arXiv:2604.17066cs.LGmath.PR2026-04

提出RSR方法,实现大规模关联系统的快速不确定性量化。

Reference-state System Reliability method for scalable uncertainty quantification of coherent systems

论文配图:Reference-state System Reliability method for scalable uncertainty quantification of coherent systems
图 1 · 摘自论文原文
  • 用参考状态分类蒙特卡洛样本,避免复杂分解
  • 119节点295边图10秒内完成状态概率计算
  • 支持超大规模参考状态与多状态系统,适合实时风险评估

关联系统广泛应用于基础设施网络和供应链等场景,其概率评估因现有基于分解的方法在组件数量增加时扩展性差而面临挑战。本文提出参考状态系统可靠性(RSR)方法:与以往方法不同,RSR不将状态空间分解为互斥超立方体,而是利用参考状态对蒙特卡洛样本进行分类,显著降低计算成本对参考状态数量的敏感性。通过将样本与参考状态存储为矩阵,并使用批处理矩阵运算加速比较,充分借助现代机器学习驱动的高吞吐量计算能力。实验表明,RSR可在10秒内完成一个含119个节点和295条边的图的系统状态概率评估,展现出实时风险评估潜力。此外,RSR可扩展至数十万级参考状态,远超现有方法极限,并自然适用于多状态系统。然而,当边界参考状态数量极大时,收敛速度变慢,此问题与现有方法共通,提示未来需探索基于学习的系统状态边界表征。

原文摘要 · Abstract (English)

Coherent systems are representative of many practical applications, ranging from infrastructure networks to supply chains. Probabilistic evaluation of such systems remains challenging, however, because existing decomposition-based methods scale poorly as the number of components grows. To address this limitation, this study proposes the Reference-state System Reliability (RSR) method. Like existing approaches, RSR characterises the boundary between different system states using reference states in the component-state space. Where it departs from these methods is in how the state space is explored: rather than using reference states to decompose the space into disjoint hypercubes, RSR uses them to classify Monte Carlo samples, making computational cost significantly less sensitive to the number of reference states. To make this classification efficient, samples and reference states are stored as matrices and compared using batched matrix operations, allowing RSR to exploit the advances in high-throughput matrix computing driven by modern machine learning. We demonstrate that RSR evaluates the system-state probability of a graph with 119 nodes and 295 edges within 10~seconds, highlighting its potential for real-time risk assessment of large-scale systems. We further show that RSR scales to problems involving hundreds of thousands of reference states -- well beyond the reach of existing methods -- and extends naturally to multi-state systems. Nevertheless, when the number of boundary reference states grows exceedingly large, RSR's convergence slows down, a limitation shared with existing reference-state-based approaches that motivates future research into learning-based representations of system-state boundaries.

不确定性量化系统可靠性大规模计算

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