Physics‐informed Polynomial Chaos Expansion for Uncertainty Quantification of S‐N Curves

Abstract The paper presents an application of physics‐informed polynomial chaos expansion for uncertainty quantification of a characteristic fatigue curve (S‐N curve) representing a number of loading cycles leading to a failure of a material or a product. Since there is a significant uncertainty affecting the S‐N curve caused by variability of material parameters, it is crucial to also identify a joint probability distribution of the S‐N curve instead of a deterministic curve. Therefore, the employed method combines physics of the approximated curve in form of deterministic Woehler curve with data from experiments affected by uncertainty of material parameters. The proposed method respects the local variability of the initially identified fatigue curve and it could serve for identification of an optimal experimental design in specific regions of the fatigue curve, which will sequentially improve the accuracy of the identified curve as well as local statistics. The presented theoretical method is applied for identification of S‐N curve based on laboratory experiments of concrete fasteners. The results demonstrated that the proposed method facilitates sequential enrichment of experimental design based on p ‐adaptivity and variance‐based active learning. The active learning led to a substantial reduction in the size of the dataset while ensuring the integrity of the approximations.