Causality Constrained Deep Learning for Explainable Risk Analysis of Bridge Pier Settlement

Deep learning (DL) has significantly enhanced risk management in highway bridge operation. Although DL models exhibit strong predictive capabilities, their outputs derive from “black box” processes and cannot characterize uncertainty, leading to an unreliable risk decision-making. Thus, this study explores the following question: How to accurately predict bridge pier settlement in a trustworthy approach, and quantify risk uncertainty? To address this, we develop a causality constrained gated recurrent unit model to capture causal relationships inherent in monitoring data, further collaborated with a sampling method to analyze pier settlement risk under uncertainty. The proposed approach encompasses (1) introducing a transfer entropy (TE)-based causal inference method to quantify the causal relationships between factors of highway bridge operation system; (2) developing a TE-constrained loss function to guide model gradient updates to be consistent with causalities; and (3) applying the Markov chain Monte Carlo sampling to assess pier settlement risk considering uncertainty. Two real-world bridge projects in Guizhou, China, were used to validate the proposed method. The results indicate that the proposed approach achieves high accuracy in predicting pier settlement and quantifies its risk uncertainty effectively.