基于Monte Carlo仿真的小概率事件评估算法稳定性研究

应用极值理论对小概率事件进行评估的过程中,运用仿真的方法突破了客观条件对评估样本数量的限制,样本选取数量与评估概率的关系以及极值风险评估算法稳定性是亟待讨论的理论难点问题.以飞行风险为研究对象,分析了对评估稳定性造成主要影响的随机性因素,建立了用于稳定性分析的综合考虑“物理特性”和“随机特性”的典型人-机系统仿真模型.根据仿真评估结果,归纳了评估概率随样本数量的变化规律和Monte Carlo仿真对评估稳定性的影响,提出了合理选取样本数量和评估次数的方法.研究内容可为提高小概率事件评估的稳定性、减小评估误差提供参考和借鉴.

Arithmetic Stability Analysis of Extreme Risk Evaluation Based on Monte Carlo Simulation Method

In the research of small probability risk evaluation based on Extreme Value Theory (EVT),the limitation of sample number is cancelled by the use of system simulation. Arithmetic stability and relationship between numbers of the extreme value sample and evaluated probability are difficult problems to be solved in EVT.In the background of flight risk evaluation,the main stochastic factors that influence evaluation stability were analyzed. A representative "pilot-aircraft" system model for stability analysis considering physical and stochastic factors was established.The effect of Monte Carlo method on the evaluation stability and the relationship between the number of the extreme value samples and evaluated probability are calculated.Approach to get reasonable number of samples and evaluation times are proposed.The content can serve as reference for improving the stability and reducing the error of small probability evaluation.