A Physics-Based Tweedie Exponential Dispersion Process Model for Metal Fatigue Crack Propagation and Prognostics

Abstract

Most structural faults in metal parts can be attributed to fatigue crack propagation. The analysis and prognostics of fatigue crack propagation play essential roles in the health management of mechanical systems. Due to the impacts of different uncertainty factors, the crack propagation process exhibits significant randomness, which causes difficulties in fatigue life prediction. To improve prognostic accuracy, a physics-based Tweedie exponential dispersion process (TEDP) model is proposed via integrating Paris Law and the stochastic process. This TEDP model can capture both the crack growth mechanism and uncertainty. Compared with other existing models, the TEDP taking Wiener process, Gamma process, and inverse process as special cases is more general and flexible in modeling complex degradation paths. The probability density function of the model is derived based on saddle-joint approximation. The unknown parameters are calculated via maximum likelihood estimation. Then, the analytic expressions of the distributions of lifetime and product reliability are presented. Significant findings include that the proposed TEDP model substantially enhances predictive accuracy in lifetime estimations of mechanical systems under varying operational conditions, as demonstrated in a practical case study on fatigue crack data. This model not only provides highly accurate lifetime predictions, but also offers deep insights into the reliability assessments of mechanically stressed components.