Sparse grey forecasting model learning and applications to fatigue life prediction of aircraft lap joint structures

A key challenge in the study of grey forecasting models is model structure discovery: converting measurement data into equations that are not only predictive, but provide a deeper understanding of the underlying dynamics inherent in the observations. The predominant approach relies on the cumulative sum operator, a knowledge-based technique that requires a well-characterized shape and extensive empirical experience. In this work, we propose a paradigm for data-driven modelling that simultaneously learns the structures of grey forecasting models and estimates the measurement noise at each observation. First, in the context of a state-space framework utilizing the integral representation of the grey model as a state equation, a candidate feature library is designed to explicitly depict the model equation, likely in a redundant form, and solved by sparse learning. Then, by combining signal-noise decomposition and time-stepping constraints, a regularized objective function is formulated to jointly learn model structure and noise. Next, large-scale simulations are designed to investigate the finite sample performance of the proposed method, including model structural identification accuracy, forecasting accuracy, and denoising capability. The results demonstrate high accuracy in model structure learning and robustness to measurement noise. Finally, we conduct fatigue testing on aircraft lap joints to collect crack propagation data. The proposed method is then applied to uncover dynamic patterns in the evolution of fatigue cracks and predict the remaining useful life of aircraft lap joint structures.