Fatigue crack prognosis using Bayesian probabilistic modelling

Abstract

Prognosis of fatigue crack growth for mechanical and structural components is vital for aging military aircraft operated near or beyond their original design lives. For modern aircraft, prognostics and health management is supposed to be a designed-in capability; however, prognosis of mechanical and structural damage is yet to fully mature. This paper presents a scheme adopting Bayesian probabilistic modelling, extended Kalman filter (EKF) in particular, to predict fatigue crack growth in a common aircraft structural material: 2024-T3 aluminum alloy. In this scheme, the state model is the widely adopted Paris law in fracture mechanics (used to model the physics of crack growth), and the measurement model is a simple random walk model. The scheme is validated using a set of published crack growth test data, often referred to as the Virkler data, where the state model parameters are derived from one half of the data and the crack length prediction is made on the other half of the data. The EKF framework is further validated using a set of gear tooth crack propagation test data, where the crack length is the unobservable (or hidden) state variable, and the observable variable is a feature extracted from the gear vibration signal. The state model is also derived from the Paris law and the measurement model is developed using the observed relationship between the known crack length, the applied stress, and the energy of the impulsive signature extracted from an optimized sinusoidal model for gear vibration signals. Using the recursive EKF solution, we are able to achieve promising prognostic results in terms of the accuracy of the prediction, and demonstrate the method's robustness in dealing with uncertainties in the parameters defining the Paris law and the uncertainties in the measurements. Compared to other studies, the proposed method is a much simpler and more robust approach to the prognosis of fatigue crack size in mechanical structures and rotating components.

Digital Twin-Driven Remaining Useful Life Prediction for Gear Performance Degradation: A Review

“…Although the process is complex, it provides new ideas for Paris' law. Armstrong and coworkers [63] took the spur gear as the research object, using the Bayesian probability modeling and the Kalman filter to reduce the unreliability of Paris' law parameter determination, which is helpful to improve the accuracy of gear crack degradation life calculation. Tuegel et al [64] proposed that models, such as the fatigue crack model, can be used to predict the RUL and gear performance degradation of the equipment in DT.…”

Predicting Crack Growth and Fatigue Life with Surrogate Models

“…The procedure is summarized in Algorithm 5. In [29,30], the authors assume a normal distribution of C, even though the material parameter is only defined on the positive domain. Sampling C from a normal distribution could lead to realizations that are non-phyiscal.…”

“…A schematic representation of the model is depicted in Figure 5. As in [29,30], a normal distribution for the time to failure is assumed:…”

“…As in [29,30], this study assumes * to be fixed. According to [30], the exponent is set to * = 2.9. This is also quite close to what is proposed in [44].…”

“…Sampling C from a normal distribution could lead to realizations that are non-phyiscal. Since in [30,45], it is stated that the PDF (N| ) of N over a fixed crack length follows predominantly a lognormal distribution, it can be derived that C follows a lognormal distribution, too. By making the assumption that does not depend on , ;…”