相关正态变量情况下基于自适应超球重要抽样的可靠性灵敏度分析的转换法

THE TRANSFORM METHOD ON SELF-ADAPTIVE RADIAL-BASED IMPORTANCE SAMPLING FOR RELIABILITY SENSITIVITY ANALYSIS WITH CORRALATED NORMAL VARIABLES

在将相关正态变量转换成独立正态变量的基础上,首先建立了基于Monte Carlo模拟的相关正态变量可靠性灵敏度分析的转换法,并对其可靠性灵敏度估计值作了方差分析.其次将Monte Carlo转换法与自适应超球重要抽样法相结合,建立了相关正态变量可靠性灵敏度分析的自适应超球重要抽样转换法.所建立方法利用抽样样本提供的信息,通过迭代逐步确定最优超球半径,极大地提高了算法的稳健性和效率.由于自适应超球重要抽样转换法融合了Monte Carlo法的普适稳健性和超球重要抽样的高效性,因此它对于高度非线性隐式极限状态方程、多个失效模式串、并及混联系统、多个最可能失效点问题均具有很强的适应性,算例结果充分证明了这些优点.

For the reliability sensitivity estimation with correlated normal variables,the Transform Method（TM） based on Monte Carlo simulation has been established firstly through transforming the correlated normal variables into independent ones,and then,the variances have been analyzed in detail.Following,the TM is combined with a self-adaptive radial-based importance sampling（ARBIS） method for the reliability sensitivity analysis with correlated normal variables.Using the information provided by the required samples,the optimal radii of the ARBIS method can be determined by gradual iteration,which enables the robustness and the accuracy of ARBIS method to be improved greatly.Since the universality and the robustness of the Monte Carlo simulation and the high efficiency of the radial-based importance sampling are merged into the ARBIS-based TM,the established method is strongly applicable to highly non-linear implicit limit state equation,systems with multiple failure modes in series,in parallel or in mixed states,and the multiple Most Possible Points（MPP）.The examples given in the paper show these advantages finally.