Abstract It is common to evaluate high-dimensional normal probabilities in many uncertainty-related applications such as system and time-dependent reliability analysis. An accurate method is proposed to evaluate high-dimensional normal probabilities, especially when they reside in tail areas. The normal probability is at first converted into the cumulative distribution function of the extreme value of the involved normal variables. Then the series expansion method is employed to approximate the extreme value with respect to a smaller number of mutually independent standard normal variables. The moment generating function of the extreme value is obtained using the Gauss-Hermite quadrature method. The saddlepoint approximation method is finally used to estimate the cumulative distribution function of the extreme value, thereby the desired normal probability. The proposed method is then applied to time-dependent reliability analysis where a large number of dependent normal variables are involved with the use of the First Order Reliability Method. Examples show that the proposed method is generally more accurate and robust than the widely used randomized quasi Monte Carlo method and equivalent component method.

中文翻译：

---

多元正态积分的近似及其在瞬态可靠性分析中的应用

摘要 在许多与不确定性相关的应用（例如系统和瞬态可靠性分析）中，评估高维正态概率是很常见的。提出了一种准确的方法来评估高维正态概率，特别是当它们位于尾部区域时。首先将正态概率转换为所涉及的正态变量极值的累积分布函数。然后采用级数展开法对较少数量的相互独立的标准正态变量逼近极值。使用Gauss-Hermite正交法获得极值的矩生成函数。最后采用鞍点逼近法估计极值的累积分布函数，从而达到期望的正态概率。然后将所提出的方法应用于依赖于时间的可靠性分析，其中使用一阶可靠性方法涉及大量因变量。实例表明，所提出的方法通常比广泛使用的随机准蒙特卡罗方法和等效分量方法更准确和鲁棒。