Filter-Coupled Heteroscedastic Gaussian Process Regression for S–N Curve Prediction of Injection-Molded Short Glass-Fiber-Reinforced Thermoplastics

Predicting the fatigue behavior of injection-moulded short glass-fiber-reinforced thermoplastics is hindered by the large, irreducible scatter of fatigue data and by the strong dependence of the response on the moulding conditions, which conventional point-estimate models neither reproduce nor quantify. This study presents a physics-informed heteroscedastic Gaussian process regression model (Pi-HGPR) that reconstructs the S–N curve of a given processing condition by predicting the fatigue stress amplitude as a function of the number of cycles, the injection temperature, the packing pressure, the specimen orientation, and the stress ratio, and that returns a 95% prediction band rather than a single value. The model combines a damage process-type physical mean, an anisotropic Matérn 5/2 covariance with Automatic Relevance Determination, and a local dispersion filter coupled to the process likelihood, which makes the noise level input-dependent. Trained on S–N curves compiled from the literature and assessed under two out-of-fold validation protocols (point-wise interpolation and leave-condition-out extrapolation), the model reaches a coefficient of determination of R2=0.839 in interpolation and R2=0.649 in leave-condition-out extrapolation, outperforming Random Forest and gradient-boosting baselines in both regimes, with a global empirical coverage of the prediction band of 92.9% and 86.2%, respectively, slightly below its nominal value and lower (76–81%) in sparsely sampled regions of the processing space. Automatic Relevance Determination identifies the packing pressure and the injection temperature as the most influential inputs, ahead of the stress ratio and the specimen orientation. Framing the task as predicting the stress amplitude along the low-scatter direction of the S–N field, and incorporating an input-dependent uncertainty, yields an accurate model within the tested processing window and provides reliable extrapolation limits governed by experimental data coverage rather than the learner.