Time-variant reliability analysis plays a vital role in improving the validity and practicability of product reliability evaluation over a specific time interval. Sampling-based extreme value method is the most direct way to implement accurate reliability assessment. Its adoption for time-variant reliability analysis, however, is limited due to the computational burden caused by repeatedly evaluating performance function. This paper proposes a semi-analytical extreme value method to improve the computational efficiency of extreme value method. The time-variant performance function is transformed into dependent instantaneous performance functions in which the stochastic processes are discretized by the expansion optimal linear estimation method to simulate the dependence among different time instants. Each instantaneous function is separately approximated by Taylor series expansion at the most probable point through instantaneous reliability analysis. Based on the approximated performance functions, the computational cost of sampling-based extreme value method is significantly reduced. Results of three numerical examples demonstrate the efficacy of the proposed method.

时变可靠性分析在特定时间间隔内提高产品可靠性评估的有效性和实用性方面起着至关重要的作用。基于采样的极值方法是实施准确的可靠性评估的最直接方法。然而，由于重复评估性能函数而导致的计算负担，其在时变可靠性分析中的采用受到限制。本文提出了一种半解析极值方法，以提高极值方法的计算效率。时变性能函数被转换为相关的瞬时性能函数，其中的随机过程通过扩展最优线性估计方法离散化，以模拟不同时刻之间的相关性。通过瞬时可靠性分析，可以在最可能的位置通过泰勒级数展开式分别估算每个瞬时函数。基于近似的性能函数，显着降低了基于采样的极值方法的计算成本。三个数值示例的结果证明了该方法的有效性。