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Smart Structures and Systems Volume 25, Number 3, March 2020 , pages 369-384 DOI: https://doi.org/10.12989/sss.2020.25.3.369 |
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Sparse reconstruction of guided wavefield from limited measurements using compressed sensing |
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Baijie Qiao, Zhu Mao, Hao Sun, Songmao Chen and Xuefeng Chen
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| Abstract | ||
| A wavefield sparse reconstruction technique based on compressed sensing is developed in this work to dramatically reduce the number of measurements. Firstly, a severely underdetermined representation of guided wavefield at a snapshot is established in the spatial domain. Secondly, an optimal compressed sensing model of guided wavefield sparse reconstruction is established based on l1-norm penalty, where a suite of discrete cosine functions is selected as the dictionary to promote the sparsity. The regular, random and jittered undersampling schemes are compared and selected as the undersampling matrix of compressed sensing. Thirdly, a gradient projection method is employed to solve the compressed sensing model of wavefield sparse reconstruction from highly incomplete measurements. Finally, experiments with different excitation frequencies are conducted on an aluminum plate to verify the effectiveness of the proposed sparse reconstruction method, where a scanning laser Doppler vibrometer as the true benchmark is used to measure the original wavefield in a given inspection region. Experiments demonstrate that the missing wavefield data can be accurately reconstructed from less than 12% of the original measurements; The reconstruction accuracy of the jittered undersampling scheme is slightly higher than that of the random undersampling scheme in high probability, but the regular undersampling scheme fails to reconstruct the wavefield image; A quantified mapping relationship between the sparsity ratio and the recovery error over a special interval is established with respect to statistical modeling and analysis. | ||
| Key Words | ||
| guided wavefield; compressed sensing; sparse measurements; laser Doppler vibrometer; full-field reconstruction; piezoelectric structural health monitoring | ||
| Address | ||
| (1) Baijie Qiao, Xuefeng Chen: The State Key Laboratory for Manufacturing Systems Engineering, Xi\'an, 710061, PR China. (2) Baijie Qiao, Zhu Mao, Songmao Chen: Department of Mechanical Engineering, University of Massachusetts Lowell, Lowell, MA 01854, USA; (3) Hao Sun: Department of Civil Engineering, Northeastern University, Boston, MA 02115, USA. | ||