Uncertainty Analysis on Vehicle-Bridge System with Correlative Interval Variables Based on Multidimensional Parallelepiped Model

For vehicle-bridge system, structural uncertainties, especially the interval variables with correlation, have a great influence on dynamic response. Therefore, this paper proposes an effective uncertainty analysis method for vehicle-bridge system based on multidimensional parallelepiped (MP) model, which can reasonably deal with the correlation of interval variables. First, the vehicle-bridge system is simplified as a four degrees-of-freedom mass-spring vehicle model running on a simply supported beam. MP model is adopted to describe the uncertainties of all the interval variables. Second, via affine coordinate system transform, the interval variables with correlation are transformed as the independent variables, which is very convenient for uncertainty analysis. Finally, the uncertain dynamic response is approximated through the first-order Taylor interval expansion, and the upper and lower bounds can be calculated using the dynamic response at midpoints and the partial difference multiplied by interval radius. Because the correlation is sufficiently considered, the uncertainty analysis results on vehicle–bridge interaction system will be much more accurate than the traditional interval analysis method (IAM). Numerical example demonstrates the correctness and effectiveness of the proposed method.