The input variable of engineering structure inevitable has certain uncertainty. How to quantify the influence of those uncertainties on the uncertainty of structural response is an important issue in structural design. Non-probabilistic reliability importance analysis is one of the methods to quantify this influence when variable data information is insufficient. Although the method has great advantages for variables with insufficient data information, there is no efficient calculation method at present, and the excessive computational cost seriously hinders its application in actual engineering structures. In this paper, the multiplicative dimensional reduction method, Taylor series expansion and unary quadratic function are combined to put forward an efficient algorithm to estimate two non-probabilistic reliability importance indices. With the proposed method, all the calculation processes used to solve the extreme value of function are replaced by an approximate analytical solution. Since the proposed method is an approximate analytical solution, the calculation efficiency is extremely high. Three examples are investigated to verify the accuracy and efficiency of the proposed method.

工程结构的输入变量必然具有一定的不确定性。如何量化这些不确定性对结构响应不确定性的影响是结构设计中的重要问题。当可变数据信息不足时，非概率可靠性重要性分析是量化此影响的方法之一。尽管该方法对于数据信息不足的变量具有很大的优势，但是目前还没有一种有效的计算方法，而过高的计算量严重阻碍了其在实际工程结构中的应用。本文将乘法降维方法，泰勒级数展开和一元二次函数相结合，提出了一种有效的算法来估计两个非概率可靠性重要性指标。使用所提出的方法，所有用于求解函数极值的计算过程都将被近似的解析解决方案代替。由于所提出的方法是一种近似的解析解决方案，因此计算效率非常高。研究了三个例子，以验证所提方法的准确性和效率。