ORTHOGONAL FUNCTION IN MOVING LOADS IDENTIFICATION ON A MULTI-SPAN BRIDGE

Assumed mode shapes are often used to determine the responses of a bridge deck under the passage of moving loads. However, the use of these mode shapes in the inverse problem of force identification would lead to unnecessary errors due to their inherent inaccuracy. Direct differentiation of the measured responses is usually used to obtain the velocities and accelerations, and this practice leads to large errors when measurement noise is included. This paper derives the analytical vibration mode shapes of a continuous beam on rigid supports from the eigenvalue and eigenfunction analysis, thus eliminating the modelling errors from the assumed mode shapes. A generalized orthogonal function approach is proposed to obtain the derivatives of the bridge modal responses, and this eliminates the errors due to measurement noise. The moving loads are identified using the regularization method on the equations of motion. Computational simulations and laboratory test results show that the method is effective and accurate for identifying a group of moving loads.