A new bivariate dimension reduction method for efficient structural reliability analysis. (15th January 2019) - Xu, Jun; Dang, Chao
Highlights: A new BDRM is proposed to evaluate the statistical moments. The SGLD model is fitted to recover the performance function's PDF. The proposed method is compared with some other well-developed methods. The computational results demonstrate the efficiency and accuracy of the proposed method. Abstract: This paper presents a new bivariate dimension reduction method (BDRM) for statistical moments evaluation and structural reliability analysis with accuracy and efficiency. A high-order unscented transformation (HUT) is introduced to evaluate the two-dimensional integrals involved in BDRM, and the free parameter involved in HUT is suggested. In this regard, the proposed BDRM can be formulated accordingly for statistical moments assessment. Then, the performance function's probability density function (PDF) is reconstructed by the shifted generalized lognormal distribution (SGLD) with the available statistical moments as constraints. Thus, the failure probability can be straightforwardly obtained by a simple integral over the PDF. The proposed method is verified by five numerical examples, including linear and non-linear, explicit and implicit performance functions. Besides, some other existing methods are also employed to demonstrate the advantages of the proposed method. It is found that the proposed method can keep the trade-off of accuracy and efficiency for structural reliability analysis.