中文摘要：

对有限样本条件下的复杂系统风险发生概率评估问题,提出了小样本评估小概率事件的建模方法,通过非线性函数逼近累积概率与临界参数极值之间的映射关系.建立了风险概率评估数学模型,通过非线性回归方法得到了风险概率评估基本模型.对原始数据在评估模型中产生的误差作为目标函数,建立概率评估优化模型.并采用改进遗传算法对分布参数进行优化计算.以飞行安全为例,实现了有限样本情况下的飞行风险概率的计算,并通过最优逼近函数提高了计算精度.

英文摘要：

To assess the complex system＇s risk probability while the number of the simples was limited, the small probability assessment modeling method by small simples was put forward, and the mapped relationship between the cumulating probability and the extremum of the critical parameter was approached by nonlinear function. The risk probability assessment mathematic model was developed, and the basic assessment model was obtained by using nonlinear regress. The offered simples can not completely accorder with the assessment model, so the error was regarded as the object function, and the optimum probability assessment model was presented. In order to optimize the model＇s distribution parameter, the improved genetic algorithm was adopted. The applied example of flight safety assessment was showed, and the flight risk probability was calculated by the limited simples. The precise is improved by the optimum approach function.