Output-only modal identification based on hierarchical Hough transform

• Published in: Journal of mechanical science and technology Vol. 30; no. 7; pp. 2941 - 2951
• Main Authors: Jin, Yi, Qin, Shaoqian, Guo, Jie, Zhu, Chang’an
• Format: Journal Article
• Language: English
• Published: Seoul Korean Society of Mechanical Engineers 01.07.2016; Springer Nature B.V; 대한기계학회
• Subjects: Algorithms; Cantilever beams; Computer simulation; Control; Damping; Degrees of freedom; Dynamical Systems; Engineering; Fourier transforms; Free vibration; High speed cameras; Hough transformation; Hough transforms; Hyperplanes; Industrial and Production Engineering; Mathematical analysis; Mathematical models; Mechanical Engineering; Modal identification; Resonant frequencies; Resonant frequency; Vibration; 기계공학; Sparse component analysis; Blind source separation; Hough transform; Modal analysis
• ISSN: 1738-494X; 1976-3824
• DOI: 10.1007/s12206-016-0603-x

Sparse component analysis (SCA) has been introduced to the output-only modal identification for several years. This paper proposes a new method based on hierarchical Hough transform to extract the modal parameters of mechanical structures. First, the measured system responses are transformed to Time-frequency (TF) domain using Short time Fourier transform (STFT) to get a sparse representation. Then, Hough transform is applied to the TF coefficients hierarchically to identify the hyperplanes and the mixing matrix is calculated. Finally, the modal responses are recovered by using l 1 -optimization and inverse STFT. From the recovered modal responses, natural frequencies and damping ratios are extracted. Numerical simulation of a 4 Degree-of-freedom (DOF) spring-mass system verifies the validity of the method. Free vibration of a steel cantilever beam is captured by a high-speed camera and then analyzed by the proposed method. The comparison of the estimated natural frequencies and damping ratios illustrates the good performance of the proposed algorithm.