The Dynamic Direct And Inverse Problems Of Bridge Subjected To Moving Load

Bridge is the important hub of transportation engineering.The bridge vibration under the moving load has always been the focus of scholars’ attention.On the one hand,the analysis of the dynamic response of the bridge under the moving load,has important theoretical value to the design of bridge,and the improvement the driving comfort and the structural safety.On the other hand,the damage of bridge and the unknown moving load are recognized by using the vibration response of the bridge under the moving load.It’s more beneficial to the real-time health monitoring,also with the damage diagnosis and the evaluation of bridge system,has important practical engineering application value and significance.Thus this article analyzes the solution of bridge dynamic response under moving load(that’s the direct problem of dynamics)and the synchronous identification of bridge structure damage and moving load(that’s the invers problem of dynamics).The main research work includes:(1)A semi-analytic method based on the structural finite element model(FEM)is proposed to analyze the vertical dynamic response of the general beam bridge under moving force.In this semi-analytic method the discrete modes is calculated by the modal analysis of FEM firstly.Regardless of the element type or shape function,an improved recovery method based on the sampling theorem is presented to recover the structural continuous modes with analytical expression.Then,the closed-form solution of the vertical dynamic response of a general beam bridge under moving force is derived.The validity of the presented method is verified by comparing with the analytical solution of a simply supported uniform beam under moving force.Further,the vibration analysis of a three-span non-uniform continuous beam bridge under moving force is done through the analytical expression of the semi-analytic solution.The influences of the speed of moving force and the damage of bridge on the vertical dynamic response were discussed comprehensively.At the same time,the mechanism of structural resonance at different load moving velocity is clarified,and the corresponding formula of the critical moving speed at maximal or minimal deflection of the mid-span section is given.(2)In view of the simultaneous existence of unknown structural damage and unknown moving load excitation,a synchronous identification method based on Federated Extended Kalman Filter algorithm(FEKF)is proposed by using the dynamic response of the beam bridge under moving force.So the l1 regularization is combined with FEKF to improve the ill-posedness of the inverse problem solving process.The numerical analysis about a simply supported beam show that the proposed method has excellent robustness,it can synchronous identify the damage of the beam bridge and moving force accurately.(3)A Federated Extended Kalman Filter algorithm with l1 regularization is proposed to identify structure damage under multiple measurement information fusion.When the measurement information is not complete,to obtain multiple sets of measurement data under different measuring points by changing the sensor in the structure of the measurement position.And each group of different measurement information each constitute the FEKF of different subsystems,the optimal estimate of structural damage has been obtained by only merging public variables.The effectiveness of the method is verified by a simply supported beam and a two-dimensional frame structure under free vibration.This method can also continue to promote the role of the bridge under moving load.