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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ming-Na Tong & Fu-Qiang Shen & Chen-Xing Cui, 2022. "The Inverse Transformation of L-Hermite Model and Its Application in Structural Reliability Analysis," Mathematics, MDPI, vol. 10(22), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4318-:d:975973
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    References listed on IDEAS

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    1. Rebba, Ramesh & Mahadevan, Sankaran, 2006. "Validation of models with multivariate output," Reliability Engineering and System Safety, Elsevier, vol. 91(8), pages 861-871.
    2. Vlad Stefan Barbu & Guglielmo D’Amico & Thomas Gkelsinis, 2021. "Sequential Interval Reliability for Discrete-Time Homogeneous Semi-Markov Repairable Systems," Mathematics, MDPI, vol. 9(16), pages 1-18, August.
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