Estimation of statistical moments remains one of the main topics of stochastic analysis whose accuracy greatly affects reliability analysis results. In this work, conjugate unscented transformation (CUT) methods, which can balance accuracy and efficiency, are introduced for the statistical moment estimation of responses. Because of the drawbacks of existing CUT methods, a family of enhanced conjugate unscented transformation (ECUT) methods, including ECUT-4, ECUT-6, and ECUT-8 methods, is proposed for statistical moment estimation by combining the original CUT, variable transformation, and exact dimension reduction method. Then the probability density function of a performance function is reconstructed by the improved maximum entropy method (IMEM) with the available statistical moments as constraints. To demonstrate the accuracy and effectiveness of the proposed methods, five numerical examples, including linear and nonlinear, low-dimensional and high-dimensional, and explicit and implicit performance functions, are investigated, in which the results obtained from the proposed methods are compared with other existing moment methods and a Monte Carlo simulation (MCS) method. The results of the examples show that the proposed ECUT-6 and ECUT-8 methods have fairly high accuracy and efficiency for structural reliability analysis.

The system reliability analysis of complex engineering structures remains a challenge in the field of reliability. In this work, a high-order moment method using generalized factorized dimensional reduction method (GF-DRM) and iterative maximum entropy method (IMEM) is proposed for structural system reliability assessment. Firstly, the performance functions are described uniformly by equivalent description methods for various system reliability problems. Secondly, a novel point estimation method (PEM) based on GF-DRM is proposed for the high-order moments estimation of the equivalent performance function. Thirdly, the system failure probability of the structures is accurately determined by using the IMEM, which can automatically determine the order of moments. Finally, four examples, including numerical and engineering cases, are investigated to demonstrate the accuracy and efficiency of the proposed method, in which results obtained from the proposed method are compared with some other existing moment methods and Monte Carlo simulation (MCS) method. The results of the examples show the proposed method has fairly high accuracy and efficiency for structural high-order moments estimation and system reliability analysis.