Deep learning-based sparsity-free compressive sensing method for high accuracy structural vibration response reconstruction

Compressive sensing (CS) has become a promising technique for addressing the transmission and storage challenges associated with big data in structural health monitoring. However, classic CS methods require signals to have good sparsity, limiting their performance in low-sparse situations. In order to address this challenge, this paper proposes a deep learning-based CS algorithm for high accuracy reconstruction of structural vibration responses without the assumption of sparsity. The key innovations of the proposed method can be mainly divided into three points. Firstly, a novel deep neural network model is proposed, which uses two branches to reconstruct the real and imaginary parts of the signal in the frequency domain, solving the key problem that deep neural network models are difficult to extract effective features from compressed signals in the time domain. Secondly, a large-scale frequency transformation matrix is decomposed into the multiplication of two small-scale matrices, greatly reducing the number of trainable parameters, and solving the problem that the original frequency transformation block cannot be directly used to extract global frequency-domain features of structural vibration responses due to the large number of parameters. Thirdly, a Fourier Unit is introduced and its feature extraction ability is improved, further enhancing the feature extraction ability of the whole model without significantly increasing the model parameters. The model does not use the adversarial training strategy, and the training process is simple and stable. It also does not require a large amount of adjustment of hyper-parameters. The number of trainable parameters of the model is only about 4 million, and the model training can be carried out with low-cost hardware. The effectiveness of the proposed method is verified by the low sparsity vibration response of a laboratory grandstand simulator. The maximum sparsity level of the vibration response of the simulator with 30 nodes is 0.381, which is larger than the sparsity level of the vibration response of common large-scale civil structures, that is, the sparsity is smaller and the reconstruction difficulty is greater. Experimental results show that the reconstruction error of the two classic CS algorithms is more than 3 times higher than that of the proposed method across all compression ratios. The identification results of the modal parameters of the original response and the reconstructed response show excellent consistency in their frequencies and vibration modes. The maximum relative error of the first 12 frequencies is only 0.038%, and the modal assurance criterion of the first 12 mode shapes is at least 0.9962. Overall, in large-scale low-sparse situations, the proposed method has high accuracy and high computational efficiency in reconstructing structural vibration responses, which can greatly alleviate the transmission and storage problems of monitoring big data with very low hardware requirements.