Finite Element Model Updating Method for 3D Structures Using Improved Sensitivity-Based Optimization Methods

Roughly since the 1990s, the model updating problem in fields such as design, construction, repair and maintenance of mechanical systems and civil structures has been a very important, challenging, and developing subject. In general, in the model updating methods, an analytical model of a structure, which is usually formed based on its as built data by using of the finite element method, is corrected considering a set of experimental measured data obtained from vibration of the concerned structure. In fact, the main purpose of the model updating methods is to correct some structural parameters such as mass, stiffness, and damping, in order to achieve a better compromise between analytical and experimental data. We expected that a correctly updated analytical model of a structure predict dynamic behaviour of the real structure better and more accurately than its initial model. In this way, considering the structural model changes with respect to a previously constructed reference model would be measurable. On the other hand, if a structure suffers damages through some extraordinary loadings, this will also be recognizable through comparing the difference between the updated model and its reference model. In this view point, the model updating methods may be a good substitution for traditional methods of damage detection and be generally applied methods for the structural health monitoring, also seismic control and performance/behaviour evaluation of civil structures. Many methods have been developed so far in order to update finite element model of civil structures, which are generally categorized in two main groups including direct and indirect or iterative methods. In the direct methods, mass and stiffness matrices of the structure are directly updated during one step. In these methods, there is no direct relation between elements of the structural matrices and structural physical parameters. Therefore, although the updated matrices obtained from these methods have a relatively acceptable accuracy in predicting linear structural behaviour, todays they are rarely used in updating the model of real structures. On the other hand, among the researchers, the iterative methods, because directly use of sensitivity and variations of structural physical parameters to update structural models are more acceptable. Modal parameters of the structure including the natural frequencies and mode shapes are one of the most widely used data in these methods. However, since there is always a non-linear relationship between the modal data and physical parameters, the updating problem in this method is turned into a nonlinear least squares problem that must be solved using the iterative optimization methods. In these methods, the errors between the numerical results and the measured ones are considered as the objective function of the optimization problem. By minimizing the objective function by changing some pre-determined physical structural parameters of the initial analytical finite element model, through an iterative updating method, location and severities of damages are detected, as well as the correct physical parameters. This study aims at updating the finite element model of 3D structures performed through a sensitivity-based iterative optimization method known as the trust region Gauss-Newton method. This is done through finding the best values for the elemental stiffness parameters in analytical model through minimizing the difference between the frequencies and mode shapes of the real and damaged structure. Moreover, in order to reduce the number of updating parameters and avoid singularity problems due to usual numerical errors in the process of solving large-scale optimization problems, a new updating process has been implemented through several iterative stages via sequential analysis to find unknown correction factors. This process continues until the results from the two final analyses are very close during an acceptable accuracy. In order to examine performance of the proposed procedure, it is implemented for detection of several damage scenarios of a 3D three-story steel dual system of an MR structure equipped by a bracing system. Extensive analyses show that, the proposed method is a powerful model updating method to detect location and severity of sparse/minor damages of large-scale structures with the minimum possible error.