A Quantile Regression Approach to Estimating Fatigue Curves

Accurately predicting the time when the fatigue failures of materials such as fracture and plastic deformation occur at various stress ranges has a strong bearing on practical fatigue design of materials. In this study, we propose a simple regression-type alternative for estimating fatigue curves that represents a nonlinear relationship between a given stress amplitude and the fatigue life. To accommodate censored observations, we first combine Stute (1993)’ weights with the asymmetric L1 loss function in conventional quantile regression model, then, formulate and solve the corresponding optimization problem based on the structural risk minimization principle in order to ensure a good generalization capability. The current approach has a major advantage over the conventional ones that it requires few assumptions for developing the models, capable of exploring the data structure in a relatively flexible manner. All procedures and calculations are quite straightforward, and so the proposed quantile regression model has a high potential value in a wide range of applications for the inference of the fatigue life. Computational results for the data sets found in the literature present good evidences to support the argument.