Blind denoising of structural vibration responses with outliers via principal component pursuit

SUMMARY Structural vibration responses themselves contain rich dynamic information, exploiting which can lead to tackling the challenging problem: simultaneous denoising of both gross errors (outliers) and dense noise that are not uncommon in the data acquisition of SHM systems. This paper explicitly takes advantage of the fact that typically only few modes are active in the vibration responses; as such, it is proposed to re‐stack the response data matrix to guarantee a low‐rank representation, through which even heavy gross and dense noises can be efficiently removed via a new technique termed principal component pursuit (PCP), without the assumption that sensor numbers exceed mode numbers that used to be made in traditional methods. It is found that PCP works extremely well under broad conditions with the simple but effective strategy no more than reshaping the data matrix for a low‐rank representation. The proposed PCP denoising algorithm overcomes the traditional PCA (or SVD) and low‐pass filter denoising algorithms, which can only handle dense (Gaussian) noise. The application of PCP on the health monitoring data of the New Guangzhou TV Tower (Canton Tower) shows its potential for practical usage. Copyright © 2013 John Wiley & Sons, Ltd.