Extraction of influence line through a fitting method from bridge dynamic response induced by a passing vehicle

The bridge influence line (IL) is widely used in structural evaluation, damage identification, model updating, and other applications. The IL curve of an existing bridge is usually different from its designed value. It is crucial, yet challenging, to detect the actual bridge IL by measurement. In this paper, a fitting method is proposed for extracting the bridge IL from the dynamic response induced by a passing vehicle. Based on the theoretical mechanism of bridge IL under different boundary conditions, along with the features of bridge vibration, a piecewise polynomial and a series of harmonic sinusoids are established to describe the IL of the measured point and the fluctuation part of the bridge response, respectively. A mixed function obtained by linear superposition of these factors is utilized to fit the bridge dynamic response. The coefficients of the piecewise polynomial can be extracted by a least-square calculation; and subsequently, the actual IL curve of the measure point of the bridge is obtained. Numerical examples of vehicle-bridge models are adopted to validate the fitting method of IL extraction proposed in this paper, and to illustrate the efficiency by comparing it with the existing direct inverse calculation method. The validity and feasibility of this method are also demonstrated by both a laboratory experiment and a field test.