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

Abstract

Summary 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.

Recent progress and future trends on damage identification methods for bridge structures

“…Lin developed a crack localization method based on rotational frequency response functions obtained from measured translational frequency response function data; a crack location matrix was constructed using the estimated rotational frequency response functions to localize cracks, and a new numerical inverse frequency response function sensitivity method was proposed to identify crack parameters such as crack depths; results based on a numerical cantilever truss structure show that the location and depth of the crack can be identified successfully even in the presence of 5% noise level. Boumechra introduced a damage identification method for truss structure based on the inverse analysis of the static response caused by moving loads; numerical results of a truss show that the method can detect stiffness changes or reductions successfully. Tran proposed a structural damage identification method with big data using parallel computing based on multiprocessor system on chip; the performance for the local damage detection has been verified by a numerical example of a plane steel truss structure.…”

Structural system identification by measurement error‐minimizing observability method

“…According to the intrinsic characteristics of the structural response, SSI can be classified as static SSI or dynamic SSI . Compared with static SSI, dynamic SSI has been developed more extensively in the past decades.…”

“…Abdo combined the grey relation coefficient and the changes in static deflections curvature to locate the damage . With the use of the influence line principle with a static moving load, Boumechra approximated the stiffness matrix with Neumann series . This method is able to locate the damage and evaluate the damage extent when the noise level is low.…”

Constrained observability method in static structural system identification

“…When only the estimation of stiffnesses is targeted, the static SSI methods might be more interesting than the dynamic ones in some cases . In nondestructive tests of bridges, slow moving loads can be applied as quasistatic loads . Providing that the structure behaves linearly, Maxwell law of reciprocal deflections can be applied to reduce the number of sensors in the structure under moving load .…”

“…The irregular variations in curvatures, which are obtained from the displacement influence lines between the damaged and undamaged structures under moving load, can be used to locate the damages . Boumechra approximated the inverse of the global stiffness matrix by a Neumann series and used optimization technique to find the optimal correction coefficients of structural parameters such that the predicted response from these parameters is closest to the measured static response under moving loads. This method can accurately localize and quantify the damage with the displacements of selected nodes.…”