Reconstruction of undersampled damage monitoring signal based on compressed sensing

With aircraft structural safety becomes an increasingly issue, people start to use Structural Health Monitoring (SHM) technology to monitor the reliability of airframe structural materials. Fiber Bragg Grating (FBG) sensors are often used to monitor the composite materials due to their inherent advantages, but the gap between the FBG sensors´ sampling rate and the damage monitoring signals´ bandwidth has brought problem analyzing the `health condition´ of the airframe structure. To solve this problem, SHM technology, in conjunction with the reconstruction algorithms of Compressed Sensing (CS) theory, is expected to compensate the losing information of the signals sampled by FBG sensors and reconstruct the high frequency damage monitoring signals. In order to satisfy the applicable conditions of CS, this paper proposes an innovative method to convert a 1D signal to a 2D (2D) signal and has designed corresponding structurally random measurement matrix. Finally, the high frequency damage monitoring signal is reconstructed successfully and the relative error of the reconstruction is less than 30% under appropriate number of samples.