This work presents a novel surface decomposition method for the sensitivity analysis of first-passage dynamic reliability of linear systems subjected to Gaussian random excitations. The method decomposes the sensitivity of first-passage failure probability into a sum of surface integrals over the constrained component limit-state hypersurfaces. The evaluation of these surface integrals can be accomplished, owing to the availability of closed-form linear expressions of both the component limit-state functions and their sensitivities for linear systems. An importance sampling strategy is introduced to further enhance the efficiency for estimating the sum of these surface integrals. The number of function evaluations required for the reliability sensitivity analysis is typically on the order of 10^2 to 10^3. The approach is particularly advantageous when a large number of design parameters are considered, as the results of function evaluations can be reused across different parameters. Three numerical examples are investigated to demonstrate the effectiveness of the proposed method.

翻译：本文提出了一种新颖的曲面分解法，用于分析受高斯随机激励线性系统的首通动态可靠度灵敏度。该方法将首通失效概率的灵敏度分解为一系列约束分量极限状态超曲面上的曲面积分之和。由于线性系统的分量极限状态函数及其灵敏度均具有闭式线性表达式，这些曲面积分的计算得以实现。本文引入了一种重要抽样策略，以进一步提高估算这些曲面积分之和的效率。可靠度灵敏度分析所需的函数评估次数通常在10^2至10^3量级。当考虑大量设计参数时，该方法尤其具有优势，因为函数评估结果可在不同参数间重复使用。通过三个数值算例验证了所提方法的有效性。