Damage Assessment of the Z24 Bridge by FE Model Updating

Abstract

Damage to civil engineering structures can be identified with a finite element (FE) model updating method using experimental modal data. In such a procedure the uncertain properties (e.g. stiffness distribution) in the FE model are adjusted by minimizing the differences between the measured modal parameters and the numerical (FE) predictions. In civil engineering the differences in eigenfrequencies and mode shapes are minimized, mostly identified from ambient vibrations. Since the modal data are nonlinear functions of the uncertain properties, an iterative sensitivity-based minimization method is used to solve this inverse problem. In order to reduce the number of unknowns, damage functions are used. The FE model updating technique is applied to a prestressed concrete bridge with 3 spans whose girder is damaged by lowering one of the intermediate piers. The damage pattern is identified (localized and quantified) by updating the Young’s and the shear modulus. Introduction Accurate condition assessment of civil engineering structures has become increasingly important. FE model updating provides a very efficient, nondestructive, global damage identification technique. The uncertain properties of the FE model are updated by minimizing the discrepancies between the measured modal data and those computed with the numerical FE model [1, 2]. The damage identification procedure is performed in two updating processes. In the first the initial FE model is tuned to a reference state, i.e. the undamaged structure. In the second process the reference FE model is updated to obtain a model which can reproduce the experimental modal data of the damaged state. The damage is identified by comparing the differences between the reference and the damaged FE model. The technique is applied to the Z24 bridge in Switzerland. It is a prestressed concrete bridge with three spans which is damaged by lowering one of the intermediate piers. A nonlinear least squares problem is solved. The residual vector contains the test/analysis differences of the first 4 bending and/or torsion modes. Frequency residuals as well as mode shape residuals are minimized. Eigenfrequencies contain global, accurate information, whereas mode shapes provide important local, but more noisy information. Therefore, both types of residuals are weighted with an appropriate factor in the residual vector. The updating parameters are both the Young’s and the shear modulus of all the girder elements. The least squares problem is solved with a sensitivity-based Gauss-Newton algorithm. In order to improve the condition of the sensitivity matrix the number of unknown parameters is reduced by using a limited set of damage functions [2]. The girder stiffness distribution is found by combining these damage functions, multiplied with the appropriate factors which are the actual variables of the minimization problem. Only linear damage functions are used, but the method can be extended by including higher order functions. With this approach always a realistic smooth result is obtained. A damage pattern is identified which resembles the observed one. The general updating procedure and the application to the Z24 bridge are presented in the paper. General FE model updating procedure Objective function. In FE model updating an optimization problem is set up in which the differences between the experimental and numerical modal data have to be minimized by adjusting the uncertain model properties [1]. The experimental modal data, i.e. the eigenfrequencies and mode shapes , are obtained from measurements. In civil engineering, the measurements are often obtained in operational conditions (ambient vibrations), which means that the exciting forces (coming from wind, traffic,. . . ) are unknown. As a consequence, an absolute scaling of the mode shapes is missing. Furthermore, only the translation degrees of freedom of the mode shapes can be measured. The minimization of the objective function is stated as a nonlinear least squares problem: