Modeling of uncertainty in bridge-vehicle system and the interaction force identification

Abstract

Bridge-vehicle interaction problem plays an important role in the bridge design, the bridge condition assessment and the overweight vehicle control. The topics including dynamic analysis of the bridge structure under moving vehicles and the identification of moving vehicle axle loads from the measured bridge responses have drawn much attention in recent years. Most of the existed approaches to solve the above topics are deterministic in which the uncertainty in the bridge-vehicle system and the loading processes is ignored. Moreover, the road surface roughness is treated as deterministic samples of irregular profile according to its power spectrum density defined in the ISO standard. A few research work has addressed the stochastic analysis of bridge-vehicle interaction problem in which the road surface roughness and the parameters in vehicle system were assumed as Gaussian random variables/processes and the perturbation method was employed to handle the uncertainties involved. Since the randomness in the bridge structure has not been introduced in the bridge-vehicle interaction problem and the perturbation method adopted in the previous research works tends to loss accuracy with the increasing in variation of uncertainty, the methods proposed in this Thesis aim to fulfill these gaps and to provide theoretical studies on the stochastic analysis of the bridge-vehicle interaction problem as well as on the identification of vehicle axle loads from samples of bridge response with uncertainties in both system parameters and road surface roughness. The bridge is modeled as a simply supported planar Euler-Bernoulli beam with a vehicle either modeled as multiple forces or a mass-spring system moving on top. The finite element method is adopted to build the bridge-vehicle interaction model in which the system parameters as well as the road surface roughness are assumed as random processes. Firstly, only the randomness in road surface roughness is included and to be assumed as Gaussian random process represented by the Karhunen-Loève Expansion. Based on the formulated model, both the dynamic analysis and the moving force identification are conducted. Secondly, the uncertainty in the material properties of the bridge structure which is assumed to be small and have Gaussian property is further included. A stochastic finite element model is formulated with the Karhunen-Loève Expansion representing the Gaussian random processes in the equation of motion of the system. Based on the model, a general stochastic moving force identification algorithm is proposed to identify the statistics of the vehicle axle loads from samples of bridge response with uncertainty in both the excitations and system parameters. Finally, to model larger variation of uncertainty in the system parameters, the Spectral Stochastic Finite Element Method is adopted with the Karhunen-Loève Expansion and the Polynomial Chaos Expansion representing the Gaussian and non-Gaussian random processes, respectively. The system parameters are assumed as Gaussian random processes and will be further extended to non-Gaussian case which is regarded to be more appropriate. Dynamic analysis on the bridge-vehicle interaction problem with large variation of uncertainty in both system parameters and excitation forces is conducted. All the methods proposed in this Thesis are verified with numerical examples in which the Monte Carlo Simulation is adopted to obtain the reference solutions. Results show that the proposed methods on the dynamic analysis of the bridge-vehicle interaction problem and on the identification of statistics of moving vehicle axle loads with uncertainties are effective and with good performance in the response statistics prediction even when large variation of uncertainties are existed in both the system parameters and the excitations.