Time-variant reliability analysis (TRA) is widely utilized to assess the performance of engineering structures under various time-variant uncertainties. Recently, the time discretization-based TRA (TDTRA) methods have been developed, which can achieve satisfactory accuracy but need to excessively perform most probable point (MPP) searches at many equidistant time instants. To improve the efficiency of TDTRA, this paper proposes a TRA method based on approximating the MPP trajectory, referred to as AMPPT. First, this paper introduces a new concept of the MPP trajectory (MPPT), which is defined as the moving path of the MPP in the U-space when time changes. Then, a one-dimensional Kriging model is constructed to approximate the MPPT by the adaptive sampling method, which only performs MPP searches at several critical time instants. To further improve the computational efficiency, a warm-starting strategy is proposed to accelerate the MPP search. Then, the approximated MPPT is employed to transform the time-variant response into an equivalent Gaussian process. Finally, the spectral decomposition method and Monte Carlo simulation are used to compute the time-variant reliability. Comparative studies on four numerical examples and one practical engineering example of the solid rocket engine shell verify that the proposed AMPPT outperforms TDTRA in terms of both accuracy and efficiency. Test results also indicate that the efficiency gain of the proposed AMPPT comes from not only the reduction in the number of MPP searches but also the acceleration of the MPP search itself.

时变可靠性分析（TRA）被广泛用于评估各种时变不确定性下的工程结构性能。最近，已经开发了基于时间离散化的TRA（TDTRA）方法，该方法可以实现令人满意的精度，但是需要在许多等距时刻过度执行最可能点（MPP）搜索。为了提高TDTRA的效率，本文提出了一种基于近似MPP轨迹的TRA方法，称为AMPPT。首先，本文介绍了MPP轨迹（MPPT）的新概念，它定义为MPP在U空间中随时间变化的移动路径。然后，构建一维Kriging模型以通过自适应采样方法近似MPPT，该方法仅在几个关键时刻执行MPP搜索。为了进一步提高计算效率，提出了一种热启动策略来加速MPP搜索。然后，采用近似的MPPT将时变响应转换为等效的高斯过程。最后，采用谱分解法和蒙特卡罗模拟法计算时变可靠性。对固体火箭发动机壳体的四个数值示例和一个实际工程示例的比较研究证明，所提出的AMPPT在准确性和效率方面都优于TDTRA。测试结果还表明，提出的AMPPT的效率提高不仅来自MPP搜索数量的减少，还来自MPP搜索本身的加速。近似的MPPT用于将时变响应转换为等效的高斯过程。最后，采用谱分解法和蒙特卡罗模拟法计算时变可靠性。对固体火箭发动机壳体的四个数值示例和一个实际工程示例的比较研究证明，所提出的AMPPT在准确性和效率方面都优于TDTRA。测试结果还表明，提出的AMPPT的效率提高不仅来自MPP搜索数量的减少，还来自MPP搜索本身的加速。近似的MPPT用于将时变响应转换为等效的高斯过程。最后，采用谱分解法和蒙特卡罗模拟法计算时变可靠性。对固体火箭发动机壳体的四个数值示例和一个实际工程示例的比较研究证明，所提出的AMPPT在准确性和效率方面都优于TDTRA。测试结果还表明，提出的AMPPT的效率提高不仅来自MPP搜索数量的减少，还来自MPP搜索本身的加速。对固体火箭发动机壳体的四个数值示例和一个实际工程示例的比较研究证明，所提出的AMPPT在准确性和效率方面都优于TDTRA。测试结果还表明，提出的AMPPT的效率提高不仅来自MPP搜索数量的减少，还来自MPP搜索本身的加速。对固体火箭发动机壳体的四个数值示例和一个实际工程示例的比较研究证明，所提出的AMPPT在准确性和效率方面都优于TDTRA。测试结果还表明，提出的AMPPT的效率提高不仅来自MPP搜索数量的减少，还来自MPP搜索本身的加速。