标题： 极限状态函数图的几何学与子集模拟 显示英文标题

标题： The Geometry of Limit State Function Graphs and Subset Simulation

摘要： 在过去十五年中，子集采样方法作为计算小概率事件的工具，在可靠性问题中经常被使用。 该方法通过原始极限状态函数的适当更高层次来估算失效域的概率内容的初始蒙特卡罗估计值进行外推。 然后迭代地估算逐渐减小到原始失效域的失效域的条件概率。 但有一些假设对于方法正确运行而言是必需的，并非立即显而易见失效域结构的假设。 这里研究了一些例子，表明至少在某些情况下，如果这些前提条件未满足，则可能获得不准确的结果。 为了进一步发展子集采样方法，无疑有必要找到一种方法，可以检查这些隐含假设是否未被违反。 此外，也许重要的是进一步改进这一概念，以摆脱这些限制。 显示英文摘要

摘要： In the last fifteen the subset sampling method has often been used in reliability problems as a tool for calculating small probabilities. This method is extrapolating from an initial Monte Carlo estimate for the probability content of a failure domain found by a suitable higher level of the original limit state function. Then iteratively conditional probabilities are estimated for failures domains decreasing to the original failure domain. But there are assumptions not immediately obvious about the structure of the failure domains which must be fulfilled that the method works properly. Here examples are studied that show that at least in some cases if these premises are not fulfilled, inaccurate results may be obtained. For the further development of the subset sampling method it is certainly desirable to find approaches where it is possible to check that these implicit assumptions are not violated. Also it would be probably important to develop further improvements of the concept to get rid of these limitations.