Compressive sensing of wind speed based on non-convex lp-norm sparse regularization optimization for structural health monitoring

Large-span spatial structures are quite sensitive to wind load because of their notable structural flexibility and low fundamental frequency. Structural health monitoring (SHM) of wind applied to this type of structure is the most direct and effective method of guaranteeing their safety. However, SHM produces a large amount of observation data, and these data often contain compressible redundant information and are usually sparse in the amplitude-frequency domain. To improve their transmission efficiency and quality and explore the characteristics of measured wind load on the surface of a large-span roof, we proposed l(p)-norm (0 < p < 1) sparse regularization based on compressive sensing for compression and reconstruction of wind speed data in the amplitude-frequency domain. The present compressed data were obtained through a low-rate sparse sampling method according to compressive sensing theory, which is more robust than the traditional sampling method. The alternating direction method of multipliers and the l(p) shrinkage method were applied to solve nonconvex optimization of reconstructing original data from incomplete measurements. The effectiveness of the proposed method was verified through a field test on a large-span steel roof of a railway station in southern China. The experimental results showed that the proposed method was superior to the smoothed l(0) method and typical l(1) based on the fast iterative shrinkage thresholding method. The reconstruction error was very low; even when the sampling rate was 10%, the signal-to-noise ratio of the reconstruction signal was 21.27, and the absolute error of reconstruction was <0.05. In addition, the distributions of wind power density and wind rose were consistent before and after compression.