可靠性灵敏度分析的重要抽样方法

基于重要抽样模拟,提出一种新的求解可靠性参数灵敏度的方法.所提方法依据失效概率对基本变量分布参数偏导数的积分表达式,推导可靠性灵敏度分析的重要抽样计算公式,该公式为一推导的函数在失效域中的数学期望形式,而该数学期望可以利用重要抽样函数获取的落入失效域中的样本来估计.算例结果表明,所提方法在保证同样计算精度的情况下具有比Monte Carlo模拟法更高的计算效率.

RELIABILITY SENSITIVITY ANALYSIS METHOD BASED ON IMPORTANCE SAMPLING

A new reliability sensitivity analysis method has been presented on the basis of importance sampling simulation.The reliability sensitivity is usually defined as a partial derivative of failure probability with respect to distribution parameter of basic random variable and is calculated by an integral expression.Based on the definition and the expression of the reliability sensitivity,the formulae of the presented importance sampling reliability sensitivity are derived.The formulae are expressed as a mathematical expectation of a function over the failure region.Furthermore,the required mathematical expectation can be evaluated by the importance samples locating at the failure region.The illustrations show that the presented method is more efficient than Monte Carlo simulation method at the same acceptable precision.