The physical heart of the framework is a corrosion-fatigue deterioration model built on decades of established fracture mechanics. Fatigue cracks at welded joints are represented as semi-elliptical surface flaws, characterized by a depth that grows through the plate thickness and a half-length that spreads along the surface. The stress intensity factor range at both the deepest point and the surface intersection of the crack is computed with the Newman-Raju formulation, one of the most widely trusted equations in fatigue assessment. Crack growth per loading cycle then follows the Paris law, the classic power-law relationship between growth rate and stress intensity, refined by the Walker correction to capture the strong influence of stress ratio. This last detail matters enormously for welds, because tensile residual stresses left behind by welding can push the effective stress ratio near the crack tip toward unity, meaning nearly the entire loading cycle drives the crack forward.

What makes the model genuinely a corrosion-fatigue model rather than a simple fatigue calculation is its explicit coupling of environmental degradation with crack propagation. Corrosion depth evolves over time following a power-law relation governed by a corrosion coefficient and exponent, continuously reducing the effective plate thickness. As the plate thins, the geometric correction factors and stress intensity factors change, accelerating crack growth. On top of that geometric effect, an environmental amplification factor multiplies the Paris coefficient, representing the direct chemical acceleration of cracking in aggressive media. In verification simulations, the consequences were striking: an identical welded detail predicted to survive 14.645 million cycles in air lasted only 7.344 million cycles under corrosion-fatigue conditions, a life reduction of nearly fifty percent, driven by a final corrosion depth of just 0.265 millimeters. Even a seemingly trivial loss of thickness, the authors show, compounds through the nonlinear crack-tip stress field into a dramatic shortening of service life.

Before trusting these predictions, the researchers subjected their implementation to a rigorous verification campaign. A convergence study demonstrated that refining the numerical integration step from 10,000 cycles down to 1,000 cycles reduced the relative error in predicted fatigue life below 0.01 percent, while the final crack geometry remained essentially unchanged. The implemented code reproduced the prescribed Paris-law exponent exactly, recovering a fitted slope of 3.00 with a coefficient of determination of 1.00 in log-log space. Most importantly, an independent benchmark against published corrosion-fatigue experiments on welded joints with artificial corrosion pits, conducted without any recalibration of model parameters, reproduced the experimentally observed degradation trends. The framework achieved a Spearman rank correlation of 0.883 with the nine experimental specimens and matched the direction of the stress-range trend, the pit-depth trend, and their interaction in every case, evidence of trend-level physical consistency rather than a guarantee of absolute life prediction.

The computational bottleneck, however, comes when physics meets probability. Reliability assessment demands thousands to millions of simulations, because uncertainty in crack geometry, loading, material behavior, and corrosion severity must all be propagated through the model. Solving the full fracture-mechanics equations that many times is prohibitively expensive. The authors’ solution is a physics-informed surrogate: they sampled the seven governing input variables, including initial crack depth, aspect ratio, stress concentration factor, stress ratio, and three corrosion parameters, using Latin Hypercube Sampling, a stratified technique that covers the multidimensional uncertainty space far more efficiently than naive random sampling. Each sampled combination was run through the physics model, producing a synthetic dataset of nearly 10,000 virtual experiments in which every record is guaranteed to obey the governing equations.

Onto this physically consistent dataset they trained an XGBoost model, a gradient-boosted decision tree algorithm renowned for its accuracy on nonlinear regression problems. Configured with 500 trees, a maximum depth of six, and a learning rate of 0.05, the surrogate predicted the logarithm of corrosion-fatigue life with a coefficient of determination of 0.976 and a mean absolute percentage error of only 3.49 percent on an independent test set of 1,915 samples. Five-fold cross-validation confirmed stable performance across data subsets, with no systematic bias in either the short-life or long-life regions. In effect, the surrogate compresses a computationally heavy fracture-mechanics simulation into a millisecond-scale prediction while inheriting the physics embedded in its training data, making million-sample Monte Carlo reliability analysis suddenly practical.

