Bridge weigh-in-motion system development using superposition of dynamic truck/static bridge interaction

In this paper, we extend the development of a weigh- in- motion (WIM) system for use on in-service highway bridges. We consider the problem of using a bridge\´s elastic response due to a passing truck to estimate the unknown truck parameters axle spacing, speed, axle weights, and gross weight by minimizing the difference between measured deflection profiles and approximated ones. For this problem, the bridge is modeled as a static Euler beam, and the truck is modeled as two "quarter cars" which include a linear representation of the suspension dynamics. A general model of the truck is discussed which is a superposition of the solutions of the truck\´s equations of motion with parameters such as weight, natural frequencies, dampings, and initial conditions unknown. Three deflection measurements are taken along the beam over time, and an optimization routine is employed to estimate the values of the unknown truck parameters. A variety of different truck configurations are considered. With zero measurement noise in the data, the errors in the weight estimates were 0.3%. Measurement noise of different magnitudes up to 10 microns was then added to the data and the estimates of all truck parameters were within 1.5%.