Structural Reliability Analysis Using Generalized Distribution Reconstruction Method with Novel Improvements

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.