Efficiency is greatly concerned in reliability analysis community, especially for the problems with high-dimensional input random variables, because the computation cost of common reliability analysis methods may increase sharply with respect to the dimension of the problem. This paper proposes a novel meta-model based on the concepts of polynomial chaos expansion (PCE), dimension-reduction method (DRM), and information-theoretic entropy. Firstly, a PCE method based on DRM is developed to approximate the original function by a series of PCEs of univariate components. Compared with the PCE of the original function, the DRM-based PCE can reduce the computational cost. Before constructing the meta-model, a prior of the degree of the PCE is required, which determines the accuracy and efficiency of the PCE. However, the prior is usually determined by experience. According to the maximum entropy principle, this paper proposes an adaptive method for the selection of the polynomial chaos basis efficiently. With the adaptive PCE method based on DRM, a novel meta-model method is proposed, with which the reliability analysis can be achieved by Monte Carlo simulation efficiently. In order to verify the performance of the proposed method, three numerical examples and one structural dynamics engineering example are tested, with good accuracy and efficiency.

在可靠性分析领域，效率尤其受到关注，特别是对于具有高维输入随机变量的问题，因为常见的可靠性分析方法的计算成本可能相对于问题的维度急剧增加。本文基于多项式混沌扩展（PCE），降维方法（DRM）和信息理论熵的概念，提出了一种新颖的元模型。首先，开发了一种基于DRM的PCE方法，以一系列单变量PCE逼近原始函数。与原始功能的PCE相比，基于DRM的PCE可以降低计算成本。在构建元模型之前，需要先获得PCE程度，然后再确定PCE的准确性和效率。然而，先验通常由经验决定。根据最大熵原理，提出了一种有效选择多项式混沌基础的自适应方法。利用基于DRM的自适应PCE方法，提出了一种新的元模型方法，通过蒙特卡洛仿真可以有效地进行可靠性分析。为了验证所提方法的性能，对三个数值实例和一个结构动力学工程实例进行了测试，具有良好的准确性和效率。通过蒙特卡洛仿真可以有效地进行可靠性分析。为了验证所提方法的性能，对三个数值实例和一个结构动力学工程实例进行了测试，具有良好的准确性和效率。通过蒙特卡洛仿真可以有效地进行可靠性分析。为了验证该方法的性能，对三个数值实例和一个结构动力学工程实例进行了测试，具有较高的准确性和效率。