Generalization bounds and sample complexity for remaining useful life prediction from complete degradation trajectories

Predicting the remaining useful life (RUL) of industrial equipment is critical for maintenance, yet training accurate models requires expensive, scarce run-to-failure data. Practitioners currently lack a principled way to determine how many failure trajectories are needed to achieve a target level of prediction accuracy. This paper addresses this gap by developing a statistical learning theory framework specifically for RUL prediction.

Unlike standard supervised learning, RUL prediction involves time-series trajectories with specific physical constraints. The authors treat each complete degradation trajectory (CDT) as a single observation, allowing them to bypass issues with temporal correlation within a unit. They derive distribution-free generalization bounds using the pseudo-dimension of the hypothesis class and quantify the impact of three key factors: model complexity, the incorporation of domain-specific degradation physics, and data quality issues like right-censoring and fleet variability.

• Fundamental Learning Rates: The authors prove that the generalization error decreases at a rate of O(p/n), where p is the model complexity and n is the number of trajectories. They demonstrate that this rate is minimax-optimal, meaning it cannot be improved upon in a general setting.
• Physics-Informed Efficiency: By constraining neural networks with known degradation physics (e.g., exponential or power-law models), the effective model complexity is significantly reduced. This leads to a theoretical reduction in required training data by up to 100x for deep architectures.
• Data Quality and Bias: The study provides closed-form expressions for how fleet variability and right-censored data (units removed before failure) degrade model performance, offering a rigorous basis for planning data collection strategies.