Structural Reliability Analysis Using Generalized Distribution Reconstruction Method with Novel Improvements
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 10, Issue 2
Abstract
The probability density function (PDF) of structural responses is one of the significant fundamentals for structural reliability analysis. Nonetheless, it is still challenging to compute the PDF, especially when the distribution tail is concerned for the structural reliability. Because an arbitrary PDF is the exact inverse Fourier transform of its corresponding characteristic function (CF), working with the CF provides an alternative to obtain the PDF. Recently, based on the inverse Fourier transform of CF, which can be numerically calculated with the complex fractional moments, a generalized distribution reconstruction (GDR) method was proposed in the literature. This paper aims to provide new improvements to the GDR method, including (1) giving a theoretical explanation to demonstrate why the GDR method could reconstruct the PDF in an accurate way; (2) proposing two new expressions to approximate the CF with fewer undetermined parameters, which strictly satisfy the mathematical properties of CF; and (3) deriving an analytical PDF such that possible errors from the numerical inverse Fourier transform can be avoided. Analytical distributions and practical applications are studied to illustrate the efficiency and accuracy of the proposed approach. Some open issues to be further investigated are outlined as well.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The financial supports from the National Natural Science Foundation of China (NSFC Grant No. 52208206), the Fundamental Research Funds for the Central Universities, China (Grant Nos. G2022KY05103 and G2021KY05103), and the Natural Science Foundation of Shaanxi Province, China (Grant No. 2022JQ-513) are highly appreciated. Specifically, we would like to greatly thank Professor Jun Xu from Hunan University, China, for his constructive suggestions on this work.
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Published In
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 10 • Issue 2 • June 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Dec 20, 2023
Accepted: Jan 18, 2024
Published online: Apr 8, 2024
Published in print: Jun 1, 2024
Discussion open until: Sep 8, 2024
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