The Inverse Transformation of L-Hermite Model and Its Application in Structural Reliability Analysis

Ming-Na Tong, Fu-Qiang Shen () and Chen-Xing Cui
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Ming-Na Tong: School of Hydraulic and Civil Engineering, Zhengzhou University, 100 Kexuedadao Rd., Zhengzhou 450001, China
Fu-Qiang Shen: School of Hydraulic and Civil Engineering, Zhengzhou University, 100 Kexuedadao Rd., Zhengzhou 450001, China
Chen-Xing Cui: School of Civil Engineering, Central South University, 22 Shaoshannan Rd., Changsha 410075, China

Mathematics, 2022, vol. 10, issue 22, 1-15

Abstract: In probabilistic analysis, random variables with unknown distributions are often appeared when dealing with practical engineering problem. A Hermite normal transformation model has been proposed to conduct structural reliability assessment without the exclusion of random variables with unknown probability distributions. Recently, linear moments (L-moments) are widely used due to the advantages of stability and insensitivity. In this paper, the complete expressions of the inverse transformation of L-moments Hermite (L-Hermite) model have been proposed. The criteria are proposed to derive the complete inverse transformation of performance function and the complete expressions of the inverse transformation of L-Hermite model are formulated. Moreover, a first-order reliability method for structural reliability analysis based on the proposed inverse transformation of L-Hermite model is then developed using the first four L-moments of random variables. Through the numerical examples, the proposed method is found to be efficient for normal transformations since the results of the proposed L-Hermite are in close agreement with the results of Rosenblatt transformation. Additionally, the reliability index obtained by the proposed method using the first four L-moments of random variables provides a close result to the reliability index obtained by first-order reliability method with known probability density functions in structural reliability assessment.

Keywords: normal transformation; L-moments; complete expression; Hermite model; structural reliability; inverse transformation; complete expressions; first-order reliability method; random variables; practical engineering (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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