Abstract
In structural reliability analysis, simulation methods are widely used. The statistical characteristics of failure probability estimate of these methods have been well investigated. In this study, the sensitivities of the failure probability estimate and its statistical characteristics with regard to sample, called ‘contribution indexes’, are proposed to measure the contribution of sample. The contribution indexes in four widely simulation methods, i.e., Monte Carlo simulation (MCS), importance sampling (IS), line sampling (LS) and subset simulation (SS) are derived and analyzed. The proposed contribution indexes of sample can provide valuable information understanding the methods deeply, and enlighten potential improvement of methods. It is found that the main differences between these investigated methods lie in the contribution indexes of the safety samples, which are the main factors to the efficiency of the methods. Moreover, numerical examples are used to validate these findings.
Highlights
Reliability analysis plays an important role in the structural design
Three contribution indexes have been proposed, which are the relative changes when a sample is included in reliability calculation or not
Summarizing the arguments, the following findings can be concluded: (1) For Monte Carlo simulation, results show that the contribution of the failure sample to the estimate is bigger than that of safety sample in failure probability estimation
Summary
Reliability analysis plays an important role in the structural design. In reliability analysis, the evaluation of the failure probability is a basic problem. Note that these mathematical techniques are commonly developed for measuring the importance of input variables of computational models It can be seen from above, the simulation-based reliability analysis and sensitivity analysis have been extensively studied [29,30] and applied [31,32], the estimate as well as the statistical characteristics are usually computed at the same time. Three contribution indexes have been proposed, which are associated with the sensitivity of the failure probability estimate with respect to sample, i.e., the contribution (sensitivity) of sample to the estimate of failure probability and its statistical characteristics in simulation-based method These indexes in four widely used simulation-based methods are derived and examined, i.e., Monte Carlo simulation (MCS), importance sampling (IS), line sampling (LS) and subset simulation (SS).
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