Adaptive estimation for statistical moments of response based on the exact dimension reduction method in terms of vector

Abstract Obtaining the statistical moments of system responses remains one of the main topics of stochastic analysis. This paper presents a new adaptive point estimate method (PEM) based on the exact dimension reduction method in terms of vector. Firstly, the rigorous and exact dimension reduction method in terms of vector is derived theoretically. Secondly, by introducing the nonnormal-to-normal transformation, the original variables are transformed into independent standard normal variables which are classified into several sub-vectors based on the delineation of the cross terms, and then the response moments can be described by an explicit function of the moments of multiple component functions. Thirdly, by combining with the two different approaches for estimating the moments of component sub-vector function, an adaptive PEM based on the exact dimension reduction method in terms of vector, which comprises two sub-methods, is proposed. Finally, several examples illustrate the accuracy and efficiency of the proposed method.

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