Output-only modal identification by compressed sensing: Non-uniform low-rate random sampling

Abstract

Modal identification or testing of structures consists of two phases, namely, data acquisition and data analysis. Some structures, such as aircrafts, high-speed machines, and plate-like civil structures, have active modes in the high-frequency range when subjected to high-speed or broadband excitation in their operational conditions. In the data acquisition stage, the Shannon–Nyquist sampling theorem indicates that capturing the high-frequency modes (signals) requires uniform high-rate sampling, resulting in sensing too many samples, which potentially impose burdens on the data transfer (especially in wireless platform) and data analysis stage.This paper explores a new-emerging, alternative, signal sampling and analysis technique, compressed sensing, and investigates the feasibility of a new method for output-only modal identification of structures in a non-uniform low-rate random sensing framework based on a combination of compressed sensing (CS) and blind source separation (BSS). Specifically, in the data acquisition stage, CS sensors sample few non-uniform low-rate random measurements of the structural responses signals, which turn out to be sufficient to capture the underlying mode information. Then in the data analysis stage, the proposed method uses the BSS technique, complexity pursuit (CP) recently explored by the authors, to directly decouple the non-uniform low-rate random samples of the structural responses, simultaneously yielding the mode shape matrix as well as the non-uniform low-rate random samples of the modal responses. Finally, CS with ℓ1-minimization recovers the uniform high-rate modal response from the CP-decoupled non-uniform low-rate random samples of the modal response, thereby enabling estimation of the frequency and damping ratio. Because CS sensors are currently in laboratory prototypes and not yet commercially available, their functionality—randomly sensing few non-uniform samples—is simulated in this study, which is performed on the examples of a numerical structural model, an experimental bench-scale structural model, and a real-world seismic-excited base-isolated hospital buildings. Results show that the proposed method in the CS framework can identify the modes using non-uniform low-rate random sensing, which is far below what is required by the Nyquist sampling theorem.