Damage detection in beam and truss structures by the inverse analysis of the static response due to moving loads

The detection and the localization of damages in a bridge have been always one of the major concerns of infrastructure managers, engineers, and researchers. In addition to the dynamic techniques that were well imposed in the diagnosis of bridges, several static methods have been developed. The idea of this work is to exploit the measurement results about a bridge deflection submitted to a moving load. By using the displacements response, important data about the displacement of a structural point could be gathered. When the structure's geometry and the material characteristics are known, a finite element model, supposed to be the most similar, could be developed. The numerical structural model and the static displacements data are used to develop an equilibrium equations system where unknowns are the possible stiffness changes in the finite element model. Thus, the global stiffness matrix of the studied structure is a polynomial matrix. The equilibrium equations system is a static inverse problem requiring resolution. To facilitate the mathematical development, the inverse of the global stiffness matrix is expressed by a Neumann series. Then, the resolution of the system is done by a code developed in Matlab. To confirm the good convergence of the developed mathematical method, numerical tests are carried out by considering beams and a 3D truss bridge subjected to a moving load. Thereafter, an analysis concerning the influence of the noise in the displacements data on the accuracy of the inverse analysis and the convergence of the results is made. It has been shown that the large number of data reduces the noises effect and the damages detection can be ensured.