  Compressive sensing (CS) has been studied and applied in structural health
monitoring for wireless data acquisition and transmission, structural modal
identification, and spare damage identification. The key issue in CS is finding
the optimal solution for sparse optimization. In the past years, many
algorithms have been proposed in the field of applied mathematics. In this
paper, we propose a machine-learning-based approach to solve the CS
data-reconstruction problem. By treating a computation process as a data flow,
the process of CS-based data reconstruction is formalized into a standard
supervised-learning task. The prior knowledge, i.e., the basis matrix and the
CS-sampled signals, are used as the input and the target of the network; the
basis coefficient matrix is embedded as the parameters of a certain layer; the
objective function of conventional compressive sensing is set as the loss
function of the network. Regularized by l1-norm, these basis coefficients are
optimized to reduce the error between the original CS-sampled signals and the
masked reconstructed signals with a common optimization algorithm. Also, the
proposed network can handle complex bases, such as a Fourier basis. Benefiting
from the nature of a multi-neuron layer, multiple signal channels can be
reconstructed simultaneously. Meanwhile, the disassembled use of a large-scale
basis makes the method memory-efficient. A numerical example of multiple
sinusoidal waves and an example of field-test wireless data from a suspension
bridge are carried out to illustrate the data-reconstruction ability of the
proposed approach. The results show that high reconstruction accuracy can be
obtained by the machine learning-based approach. Also, the parameters of the
network have clear meanings; the inference of the mapping between input and
output is fully transparent, making the CS data reconstruction neural network
interpretable.
