Linear Moments-based Monte Carlo Simulation for Reliability Analysis with Unknown Probability Distributions

Abstract

Within the realm of structural reliability analysis, the uncertainties tied to resistance and loads are conventionally embodied as random variables possessing established cumulative distribution functions (CDFs). Nevertheless, real-world scenarios often involve cases where the CDFs of random variables are unknown, necessitating the probabilistic traits of these variables solely through statistical moments. In this study, for the purpose of integrating random variables characterized by an unknown CDF into the framework of Monte Carlo simulation (MCS), a linear moments (L-moments)-based method is proposed. The random variables marked by an unknown CDF are rendered as a straightforward function of a standard normal random variable, and the formulation of this function is determined by utilizing the L-moments, which are typically attainable from the statistical data of the random variables. By employing the proposed approach, the generation of random numbers associated with variables with unknown CDFs becomes a straightforward process, utilizing those derived from a standard normal random variable constructed by using Box-Muller transform. A selection of illustrative examples is presented, in which the efficacy of the technique is scrutinized. This examination reveals that despite its simplicity, the method demonstrates a level of precision that qualifies it for incorporating random variables characterized by unspecified CDFs within the framework of MCS for purposes of structural reliability analysis.