Failure probability estimate of corroded reinforced concrete structures based on sparse representation of steel weight loss distributions

• The K-SVD algorithm derives a sparse representation of high-dimensional SWL distributions. • Non-standard distribution features of SWL are derived that can capture detailed spatial variations. • The orthogonal matching pursuit algorithm reduces the dimensions of SWL distributions. • Surrogate model based on sparse representation of SWL distributions enhances accuracy in estimating load-bearing capacity. • Failure probability estimates using sparse representation of SWL distributions show reduced variance. Uncertainties associated with the non-uniform spatial distribution of steel weight loss (SWL) should be considered appropriately when estimating the load-bearing capacity loss of corroded reinforced concrete (RC) structures. Addressing these uncertainties necessitates a probabilistic analysis using high-dimensional SWL data, which can lead to inaccurate condition assessments for corroded RC structures. This paper presents a dimension-reduction approach for SWL distribution based on the K-means singular vector decomposition (K-SVD) algorithm, which enforces a sparse representation of SWL distributions using a combination of non-standard distribution features learned from experimental SWL data. The K-SVD algorithm involves an iterative two-stage supervised learning process. In the dictionary learning stage, K-SVD identifies non-standard distribution features tailored to the localized characteristics of SWL data, based on which the orthogonal matching pursuit (OMP) algorithm is employed in the coding learning stage to derive a sparse representation of SWL distributions. The efficacy of K-SVD is evaluated using 83 experimental samples of SWL distributions. The results reveal that the K-SVD algorithm can derive a sparse representation of SWL distribution while preserving the distribution details of SWL. With just 15 learned non-standard distribution features, K-SVD achieves the same accuracy in reconstructing 168-dimensional SWL distribution data as the baseline Karhunen-Loève OMP (KL-OMP) method, which uses 75 standard features. Subsequently, the sparse representation is used to compute the flexural failure probability of corroded RC beams, for which a Kriging surrogate model is constructed. The results show that the sparse representation significantly enhances the accuracy of the Kriging surrogate model and improves the computational stability of the flexural failure probabilities, which is crucial for accurately assessing the condition of corroded RC structures.