A physics-guided residual correction and uncertainty quantification method for interval prediction of combined high- and low-cycle fatigue life under small-sample conditions

Accurate interval prediction of combined high- and low-cycle fatigue (CCF) life under small-sample conditions remains challenging, as conventional damage models may introduce systematic bias and purely data-driven models may show unstable generalization. This study proposes a physics-guided residual correction and uncertainty quantification method for CCF life interval prediction. The Miner linear damage model is used as a physics-based baseline, and the Miner residual is defined in the logarithmic life domain. Physically informed damage descriptors, including the low-cycle damage ratio, high-cycle damage ratio, life scale ratio, and coupled low–high-cycle damage parameter, are then constructed. Based on these descriptors, a support vector regression (SVR) model is used to learn the Miner residual and correct the physics-based baseline prediction. Residual uncertainty is quantified using the empirical distribution of the remaining prediction residuals, and the 90% prediction interval, 95% prediction interval, and engineering conservative interval (ECI) are constructed using residual quantiles. Thus, point prediction, interval prediction, and empirical safe life estimation are achieved in a unified framework. The method is validated using 43 CCF samples from seven materials through leave-one-out cross-validation (LOOCV). The proposed method achieves an RMSE log 10 of 0.0895. The 95% prediction interval obtains a prediction interval coverage probability of 97.67% with a normalized mean prediction interval width of 0.1123. On the present LOOCV-based validation dataset, the ECI covers all samples, with an error factor of 1.4950. Compared with Miner, Manson–Halford, SVR, and XGBoost, the proposed method provides narrower empirical intervals at comparable coverage levels.