Compressive sensing-based vibration signal reconstruction using sparsity adaptive subspace pursuit

Wireless sensors produce large amounts of data in long-term online monitoring following the Shannon-Nyquist theorem, leading to a heavy burden on wireless communications and data storage. To address this problem, compressive sensing which allows wireless sensors to sample at a much lower rate than the Nyquist frequency has been considered. However, the lower rate sacrifices the integrity of the signal. Therefore, reconstruction from low-dimension measurement samples is necessary. Generally, the reconstruction needs the information of signal sparsity in advance, whereas it is usually unknown in practical applications. To address this issue, a sparsity adaptive subspace pursuit compressive sensing algorithm is deployed in this article. In order to balance the computational speed and estimation accuracy, a half-fold sparsity estimation method is proposed. To verify the effectiveness of this algorithm, several simulation tests were performed. First, the feasibility of subspace pursuit algorithm is verified using random sparse signals with five different sparsities. Second, the synthesized vibration signals for four different compression rates are reconstructed. The corresponding reconstruction correlation coefficient and root mean square error are demonstrated. The high correlation and low error result mean that the proposed algorithm can be applied in the vibration signal process. Third, implementation of the proposed approach for a practical vibration signal from an offshore structure is carried out. To reduce the effect of signal noise, the wavelet de-noising technique is used. Considering the randomness of the sampling, many reconstruction tests were carried out. Finally, to validate the reliability of the reconstructed signal, the structure modal parameters are calculated by the Eigensystem realization algorithm, and the result is only slightly different between original and reconstructed signal, which means that the proposed method can successfully save the modal information of vibration signals.