Mechanical Engineering Journal (Mar 2017)
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.
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