Evaluation of the Performance of Methods based on Reliability and Simulation Methods in Calculating the Reliability of Structures

Calculating the failure probability of structural problems with linear boundary condition functions is usually done at a low level and by first-order methods due to simple concepts and the need for few calculations. These methods are only suitable for providing an estimate of the probability of structural failure, and especially when the function expressing the performance of the structure is linear, they are accurate in providing the final answer. But when the limit function is nonlinear, due to inherent problems in this method, they are unable to accurately estimate the safety level of the structure. For such problems, it is necessary to use accurate methods of estimating the probability of failure, such as simulation methods. The use of concepts in the first and second order methods of reliability along with the use of an optimization algorithm will reduce the volume of calculations, but this factor causes assumptions and simplifications, derivation of functions and estimating the sensitivity of failure probability is also a part of the structure design process. It can be proven that for many design problems with nonlinear boundary condition function, the answer provided by these methods will not satisfy the probabilistic constraints of the problem, or the answer provided is not the most economical design option. Also, many existing methods in this group are unable to provide answers for problems with low failure probability, especially when the variables of the problem have non-normal density functions. Therefore, the present study has investigated the performance of these methods in dealing with various structural problems, and the strengths and weaknesses of each method are discussed. Three different issues have been studied in this research with seven analytical and simulation method, to achieve this goal. The first problem is to verify the results. In this case, the failure probability of a reinforced concrete beam was calculated by the Monte Carlo Simulation (MCS) and compared with the results obtained from the precise gradient method used in previous studies. The results of this problem showed a 0.5% error in the results, indicating the accuracy of the responses. The existence of very small differences between the results obtained from Monte Carlo and the results of previous researchers in estimating the integral of failure probability related to the discussed problems, indicates the high accuracy of the Monte Carlo method, and it is possible to use the results obtained from Monte Carlo as a suitable criterion in the analysis of these problems. used to compare the results. Also, analysis of two problems including three-span steel beam, two-degree-of-freedom seismic system using seven methods including MCS, SS, IS, LS, WSM, FORM and SORM were also put on the agenda. The results indicate that SS has high accuracy in solving nonlinear and complex problems. WSM has shown a significant decrease in the number of function calls. The LS method has a great performance in calculating the reliability of problems with a low failure probability. Therefore, in general, it can be stated that the first-order method (FORM) is the simplest safety estimation method (with low accuracy for non-linear functions) and simulation methods are the most accurate methods (with conceptual complexity or high calculations).