Predicting the Bounds of Vehicle-Induced Bridge Responses Using the Interval Analysis Method

Abstract

A method for predicting the bounds of vehicle-induced bridge responses with uncertain bridge and vehicle parameters is presented. The uncertainties in the parameters of the bridge and vehicle are represented with interval variables instead of conventional random variables with known probability distributions. First, a three-dimensional vehicle–bridge interaction (VBI) system, which has no closed-form solution and can account for road roughness, is established. Then, by introducing the interval analysis method (IAM) based on the first-order Taylor series expansion, the expressions of the bridge responses, including displacement and bending moment at the midspan, can be explicitly given as functions of the interval parameters, and the lower and upper bounds of the bridge responses are determined by the particle swarm algorithm instead of direct interval arithmetic to avoid excessive overestimation of the responses. The subinterval technique can also be adopted to improve the accuracy of the IAM. A numerical example is provided, and the results show that, compared with the conventional Monte Carlo method, the proposed IAM is capable of obtaining the bounds of the bridge deflection and bending moment without much sacrifice of accuracy while requiring much less computational effort. This indicates that the proposed method can be effectively and efficiently applied to predicting the bounds of the dynamic responses of complicated VBI systems with interval uncertainties. An example is also used to demonstrate the applicability of the IAM to field bridges when only limited information about the bridge and vehicle is available.