For uncertainty analysis of high-dimensional complex engineering problems, this article proposes a hybrid multiplicative dimension reduction method based on the existent multiplicative dimension reduction method. It uses the multiplicative dimension reduction method to approximate the original high-dimensional performance function which is sufficiently smooth and has a small high-order derivative as the product of a series of one-dimensional functions, and then uses this approximation to calculate the statistical moments of the function. Then the variance-based global sensitivity index is employed to identify the important variables, and the identified important variables are subjected to bivariate decomposition approximation. Combined with the univariate multiplicative dimension reduction method, the hybrid decomposition approximation is obtained. Compared with the existing method, the proposed method is more accurate than the univariate decomposition approximation when used for uncertainty analysis of engineering models and needs less computational efforts than the bivariate decomposition. In the end, a numerical example and two engineering applications are tested to verify the effectiveness of the proposed method.

为了对高维复杂工程问题进行不确定性分析，本文提出了一种基于现有的乘性降维方法的混合乘性降维方法。它使用乘法降维方法来近似原始的高维性能函数，该函数足够平滑并具有较小的高阶导数，是一系列一维函数的乘积，然后使用该近似值来计算统计矩功能的 然后，使用基于方差的全局敏感性指数来识别重要变量，并对识别出的重要变量进行二元分解近似。结合单变量乘法降维方法，得到了混合分解近似值。与现有方法相比，所提出的方法用于工程模型的不确定性分析时，比单变量分解逼近更准确，并且比双变量分解需要更少的计算量。最后，通过数值算例和两个工程应用进行了验证，验证了所提方法的有效性。