Yet fast predictions from a black-box model are of limited value in safety-critical engineering, where regulators and operators need to understand why a model says what it says. Here the framework deploys SHAP, or SHapley Additive exPlanations, a technique rooted in cooperative game theory that assigns each input variable a mathematically rigorous contribution to every prediction. The results revealed a clear hierarchy: the stress concentration factor dominated, with a mean absolute SHAP value of 4.67 million cycles, followed by the corrosion acceleration factor and the initial crack depth. These rankings are not statistical curiosities; they map directly onto the underlying mechanics. Stress concentration amplifies the crack-driving force, the amplification factor multiplies the growth rate, and a deeper initial flaw leaves less propagation distance before failure. An independent permutation importance analysis produced an almost identical ranking, with a Spearman correlation of 0.991 between the two methods, giving strong evidence that the identified hierarchy is robust rather than an artifact of one interpretability technique.

With a fast, transparent surrogate in hand, the team turned to the question that ultimately matters for infrastructure owners: how safe is the structure, and when should it be inspected? Running 100,000 Monte Carlo samples through the surrogate for a required design life of 10 million cycles yielded a failure probability of 0.746 and a negative reliability index, sobering evidence of how severely corrosion-fatigue can undermine nominal design margins. Time-dependent analysis over a 50-year service life showed reliability collapsing nonlinearly: the failure probability climbed from about 2 percent at year 5 to 20 percent at year 10, 51 percent at year 20, and 85 percent by year 50, with the steepest deterioration occurring in the first two decades. Conditional analyses confirmed that as the corrosion acceleration factor increased from its mildest to most severe range, the failure probability rose from 0.61 to 0.84, directly mirroring the SHAP finding that environmental severity is a dominant risk driver.

The final step converts these reliability curves into an actionable inspection schedule tied to engineering decision thresholds consistent with international probabilistic design guidelines such as ISO 2394 and the Eurocode basis of design. The framework identifies three critical moments: preventive monitoring should begin when the reliability index falls to 2.0, which occurs at roughly 5.7 years; detailed inspection is warranted when it reaches 1.0, at approximately 10 years; and repair or strengthening becomes necessary when it hits 0.0, corresponding to a 50 percent failure probability, at about 24.3 years. Rather than imposing uniform inspection intervals on every structure, the approach tailors intervention timing to the predicted deterioration trajectory of each asset, a shift with significant implications for life-cycle management of bridges, offshore installations, and marine infrastructure exposed to aggressive environments.

The authors are candid about the limits of their achievement. The experimental benchmark comprised only nine specimens, so the validation demonstrates trend consistency rather than comprehensive accuracy; the surrogate inherits any model-form uncertainty in the underlying fracture mechanics; localized pit nucleation and growth are represented only in reduced-order form; and the inspection plan relies on reliability thresholds alone, without economic optimization of inspection and repair costs. Future work, they note, should incorporate larger experimental datasets, propagate surrogate uncertainty through Bayesian methods, and couple reliability with life-cycle cost analysis. Even with these caveats, the study stands as a compelling demonstration of what physics-informed, explainable machine learning can deliver: not just a prediction, but a traceable chain of reasoning from the Paris law to the inspection calendar, giving engineers a tool that is simultaneously fast, physically grounded, and transparent enough to trust with the safety of the steel skeleton of modern civilization.

Subject of Research: Physics-informed explainable AI for corrosion-fatigue life prediction and reliability-based inspection planning of welded steel structures

Article Title: Physics-informed explainable artificial intelligence framework for corrosion-fatigue life prediction, reliability assessment, and inspection planning of welded steel structures

Article References: Nguyen, D.-D., & Nguyen, T.-H. (2026). Physics-informed explainable artificial intelligence framework for corrosion-fatigue life prediction, reliability assessment, and inspection planning of welded steel structures. Case Studies in Construction Materials, 25, Article e06586. https://doi.org/10.1016/j.cscm.2026.e06586

Image Credits: AI Generated

DOI: 10.1016/j.cscm.2026.e06586

Keywords: corrosion-fatigue, welded steel structures, fracture mechanics, XGBoost, explainable AI, SHAP, structural reliability, inspection planning, Paris law, Newman-Raju model, machine learning, infrastructure safety