Crack detection in ultrahigh-performance concrete using robust principal component analysis and characteristic evaluation in the frequency domain

Studying the crack propagation of ultrahigh-performance concrete (UHPC) helps us understand its mechanical mechanism and assess its structural performance. A novel method for crack separation and its characteristic evaluation was developed in this work. The proposed method introduces robust principal component analysis (RPCA) to decompose a data matrix from video streams stacked into a low-rank matrix and a sparse matrix, in which the sparse matrix represents the crack information. Compared with the cracks in a binary image, the obtained sparse matrix preserves rich crack information that can be used to quantify crack characteristics. The statistical characteristics of the crack area, the major and minor axes of the equivalent ellipse for crack regions, and the power spectral density are investigated and compared continuously. The proposed method is demonstrated by the crack development of UHPC under tensile loading. The analysis results indicate that RPCA can accurately separate cracks from the background. In the frequency domain by performing the Fourier transform of the sparse matrix, cracks are concentrated at small wavenumbers and the magnitude of small wavenumbers increases with an increase in the crack width. The relationship between the crack propagation and the stress-strain is also discussed. This work provides insight into the crack propagation of UHPC and an accumulated crack database for predicting the damage evolution of UHPC.