The Eigensensitivity Iterative Method on the Model Updating of Structural Model

During structural design and analysis, an appropriate finite element analysis model is required to capture the dynamic characteristics of structures, such as modal parameters (natural frequencies and mode shapes). However, owing to the structural complexity, model variables related to geometry and material properties (for example, moment of inertia and Young’s modulus) should be reasonably simplified. In order to minimize the difference in dynamic characteristics between simulation and actual phenomena, these variables need to be verified through tests or modified if errors exist. In this study, an iterative method of the eigensensitivity matrix, which is an iterative method, is used for updating the structural analysis model. The eigensensitivity matrix is composed of first-order partial differentials of the model variables for natural frequency and mode shape of each modes, which were used to control the regulating of variables in iteration and convergence. The mass matrix and stiffness matrix of the structure were corrected by updating model variables of the analysis model through the iterative procedure, making the analysis results close to the results in the modal test. First, in the present study, a portal beam structure was used to illustrate the updating procedure for the finite element model. The results: (I)Regardless of the noise contamination in the test results (natural frequencies and mode shapes), the model updating effects considering the two convergence indexes (Frobenius norm and Correlation Coefficients) were good. Moreover, the influence of the contaminated test results on the updating effects can be evaluated using model variables as examples. (II)The modal kinetic energy (MKE) in the finite element analysis model was applied to evaluate the appropriate number of measuring points of the modal test; eigensensitivity matrix was used to analyze and obtain the importance order of degrees of freedom in test model; and measured data was set as updating targets, a better updating effect was obtained. (III) We have combined the “residual force vector method” and the “eigensensitivity method” and proposed a two-phase evaluation method to determine the location of elements to be modified in the finite element model. In this study, the test results of a “five-story scaled steel structure” from the National Center for Research on Earthquake Engineering are regarded as an equivalent “shear beam” analysis model to be updated. Based on the sensitivities of characteristic values of the five modes to “model variables,” choosing model variables to which the characteristic value of a mode are more sensitive has better updating effects than using the“same” model variables for each mode as the updating target. Compared with the analysis results of “3D finite element” structure model, the results of the equivalent shear beam structure model after the update show better agreement with the test results. Furthermore, the updated results of model variables meet the engineering requirements. Therefore, the equivalent “shear beam” structure model and its updated results of “model variables” can be used for structural design and analysis.