Smooth mode decomposition: Theory and its applications in full-field output-only modal analysis

Abstract

Full-field output-only modal analysis (OMA) became popular due to its superior spatiotemporal resolution over traditional sensing methods. It provides rich spatial dynamic information, which is essential for high-fidelity modal models, model updating, and non-intrusive health monitoring. However, the full-field sensory techniques implementation in OMA is hurdled by the excessive storage and computational requirements and the temporal aliasing effect. This paper develops a novel modal decomposition method, called smooth mode decomposition (SMD), to tackle these hurdles by exploiting the spatial dynamics and smoothness of the observed field measurements. SMD imposes the smoothness constraint on the identified mode shapes to resolve a set of orthogonal modes, called the smooth orthogonal modes (SOMs), that maximally represent the original field while also keeping the mode shape as smooth as possible. Since the SMD seeks spatially-smooth modal structures, the requirements on the temporal sampling can be relaxed. Hence, the SMD can be applied to nonuniformly and sub-Nyquist sampled full-field measurement data. Moreover, the SOMs converge to linear normal modes of uniformly distributed parameter systems, which provides a physically meaningful decomposition of the measurement data. Through a series of numerical examples, the SMD is compared to other popular covariance-based OMA methods. These examples demonstrate the merit of the proposed method when the vibration system has nonuniform system parameters and when the data is undersampled. Further, a full-field strain measurement technique, the three-dimensional digital image correlation, is utilized where spatiotemporal displacement measurements are obtained from a vibrating cantilever beam. The SMD is shown to provide accurate mode estimates with undersampled experimental data. Statistically, SMD shows its flexibility and quality in modal identification using temporally randomly captured images, which opens an avenue for alleviating storage and processing requirements for image-based full-field OMA.