基于自适应重要抽样的可靠性灵敏度分析方法

RELIABILITY SENSITIVITY ANALYSIS BASED ON ADAPTIVE IMPORTANCE SAMPLING METHOD

针对隐式极限状态方程的小失效概率问题,提出基于自适应重要抽样的可靠性灵敏度分析方法,给出该方法的具体实现步骤。所提方法从重要抽样抽取的所有样本点中选取合适的样本,利用回归分析和隐函数求导法则,求取失效概率对基本变量分布参数的灵敏度。所提算法的精度首先用有精确解的问题进行验证,然后在工程实例中进行应用。研究结果表明,与MonteCarlo可靠性灵敏度方法相比,所提方法具有计算精度相近但计算工作量小的优点,这种优点在失效概率小的情况下体现得更加充分。

For reliability model of implicit limit state equation with small failure probability, a reliability sensitivity algorithm is presented on the basis of adaptive importance sampling. The appropriate sampling points are selected from those of the importance sampiing. Hereby the regression and the derivative rule for implicit function are employed to obtain the sensitivity of the failure probability to the distribution parameters of the basic variables. The precision of the presented method is illustrated by examples with accurate solution of sensitivity, and the presented method is then applied to an engineering example. Compared with the sensitivity analysis based on Mon- te Carlo method, the presented method has closer precision and cheaper computational cost, and these advantages are more significant for the sensitivity analysis with small failure probability.