PROBABILISTIC METHOD OF STRUCTURAL RELIABILITY ANALYSIS BY SAMPLING WITH LIMITED STATISTICAL DATA

Abstract

The article presents an approach to modernizing the data sampling algorithm for structural reliability analysis. This approach enables obtaining more conservative estimates of the failure probability in cases of incomplete or limited statistical data. Numerical examples demonstrate that an incorrect hypothesis regarding the probability distribution type of a random variable in structural reliability problems can lead to estimation errors of up to 5% in the reliability index. Furthermore, neglecting the confidence limits for the parameters of the assumed probability distribution function can result in errors of up to 60% (in a strict mathematical solution). An analysis of scientific and technical publications reveals varying preferred probability distributions for steel yield strength, depending on the steel type and stress-strain conditions. This variability complicates unambiguous selection of a specific probability distribution in real-world tasks during construction site assessments. The proposed data sampling algorithm is based on a modification of the classical Monte Carlo method. It involves selecting a random distribution function and estimating the confidence intervals for its parameters via a bootstrap approach for each generated sample value. The algorithm produces an arbitrary-sized sample containing values representing the lower and upper confidence bounds of the studied parameter. Consequently, the structural element's failure probability is expressed as an interval of values.