In actual engineering, material properties, load effects, and other factors of mechanical structures change due to long-term use. In order to understand the operation of a mechanical structure in real time, it is crucial to obtain the dynamic trajectory of its reliability. Considering the time variability of a mechanical structure over time, uncertain random variables are introduced to express the uncertainty of various parameters of structures, and the Wiener process is used to describe the strength degradation process of structures so as to solve the calculation problem of time-varying reliability of mechanical structures. Based on the advanced first-order and second moment method (AFOSM), the proposed linearized Nataf change is used to complete the transformation from related nonnormal variables to independent standard normal variables in order to simplify the calculation process of reliability solution and solve the reliability calculation problem of random parameters subjected to arbitrary distribution. The deduced random variable sensitivity factor indicates the degree of influence of different random variables on the reliability of the mechanical structure, providing a theoretical basis for the optimal design and maintenance of a mechanical structure. The proposed method is analyzed using the cantilever beam and compared with the nonlinear Nataf transform and verified by the Monte Carlo simulation results. The results show that the proposed method can effectively solve the reliability sensitivity problem of structural system strength degradation.

中文翻译：

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基于线性化 Nataf 变换的时变可靠性方法

在实际工程中，机械结构的材料特性、载荷效应等因素会因长期使用而发生变化。为了实时了解机械结构的运行情况，获得其可靠性的动态轨迹至关重要。考虑到机械结构随时间的时间变化，引入不确定随机变量来表达结构各参数的不确定性，并采用维纳过程来描述结构强度退化过程，以解决时间-机械结构的不同可靠性。基于高级一阶和二阶矩法（AFOSM），提出的线性化 Nataf 变化用于完成相关非正态变量到独立标准正态变量的转换，以简化可靠性解的计算过程，解决随机参数任意分布的可靠性计算问题。推导出的随机变量灵敏度因子表明了不同随机变量对机械结构可靠性的影响程度，为机械结构的优化设计和维修提供了理论依据。利用悬臂梁对所提出的方法进行了分析，并与非线性 Nataf 变换进行了比较，并通过 Monte Carlo 仿真结果进行了验证。