A Novel Approach to Sensitivity Study in Monte Carlo Simulation

Abstract eng:
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 approach makes use of the MCS samples that have already been generated in the baseline (or original) case. It contains two steps: (i) a Bayesian analysis (Wang et al. 2010) to group the MCS samples of the baseline case, and (ii) reassembling the Bayesian analysis results to “match” different probabilistic characterizations (e.g., mean, standard deviation, or probability distribution type) of the uncertain variable concerned in the sensitivity study. It is practically zero additional computational cost, in terms of the number of MCS samples and simulation runs, for sensitivity study, and a large number of sensitivity study cases can be performed rapidly. This is particularly beneficial when the operator in MCS involves complex analyses, such as finite element models or time-consuming system analyses, and requires significant computational effort for each MCS sample. Equations are derived for the approach, and the approach is illustrated using a slope stability example. The proposed approach not only provides the sensitivity of failure probability to uncertain variables, it also can be extended to estimate the whole probability density function of the MCS operator output. Because of the page limit, such extension is not included in this paper. Interesting readers are referred to elsewhere for details (Wang 2011). It is also worthwhile to point out that the proposed approach can be used as a theoretical basis for combining various MCS runs with different probabilistic characterizations of uncertain variables, so that the information generated in different MCS runs can be accumulated.

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