论文标题
基于故障树分析的自适应重要性采样，用于分段确定性马尔可夫过程
Adaptive importance sampling based on fault tree analysis for piecewise deterministic Markov process
论文作者
论文摘要
分段确定性马尔可夫过程（PDMP）可用于建模复杂的动力学工业系统。该建模能力的对应物是它们的仿真成本，这使得可靠性评估无法通过标准的Monte Carlo方法提取。可以通过基于跨凝集（CE）程序的自适应重要性采样（AIS）方法来获得显着的差异。这种方法的成功取决于选择PDMP委员会函数的近似近似家庭。在本文中，提出了原始家庭。它们非常适合高维工业系统。它们的形式基于与故障树分析相关的可靠性概念：最小路径集和最小切割集。提出的方法将详细讨论，并应用于学术系统和核工业的现实系统。
Piecewise deterministic Markov processes (PDMPs) can be used to model complex dynamical industrial systems. The counterpart of this modeling capability is their simulation cost, which makes reliability assessment untractable with standard Monte Carlo methods. A significant variance reduction can be obtained with an adaptive importance sampling (AIS) method based on a cross-entropy (CE) procedure. The success of this method relies on the selection of a good family of approximations of the committor function of the PDMP. In this paper original families are proposed. They are well adapted to high-dimensional industrial systems. Their forms are based on reliability concepts related to fault tree analysis: minimal path sets and minimal cut sets. The proposed method is discussed in detail and applied to academic systems and to a realistic system from the nuclear industry.
