Calculation of probability of exceedance for nonstationary non-Gaussian responses remains a great challenge to researchers in the field of structural reliability. In this paper, an analytical solution is proposed for calculating the mean upcrossing rate (MCR) of the non-stationary non-Gaussian responses by approximating the displacement and velocity responses with the bivariate vector translation process, in which the unified Hermite polynomial model (UHPM) is selected as the mapping function. The first four moments (i.e., mean value, standard deviation, skewness, and kurtosis) and cross-correlation function of the displacement and velocity responses needed in UHPM are estimated from some representative samples generated by random function-spectral representation method (RFSRM) and time-domain analysis. Under the Poisson assumption of the upcrossing events, the calculation of extreme value distribution or probability of exceedance for structural response can be determined with the proposed method. The proposed method is applicable to a wide range of structural responses, including asymmetric and hardening or softening responses. Three numerical examples are provided to demonstrate the efficiency and accuracy of the proposed method. It can be concluded that the proposed method provides an accurate and useful tool for dynamic reliability assessment in engineering applications.

计算非平稳非高斯响应的超越概率对结构可靠性领域的研究人员来说仍然是一个巨大的挑战。在本文中，通过使用双变量向量平移过程逼近位移和速度响应，提出了一种用于计算非平稳非高斯响应的平均上交叉率 (MCR) 的解析解，其中统一 Hermite 多项式模型 (UHPM) ) 被选为映射函数。UHPM 中所需的位移和速度响应的前四个矩（即平均值、标准差、偏度和峰度）和互相关函数是根据随机函数谱表示法 (RFSRM) 生成的一些代表性样本估计的，并且时域分析。在上交叉事件的泊松假设下，该方法可以确定结构响应的极值分布或超越概率的计算。所提出的方法适用于广泛的结构响应，包括不对称和硬化或软化响应。提供了三个数值例子来证明所提出方法的效率和准确性。可以得出结论，所提出的方法为工程应用中的动态可靠性评估提供了准确且有用的工具。包括不对称和硬化或软化反应。提供了三个数值例子来证明所提出方法的效率和准确性。可以得出结论，所提出的方法为工程应用中的动态可靠性评估提供了准确且有用的工具。包括不对称和硬化或软化反应。提供了三个数值例子来证明所提出方法的效率和准确性。可以得出结论，所提出的方法为工程应用中的动态可靠性评估提供了准确且有用的工具。