Adaptive estimation of statistical moments of the responses of random systems

• The criterion for delineating the existence of cross terms is proposed and proved.
• An adaptive dimensional decomposition for moment function is proposed.
• The point estimate method (PEM) based on adaptive dimensional decomposition is developed.
• The proposed PEM Is more efficient than the existing PEMs without loss of accuracy.

Estimation of statistical moments of structural response is one of the main topics for the analysis of random systems; balancing between accuracy and efficiency is still a challenge. In this work, a new point estimate method (PEM) based on adaptive dimensional decomposition is presented. Firstly, by introducing the normal-to-nonnormal transformation, a system with general variables is changed into one with independent standard normal variables. Secondly, the criterion for delineating the existence of cross terms is derived theoretically, together with its practical implementation. Thirdly, by combining with the dimension-reduction method (DRM), an adaptive dimensional decomposition for moment function is proposed and the PEM based on adaptive dimensional decomposition, which comprises two types of sub-methods, is developed. Finally, several examples are investigated to verify the accuracy, efficiency, convergence and rationale of the proposed method.