Polynomial Normal Transform Based on L-moments and Its Application to Structural Reliability

Abstract

Information on the distribution of the basic random variable is essential for the accurate analysis of structural reliability. The usual method for determining the distributions is to fit a candidate distribution to the histogram of available statistical data of the variable. Generally, such candidate distribution would have parameters that may be evaluated from the statistical moments of the statistical data. Probability distributions are usually determined using one or two parameters evaluated from the mean and standard deviation of statistical data. However, these distributions are not flexible enough to represent the skewness and the kurtosis of statistical data. Normal transformation is often used in probabilistic analysis especially when multivariate non-normal random variables are involved. This study proposes a probability distribution based on polynomial normal transform, of which parameters are determined using the first four L-moments (L-mean, L-standard deviation, L-skewness and L-kurtosis) of the available data. The simplicity, generality, flexibility and advantages of this distribution in statistical data analysis are discussed. The results are found to better than two- and three-parameter distributions, and similar to cubic normal distribution based on central moments (C-moments). With the aiming at illustrate the stability of polynomial normal transform based on L-moments, several extreme values are added to data. The proposed distribution is demonstrated to provide significant stability and flexibility. Then this method is applied to reliability index calculation, and its significance in structural reliability evaluation is discussed. The calculation results are compared with Monte Carlo calculations. Several numerical examples are further presented to demonstrate the accuracy and efficacy of the distribution for conducting reliability analyses.