Research Of Bridge Moving Load Interval Identification Based On The Second-order Taylor Expansion

Moving loads are one of the most important external effects on bridges in service,and the accurate identification of moving loads is essential in safety and reliability assessment.The moving load identification method based on finite element model(FEM)has been increasingly applied to the bridges with complex structural forms and boundary conditions.However,the actual bridge FEMs possesses uncertainties due to factors such as material,construction,damage and environment.Moving load identification based on the FEM containing errors and the deterministic method will lead to results which are inconsistent with the actual conditions.Therefore,it is necessary to consider the uncertainty in the bridge FEM.The interval analysis method has unique advantages in uncertainty analysis due to less sample information required and high computational efficiency.Traditional interval uncertainty analysis methods are mostly based on first-order Taylor expansion,which will lead to overly conservative or even invalid estimated load intervals when the uncertainty of parameters is large.In view of this,this paper proposes a moving load interval identification method based on the second-order Taylor expansion considering the model uncertainty,and validates it by numerical examples and laboratory experiments.The main research contents are as follows:(1)A FEM for dynamic response calculation of bridges under moving load excitation is established;an interval analysis method based on second-order Taylor expansion for dynamic response of bridges under moving load is proposed and verified by numerical examples of simply supported beams and continuous beams,which establishes the foundation for subsequent interval identification of moving loads.(2)A moving load interval identification method based on the second-order Taylor expansion is proposed.The identification of the moving load interval is divided into nominal value identification and interval radius identification.The deterministic moving load identification method based on the shape function and the method based on the second-order Taylor expansion are used to identify the nominal value and interval radius of the moving load,respectively.The computational efficiency is ensured by omitting the non-diagonal elements of the Hessian matrix.The effectiveness and superiority of the proposed method are verified by using simply supported beams and continuous beams with various uncertainty levels.The effects of different number of measurement points,different vehicle speeds and different noise levels on the identification results are discussed.The results indicate that more accurate results can be obtained when more number of measurement points and the lower the noise level are available,and different vehicle speeds have little effect on the identification results.(3)The experimental model of moving load is established in the laboratory.The changes of bridge parameters are simulated by setting different damage levels.The dynamic responses of the bridge subjected to the moving vehicle are collected by strain sensors,and the intervals of each axial load of the vehicle are estimated by the proposed method.The results reveal that when the actual values of the bridge parameters are differ significantly from the nominal values,the moving load interval identification method based on the second-order Taylor expansion can efficiently and accurately identify the load interval of each axis of the vehicle.