Reliability Assessment with Fuzzy Random Variables Using Interval Monte Carlo Simulation

Abstract

In this work structural reliability assessment is presented for structures with uncertain loads and material properties. Uncertain variables are modeled as fuzzy random variables and Interval Monte Carlo Simulation along with interval finite element method is used to evaluate failure probability. Interval Monte Carlo is compared with existing search algorithms used in the reliability assessment of fuzzy random structural systems for both efficiency and accuracy. The genetic algorithm as one of the well developed approaches is selected for comparison. Fuzzy randomness is used as a model for handling both aleatory and epistemic uncertainties. Fuzzy quantities are calculated using the α-cut approach. In the case of Interval Monte Carlo, bounds on response quantities are obtained for each α-cut using only one run of interval finite element method, however genetic approach requires performing Monte Carlo Simulation for each of the considered different possible combinations within the search domain (α-cut) and running finite element for each of the Monte Carlo realizations. In the presented examples both load and material uncertainties are considered. Numerical results show the computational efficiency of the Interval Monte Carlo approach and its superiority to the alternative search approaches such as optimization and genetic algorithms. In addition, results show how that Interval Monte Carlo approach provides guaranteed and sharp enclosure to the system solution.

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