Examining different methods based on reliability index and modelsimulation in estimating the failure probability of expensive structures

Reliability evaluation of structural problems with linear boundary condition functions is usually done at alow level and by first-order methods due to simple concepts and the need for a few calculations. Thesemethods are suitable for providing an estimate of the safety level of the structure, and especially when thefunction expressing the performance of the structure is linear, they are accurate in providing the final answer.But when the said function is non-linear, due to inherent problems in this method, they cannot accuratelyestimate the structure's safety level. For such problems, it is necessary to use accurate methods of estimatingthe probability of failure, such as simulation methods. One of the most widely used simulation methods isthe Monte Carlo method, which provides a correct answer to the probability of structural failure without anyrestrictions on the function form and dimensions of the problem. But this method also requires a high levelof calculations for problems with low a probability of failure, which practically makes it difficult to use inpractical engineering problems. The problem of choosing a suitable method between the two groups ofsimulation methods and methods based on the reliability index becomes more apparent when it is supposedto be combined with an optimizing algorithm for the optimal design of structures based on its reliability.Using the concepts in the first and second-order methods of reliability along with an optimization algorithmwill reduce the volume of calculations. But this factor causes assumptions and simplifications, derivation offunctions, and reliability sensitivity estimation to be a part of the structure design process. Therefore, thecurrent research focuses on the performance of these methods in dealing with various structural problems,and the strengths and weaknesses of each method are evaluated in the process of analyzing benchmarkproblems with explicit and implicit limit functions. Ten different examples in this study were evaluated byseven methods. The two weighted WSM and SS subset simulation methods have also included manyadvantages and high accuracy with very low standard deviation.

Keywords:

possibility of failure , reliability , simulation , Monte Carlo.possibility of failure , reliability , simulation , Monte Carlo.