Predicting how long a metal component will survive under twisting, bending, and combined cyclic loads has long been one of the hardest problems in structural engineering. A new open-access study published in Advanced Modeling and Simulation in Engineering Sciences presents an artificial intelligence framework that converts raw cyclic stress–strain measurements into physically meaningful inputs and uses them to predict multiaxial fatigue life across a wide range of metals. The work, led by Ebrahim Seidi and Farnaz Kaviari, was published on 24 June 2026.
The core of the approach is a domain-informed feature engineering method that transforms eight initial experimental variables into 53 candidate predictors, later refined through a statistical selection protocol to 36 features retained for modeling. These engineered descriptors capture loading conditions, von Mises and Tresca equivalent stresses and strains, Goodman-corrected mean stress effects, detailed cycle characterization, energy-based damage measures such as elastic and total strain energy density and the Smith–Watson–Topper parameter, and indicators of the multiaxial stress state. Non-proportional loading, in which the axial and shear signals are out of phase, is encoded through the axial-shear phase difference and through equivalent quantities that merge normal and shear contributions.
The training data came from a previously published dataset of 1,167 fatigue tests on metallic materials. After a multi-stage curation process, the researchers validated loading paths, removed 353 invalid or uniaxial tests, eliminated 16 samples with missing values, and filtered out non-sinusoidal waveforms, yielding 642 high-fidelity samples. Restricting the analysis to materials with at least ten test samples left 25 material types and 589 experiments spanning both stress-controlled and strain-controlled constant-amplitude multiaxial loading. The target variable was the base-10 logarithm of cycles to failure, a transformation that accommodates the enormous numerical range of fatigue lives.
Three ensemble learning models were built and systematically compared: LSBoost, a sequential error-correcting boosting method; XGBoost, which augments boosting with row and column subsampling regularization; and Deep Forest, a multi-grained cascade architecture capable of automatic feature representation learning. Hyperparameters for all three were tuned with Bayesian optimization using a Gaussian process surrogate and an expected improvement acquisition function. Rather than optimizing a single metric, the search was guided by a custom composite score balancing RMSE, MAE, R², and the generalization gap between training and validation performance, with weights of 0.3, 0.3, 0.35, and 0.05 respectively.
The evaluation protocol was designed to prevent information leakage. The 589 samples were split 80/20 into training and hold-out test sets using stratified sampling across 26 unique combinations of material and loading type, producing 471 training and 118 testing samples. Feature selection was applied only to the training subset, and hyperparameter search relied on repeated threefold cross-validation with ten repetitions, stratified by the same material-loading strata. The test set remained untouched until final evaluation, making its results an unbiased estimate of generalization to completely unseen data.
XGBoost emerged as the most accurate model, achieving a testing R² of 0.9357 with a Pearson correlation of 0.9681 and an RMSE of 0.2351 log₁₀ cycles. LSBoost followed closely with a testing R² of 0.9225, Pearson R of 0.9613, and RMSE of 0.2580, while Deep Forest yielded the lowest performance, with a testing R² of 0.8967 and RMSE of 0.2978. Both boosting models showed training R² values near unity with modest train-test gaps of 0.048 and 0.067, indicating tight fits without substantial overfitting. The optimization trajectories themselves proved informative: XGBoost favored large estimator counts above 700, low learning rates below 0.04, and aggressive row subsampling near 0.5 to 0.6, while Deep Forest displayed a remarkably flat optimization landscape in which the top five configurations differed by only about 0.001 in composite score despite spanning an order of magnitude in trees per forest.
Beyond raw accuracy, the study extracted physical insight from the trained models through permutation-based feature importance analysis. To ensure stability, each model was independently retrained 50 times with different stratified splits, and importance was evaluated with 30 permutations per feature for each of the 150 resulting models. The equivalent-stress-to-UTS ratio, based on von Mises stress, emerged as the dominant predictor across all three models by a substantial margin, with a mean ΔR² of roughly 0.16 and a cross-run coefficient of variation of 23 percent. This ratio directly quantifies how close the applied multiaxial stress state lies to the material’s ultimate failure threshold.
The axial-shear phase difference ranked second with a mean ΔR² of about 0.10, providing empirical evidence that non-proportional loading coupling is a primary driver of fatigue damage. Axial loading amplitude, the multiaxial Goodman safety factor, and shear loading amplitude completed the top five. The three highest-ranked features all showed cross-run coefficients of variation below 31 percent, and univariate correlations of the dominant ratio with fatigue life were strongly negative in both loading modes, R = −0.55 for stress-controlled and R = −0.43 for strain-controlled tests, confirming that the relationship holds regardless of control mode.
Error analysis revealed both strengths and caveats. Median prediction errors were close to zero for all three models, indicating no systematic bias, but the error distributions showed left-skewed tails corresponding to occasional overprediction of fatigue life, which the authors note is a nonconservative, unsafe outcome for design. Per-quartile analysis for XGBoost showed the lowest error in the mid-cycle range, RMSE 0.170, with higher errors at the low-cycle extreme, RMSE 0.297, reflecting the difficulty of predicting plasticity-dominated fatigue sensitive to microstructure and surface condition. Per-material evaluation showed XGBoost and LSBoost maintaining R² above 0.90 for most materials with at least three test samples, while some materials with narrow fatigue-life ranges displayed low R² despite low absolute errors, an artifact of small test subsets rather than model failure.
The authors are explicit about the framework’s boundaries. It applies specifically to constant-amplitude sinusoidal multiaxial loading; variable-amplitude and random loading involve different damage accumulation mechanisms requiring rainflow cycle counting and cumulative damage corrections not captured by the current sinusoidal parameterization. Future work, they suggest, should incorporate asymmetric loss functions such as quantile regression and conformal prediction methods to deliver calibrated, conservative lower-bound life estimates with quantified uncertainty, addressing the safety implications of the observed overprediction tail.
Subject of Research: Machine learning prediction of multiaxial fatigue life in metallic materials using physics-informed feature engineering
Article Title: Artificial intelligence-driven physics-informed feature engineering for multiaxial fatigue life prediction of metallic materials with Bayesian optimization
Article References: Seidi, E., & Kaviari, F. (2026). Artificial intelligence-driven physics-informed feature engineering for multiaxial fatigue life prediction of metallic materials with Bayesian optimization. Advanced Modeling and Simulation in Engineering Sciences, 13(1), Article 11. https://doi.org/10.1186/s40323-026-00334-9
Image Credits: AI Generated
DOI: 10.1186/s40323-026-00334-9
Keywords: multiaxial fatigue, machine learning, XGBoost, Bayesian optimization, feature engineering, metallic materials, fatigue life prediction, von Mises stress, Deep Forest, LSBoost, non-proportional loading, structural integrity
News Source: Katie Riggs. (October 29, 2026). AI Turns Raw Stress Data Into 36 Physics Features to Predict Metal Fatigue. Scienmag.
