Moving Vehicle Identification using Measured Acceleration
Jong Heon Kim
The method of identifying weight of the vehicle passing through the bridge is proposed. Vehicle weight is identified using the acceleration of the bridge based on numericaltime series analysis of the dynamic equation. After modeling the bridge by the Finite Element Method and defining both weight and velocity of the vehicle as system parameters, the inverse problem is defined as minimizing the least square error between calculated accelerations and measured accelerations of the modeled bridge. The minimization problem is a constrained nonlinear optimization problem because of the nonlinear implicit function including the velocity term, and it is solved using the Newton-Raphson method. The sensitivity is calculated by direct differentiation after both the discretization and the integral of the dynamic equation.
Time windowing technique is applied for a real-time identification. However, the aspect of both the bridge acceleration and the optimization function make the identification accuracy low. Therefore, step-by-step algorithm is proposed that is to make the initial value close to the exact solution by analyzing first before the object function becomes to make the local minimum. Further, error propagation depends on how the system parameters are defined in a time window, and it is solved by algorithm which defines the system parameters again whenever iteration of the analysis is run.
Tikhonov regularization technique is applied owing to instability of the solution, and regularization factor is determined by Geometric Mean Scheme (GMS). Regularization baseline is defined as the measured value for vehicle velocity and the value calculated by bridge acceleration and measured vehicle velocity for vehicle weight.
Several numerical examples are performed to demonstrate the validity and the effectiveness of the proposed method. The examples are one-way and two-way models for a simple beam and an one-way model for a three span continuous beam.
Moving vehicle weight identification, Acceleration of the bridge, Nonlinear optimization problem, Sensitivity, Time-windowing technique, Tikhonov regularization, Vehicle modeling