基于半张量积压缩感知的形变数据重构在航天器结构健康监测中的应用

针对航天器结构健康监测（structural health monitoring, SHM）面临的数据传输和存储量过大问题，提出一种基于半张量积压缩感知（semi-tensor product compressed sensing, STP-CS）的形变数据重构方法。该方法基于形变数据的稀疏性，利用降维的随机高斯矩阵对形变数据进行压缩采样。为了验证该方案的可行性，实验研究了不同的观测矩阵维数与重构性能的关系。结果表明：采用该方法对形变信号进行随机采样，当观测矩阵存储空间减少到传统压缩感知（compressed sensing, CS）的1/64，仍能实现较高精度的重构，有效节省了观测矩阵的储存空间；此外，重构时间也随着观测矩阵维数的降低逐渐缩短。因此，该方法为解决航天器SHM面临的数据传输和存储挑战提供了新的解决思路。

Deformation data reconstruction based on semi-tensor compressed sensing in structural health monitoring of spacecraft

The major challenges facing the real-time structural health monitoring (SHM) application in the spacecraft domain involve the transmission and the storing of a huge amount of data. In this paper, we propose an approach of the semi-tensor product compressive sensing (STP-CS) to address this problem is the SHM. The STP-CS can be regarded as a generalized version of the traditional CS in its capability of reducing the dimension of a random observation matrix. Due to the sparsity of the deflection data, a random sampling scheme is adopted based on the STP-CS to minimize the amount of the field data. The relationships between different observation matrix dimensions and the reconstruction performance are determined. The experimental results demonstrate that even if the storage space of the observation matrix is reduced to 1/64 of the traditional CS, the reconstruction can still be realized with a sufficiently high precision. In addition, the reconstruction time also decreases with the decrease of the dimension of the observation matrix. Therefore, this method provides a new tool to deal with the challenge of the data transmission and storage in the SHM of spacecraft.