Monotonic Expression of Polynomial Normal Transformation Based on the First Four L-Moments

Abstract

Structural reliability analysis without the exclusion of random variables with unknown distributions has attracted increasing attention, and many endeavors have been devoted to this aspect. Recently, linear moments (L-moments) have been found increasing use for characterizing random variables with unknown distributions, in part since they show less sensitivity to distribution tails and are more stable than the ordinary central moments (C-moments). In this paper, the clear definition of the complete monotonic expressions of the third-order polynomial normal transformation (TPNT) under different combinations of the first four L-moments of random variables is first proposed. Additionally, the applicable boundaries and monotonic regions of TPNT based on L-moments are also determined. The advantages of the TPNT based on L-moments are that it has a wider applicable range and is much more stable under a small sample size compared with the TPNT based on C-moments, which are demonstrated through numerical example studies. Through the numerical examples, the proposed TPNT based on the first four L-moments is found to be quite effective for normal transformation.