Uncertain parameter sensitivity in Monte Carlo Simulation by sample reassembling

Abstract

With the rapid development of computer technology and commonly available personal computers, Monte Carlo Simulation (MCS) is gaining popularity in reliability analysis due to its robustness and conceptual simplicity. MCS, however, does not offer insight into the effect of various uncertainties in the reliability analysis. It generally requires many repeated MCS runs to explore the sensitivity on uncertain variables. This paper presents a novel approach to the sensitivity study on uncertain variables in MCS without repeated MCS runs. The proposed approach makes use of the MCS samples that have been generated in the baseline case (i.e., MCS samples corresponding to the nominal set of statistical parameters and distribution type). The MCS samples in the baseline case are grouped by a Bayesian analysis and reassembled to “match” the new set of statistical parameters or distribution type of the uncertain parameter considered in the sensitivity study. Equations are derived for the Bayesian analysis and sample reassembling to obtain the desired sensitivity study results (e.g., failure probability and probability density function). The approach is illustrated through a slope stability problem, and the results are validated against those from repeated runs of MCS simulations. The proposed approach indicates that, by further exploring and properly utilizing the information generated from the MCS samples in the baseline case, it is possible and straightforward to obtain the sensitivity study results of interest. There is practically no additional computational cost, in terms of the number of MCS samples and simulation runs, for the sensitivity study, and a large number of sensitivity study cases can be performed rapidly. This is particularly beneficial when the operator in the MCS involves complex analyses, such as finite element models or tedious system analyses, and requires significant computational effort for each MCS sample.