Comparative Study of Latin Hypercube Sampling and Monte Carlo Method in Structural Reliability Analysis

Abstract

The Monte Carlo (MC) Method is a crucial approach to approximately calculate the reliability of structures, although it requires a large amount of calculation comprising millions of sampling realizations. The Latin Hypercube Sampling (LHS) method has been raised to improve efficiency, and in which situation this method can significantly outperform the MC method is a pivotal problem that needs to be resolved. In this thesis, comparative sampling is conducted with two methods to calculate the failure probability of a steel beam, and merits, as well as demerits, are concluded with a comparative analysis of the sampling results. The thesis compares the fundamental principles and methodology of the two methods, and the variables involved in reliability analysis are expounded. It is emphasized that the LHS method has the advantage of stratified sampling, and variables consist of loads, geometrical dimensions, and material properties. The details of the example beam are given, followed by the sampling done by two methods. The analysis extracts the noteworthy statistics in sampling, propounding the differences: the LHS method can markedly reduce the sampling number needed to obtain reliable figures with a higher coefficient of variation. Further research should be carried out to study the influence of various distributions on the difference between the two methods. Overall, this thesis provides insights for researchers in the reliability analysis field to utilize the LHS method more sensibly.