AI 中文总结
研究数据驱动的剩余使用寿命预测中样本复杂度问题，通过建立泛化界等七个围绕三个主题的结果，给出基本学习率，量化领域知识作用及数据质量影响，提供闭式表达式，跨域验证结果，为相关应用提供实用指南。
AI 中文摘要
数据驱动的剩余使用寿命（RUL）预测需要完整的退化轨迹进行训练，但此类直至失效的数据稀缺且昂贵。从业者目前缺乏关于给定模型和精度目标需要多少失效示例的原则性指导。本文为RUL预测开发了一个样本复杂度框架，包含围绕三个主题组织的七个主要结果。首先，建立基本学习率：无分布泛化界表明均方误差的均匀偏差以$O(B^{2}\sqrt{p/n})$减小，其中$p$是模型复杂度，$n$是轨迹数量，极小极大下界证明$\Theta(p/n)$率不可改进。其次，量化领域知识如何加速学习：纳入退化物理可将深度网络的数据需求降低多达两个数量级，伯恩斯坦型分析在高信噪比条件下实现极小极大最优$O(p/n)$率，闭式惩罚揭示错误假设的物理模型何时有害而非有益。第三，表征数据质量的影响：机队变异性导致不可约偏差-方差权衡，而右删失观测值会遭受效率损失，这严重取决于退化类别。针对指数、幂律和拉伸指数退化提供了闭式表达式。跨域验证针对已发表的涡轮风扇、电池和轴承基准，平均在2至3倍的范围内证实了理论预测。结果为规划数据收集、选择模型复杂度以及评估预测应用中的物理模型假设提供了实用指南。
英文摘要
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.
CommentsThis manuscript has been accepted for publication in Measurement Science and Technology. The final Version of Record is available at https://iopscience.iop.org/article/10.1088/1361-6501/ae7109/meta
Journal refMeas. Sci. Technol. 37(2026) 226203
