🤖 AI Summary
This study addresses the challenge of remaining useful life (RUL) prediction, where complete degradation data are scarce and costly to obtain, and theoretical guidance on sample requirements is lacking. The authors establish a sample complexity framework for RUL prediction, providing the first distribution-free upper bound on mean squared error generalization and a matching minimax lower bound. They quantify how physical priors reduce data requirements and uncover performance degradation mechanisms caused by model misspecification and right-censored observations. Leveraging statistical learning theory, minimax analysis, and Bernstein-type inequalities—combined with exponential, power-law, and stretched-exponential degradation models—the theoretical results are validated on benchmark datasets for turbofan engines, batteries, and bearings, achieving average errors within a factor of 2–3. These findings yield actionable guidelines for data acquisition, model complexity selection, and physics-informed model evaluation.
📝 Abstract
Data-driven remaining useful life (RUL) prediction requires complete degradation trajectories for training, yet such run-to-failure data are scarce and expensive. Practitioners currently lack principled guidance on how many failure examples suffice for a given model and accuracy target. This paper develops a sample complexity framework for RUL prediction comprising seven main results organised around three themes. First, we establish fundamental learning rates: a distribution-free generalization bound shows that the uniform deviation of the mean squared error decreases as $O(B^{2}\sqrt{p/n})$, where $p$ is the model complexity and $n$ the number of trajectories, and a minimax lower bound proves that the $Θ(p/n)$ rate is unimprovable.} \rev{Second, we quantify how domain knowledge accelerates learning: incorporating degradation physics reduces data requirements by up to two orders of magnitude for deep networks, a Bernstein-type analysis achieves the minimax-optimal $O(p/n)$ rate under high signal-to-noise conditions, and closed-form penalties reveal when an incorrectly assumed physics model hurts rather than helps. Third, we characterise the impact of data quality: fleet variability induces an irreducible bias$-$variance tradeoff, while right-censored observations suffer an efficiency loss that depends critically on the degradation class.} Closed-form expressions are provided for exponential, power-law, and stretched-exponential degradation. \rev{Cross-domain validation against published turbofan, battery, and bearing benchmarks confirms the theoretical predictions within a factor of 2$-$3 on average. The results yield practical guidelines for planning data collection, selecting model complexity, and evaluating physics model assumptions in prognostics applications.