Uncertainty quantification of fatigue properties with sparse data using hierarchical bayesian model

Data sparsity is a common issue in probabilistic fatigue modeling due to expensive testing or censored data. A hierarchical Bayesian model is proposed to address this issue and the basic concept is merged multiple stress-level data for uncertainty quantification. The hierarchical Bayesian model is utilized in modeling the relationships between fatigue life and applied stress. The fatigue life data are structured as multilevel according to stress levels. By hierarchical modeling, the probabilistic stress-cycle (P-S-N) curves are generated. The differences of variances across stress levels can be quantitatively described. The methodology is first demonstrated with relatively large number of testing data and classical statistical results can be reproduced. Following this, the method is applied to the case where the number of data is sparse and imbalanced by taking advantage of property of information sharing of hierarchical model. The results are discussed and its practical impact on the fatigue modeling and life prediction is assessed. Conclusions and future work are drawn based on the proposed study and results.