Damage detection of offshore fixed structures using low-rank filter and cointegration analysis

Abstract

Cointegration has been used to distinguish the changes in dynamic features of a structure caused by environmental variations from those related to structural damage. This paper describes the development of a novel low-rank filter to suppress the noise in damage-sensitive features and enhance the identifiability of cointegration. It has been confirmed that cointegration is highly dependent on the presence of a vector error-correction model composed of a rank-deficient long-run impact matrix Π. Therefore, the low-rank filter employs a low-rank matrix pencil A+BKC to reconstruct Π iteratively, where A is the noise-free counterpart of Π, and the matrix product BKC accounts for the influence of noise. By minimizing the Frobenius norm of the gain matrix K, the random noise in the damage-sensitive feature series can be suppressed while the cointegration relationship among the damage-sensitive features can be recovered. Comparison between the low-rank filter and two widely used denoising methods, i.e., wavelet and empirical mode decomposition, is performed with the numerical model of an offshore platform and an experimental lattice structure. Results indicate that the low-rank filter is more compatible with cointegration for simultaneously suppressing noise and revealing the damage state of the structures in the presence of environmental variations.