physically interpretable residual strength prediction of corroded pipelines via symbolic Bayesian networks

Residual strength assessment of corroded pipelines is essential for ensuring the structural integrity and safe operation of gas transportation infrastructure. Traditional empirical formulas and finite element analyses, while widely used, often lack adaptability, interpretability, or computational efficiency. Recent advances in machine learning have improved prediction accuracy; however, many models remain opaque, limiting their utility in safety-critical structural health monitoring (SHM) applications where transparency and physical insight are imperative. This study introduces a novel framework, Symbolic Bayesian Networks (SyBN), for physically interpretable residual strength prediction of corroded pipelines. SyBN combines a Bayesian Feature-Weighted Neural Network (BFW-NN) for high-accuracy prediction and uncertainty quantification with a Deep Symbolic Regression (DSR) component that generates explicit mathematical expressions representing the relationship between pipeline parameters and failure pressure. A key innovation lies in an adaptive gating mechanism that dynamically balances prediction accuracy and symbolic consistency based on sample complexity. Extensive experiments were conducted on a public benchmark dataset comprising both experimental and simulation-based measurements of pipeline burst pressure. SyBN achieved state-of-the-art performance, with an [Formula: see text] of 0.966, RMSE of 1.304 MPa, and MAE of 0.968 MPa, outperforming several classical and ensemble learning baselines. Feature importance analysis confirmed high consistency between Bayesian-derived feature weights and SHAP values, while ablation studies validated the necessity of each framework component. The SyBN framework provides an effective and interpretable solution for residual strength prediction in corroded pipelines, offering engineers explicit symbolic models that enhance transparency and support informed decision-making. This approach aligns well with the growing demand for explainable and trustworthy machine learning in SHM tasks, particularly in critical infrastructure systems.