Failure probability prediction method for variables with uncertain intervals and distribution functions

摘要

A common approach to problems of uncertainty is to model the parameters as random variablesrnor fields. Probabilistic modeling is the widely used approach for accounting the uncertainty but the uncertaintyrndoes not always imply randomness. The probabilistic method needs sufficient statistical data to validaternthe distribution assumptions. In addition, the probabilistic uncertainty should be produced by a randomrnmechanism. Therefore, if the uncertainty is not produced by a probabilistic mechanism or the PDF informationrnis not available, the bounds or intervals of variables can be used in reliability analysis. Every combinationrnof interval values requires one reliability analysis and it is practically impossible due to the number of combinationsrnand the computational cost involved. Reliability analysis for random variables requires a multidimensionalrnintegration of the joint probability density function over the entire failure region. In problems wherernboth the interval uncertainties and the random distributions are present, the complexity and cost of the failurernprediction increases exponentially. In order to make the problem tractable, a global approximation of the failurernsurface is proposed in this paper. By using this, the entire domain represented by the uncertain intervals isrnapproximated and the variation of the failure probability is obtained. Numerical examples are provided torndemonstrate the proposed method for variables with various distributions and intervals.