track the proof masses of the SDOF systems. The responses from each SDOF system, sampled at sub-Nyquist rates, are utilized to reconstruct base motion with high accuracy through the solution of an augmented compressive sensing equation. Consequently, the sensor framework enables the accurate reconstruction of vibration signals sampled at significantly lower rates than the Nyquist rate. Initially, the performance of the transducer was evaluated by reconstructing sparse and non-sparse (random) signals generated by a shaker. Subsequently, the methodology was further validated through experimental modal analysis. A modal parameter estimation study was conducted under forced vibration conditions on two laboratory-scale structures: A beam structure and a three-story shear frame. The dynamic motions of these structures under forced vibration were successfully reconstructed using vibration data sampled at ten times lower than the Nyquist rate typically required for accurate identification. The experimental results demonstrate that the transducer framework effectively reconstructs structural dynamic displacements. These reconstructed displacements were then successfully employed to accurately identify modal parameters of vibrating structures.