用贝叶斯方法预测铁轨裂纹演化，兼顾精度与安全约束。
Constrained Recurrent Bayesian Forecasting for Crack Propagation
- 基于贝叶斯框架的多步预测模型，融合内外因素影响。
- 量化认知与随机不确定性，提供预测置信区间。
- 加入物理约束提升可靠性，适合铁路维护决策参考。
铁路基础设施的预测性维护对安全保障至关重要。然而，由于内在与外部因素复杂交互及测量不确定性，准确预测裂纹演化仍是重大挑战。本文基于真实采集的裂纹长度数据，提出一种鲁棒的贝叶斯多步预测方法，用于建模铁轨裂纹随时间的演变过程。该模型捕捉多种影响裂纹扩展因素间的复杂关系，并通过贝叶斯方法同时量化认知不确定性（epistemic）与随机不确定性（aleatoric），为预测结果提供置信区间。为增强模型在铁路维护中的可靠性，引入特定约束以限制非物理的裂纹扩展行为并优先保障安全。实验揭示预测精度与约束遵守间存在权衡，凸显模型训练中的权衡决策过程。本研究为动态时序预测提供了先进建模思路，尤其适用于铁路维护，亦具跨领域应用潜力。
原文摘要 · Abstract (English)
Predictive maintenance of railway infrastructure, especially railroads, is essential to ensure safety. However, accurate prediction of crack evolution represents a major challenge due to the complex interactions between intrinsic and external factors, as well as measurement uncertainties. Effective modeling requires a multidimensional approach and a comprehensive understanding of these dynamics and uncertainties. Motivated by an industrial use case based on collected real data containing measured crack lengths, this paper introduces a robust Bayesian multi-horizon approach for predicting the temporal evolution of crack lengths on rails. This model captures the intricate interplay between various factors influencing crack growth. Additionally, the Bayesian approach quantifies both epistemic and aleatoric uncertainties, providing a confidence interval around predictions. To enhance the model's reliability for railroad maintenance, specific constraints are incorporated. These constraints limit non-physical crack propagation behavior and prioritize safety. The findings reveal a trade-off between prediction accuracy and constraint compliance, highlighting the nuanced decision-making process in model training. This study offers insights into advanced predictive modeling for dynamic temporal forecasting, particularly in railway maintenance, with potential applications in other domains.
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