A new iterative model updating technique based on least squares minimal residual method using measured modal data

Finite element (FE) models are useful for many applications in engineering community such as structural analysis, dynamic behavior prediction, structural condition assessment, and damage detection. In reality, the FE models often differ with the real structures due to significant discrepancies between test measurements and model predictions. This study is intended to propose an iterative model updating method to adjust the mass and stiffness matrices of the FE model by improving model updating formulations. Under dynamic discrepancy theory, the mass and stiffness orthogonality conditions are independently expanded to establish two model updating formulations. In the proposed iterative method, each of the improved equations is solved by a robust iterative technique named as least squares minimal residual (LSMR) to compute structural discrepancy matrices after transforming linear matrix systems of the model updating equations into linear vector systems. In the following, the mass and stiffness matrices are updated in the algorithm of the proposed iterative model updating method using the structural discrepancy matrices obtained from the LSMR technique. The major contributions of this article are to propose a new iterative finite element model updating method and introduce the novel and robust LSMR approach for the vibration-based applications. Another novelty is to enhance the two well-known model updating formulations for achieving more appropriate updating results. The efficiency and accuracy of the proposed methods are numerically verified by a simple planner truss and two shear building models. Results demonstrate that the proposed methods provide reliable estimates of finite element model updating using the measured modal data.