Bayesian inference of the spatial distribution of steel corrosion in reinforced concrete structures using corrosion-induced crack width

• The steel weight loss distribution is estimated via Bayesian inference from the observed corrosion-induced crack width. • Sequence-to-sequence correlation between steel weight loss distribution and corrosion-induced crack width is modeled. • A novel nonlinear convolution kernel is proposed for encoding steel weight loss distribution. • Sparse polynomial chaos expansion is used for predicting corrosion-induced crack width. • The Karhunen-Loève transform reduces the dimensionality of the inference. Observations of corrosion-induced crack widths offer crucial information about the corrosion states of steel reinforcements in reinforced concrete (RC) structures, enabling a cost-effective method for inferring corrosion states through inverse analysis. However, the uncertainty associated with the relationship between corrosion-induced cracking and steel weight loss necessitates a probabilistic inference method, especially when considering the spatial distributions of steel weight loss, which provides important information to estimate the load-bearing capacity loss of corroded RC structures. This paper proposes a Bayesian framework to infer the steel weight loss distribution in RC structures based on the observed corrosion-induced crack width. To reduce the dimensions of the Bayesian inference, a Karhunen-Loève transform is applied to extract the principal distribution features of the steel weight loss. The forward model of the Bayesian inference adopts a data-driven sequence-to-sequence transduction approach to predict corrosion-induced crack width from steel weight loss. This model incorporates a novel nonlinear convolution kernel for input encoding and a sparse polynomial chaos expansion for decoding, which proves more accurate and efficient than finite element simulations. The Hamiltonian Markov chain Monte Carlo (HMCMC) sampler is used to efficiently sample from the posterior distribution of the Bayesian inference. The case study of the proposed method demonstrated that Bayesian inference provides robust range estimation for the steel weight loss distribution, with its 95% confidence interval encompassing most observations. Additionally, the method efficiently inferred high-dimensional steel weight loss sequences up to 61 dimensions, taking advantage of the dimension reduction technique and the gradient-informed HMCMC sampler.