Fatigue crack growth analysis via Wiener degradation model with random effects

Aerospace structure reliability is analyzed to increase the availability and decrease the stochastic failures of the system. A degradation-based modeling method is an effective approach for reliability assessment. Degradation models are usually developed based on degradation data or understandings of physics behind the degradation processes of products or systems. Stochastic models such as the Wiener process are one of the powerful tools in this field, especially the analysis of damage expansion and fatigue crack growth. This study presents a survey of degradation modeling approaches with consideration of random effects frequently used in engineering programs. Firstly, Wiener processes are used to model the degradation process of the product, which considers measurement errors simultaneously with random effects. Moreover, the closed-form expressions of some reliability quantities such as the probability density function are derived. Then, the maximum likelihood estimation method based on the expectation-maximation algorithm is presented to estimate the unknown parameters in the degradation models. Finally, a practical case study of fatigue crack growth using proposed models is provided and compared with the basic Gamma process to demonstrate the superiority and effectiveness of the Wiener process. It is shown that the Wiener process model estimates fatigue crack growth path better than the Gamma model and by adding the measurement error parameter to the model, its accuracy is increased.