A finite element model updating technique for correcting global geometric errors using multiple models

Finite element model updating has been an area of active research for the past thirty years. The goal is to provide a model that is more representative of the structure. This updated model can then be used for additional analysis to evaluate the design or provide the designer with insight on how to improve the design, if necessary. Despite the extensive amount of research, no one method has emerged that can be applied to all circumstances. The diversity in methods applied can be traced to the inverse nature of the problem. Typically, the amount of information available from modal testing of a structure is limited. The finite element model of the structures can be quite large with hundreds or thousands of degrees of freedom. This leaves the analyst with little choice but to select a region of the finite element model by choosing elements or groups of elements for corrections. The selected elements are parameterized by extracting design parameters directly or by sensitivity methods and the parameter corrections are obtained using the method of least squares. This process usually results in an ill conditioned problem that can be sensitive to small variation or noise in the test data.; An alternate view of the updating problem is that the errors are distributed rather than localized to a specific region of the model. This is the case when variations in geometry can influence the response characteristics of a structure. This research effort proposes a new approach for updating the geometry of a finite element model using a set of models to form a basis for a perturbation space. The method is demonstrated by numerical simulations and by experiment using a series of perturbed flat plates. The numerical simulations indicate that the updating technique produces an updated model that improves the agreement between the simulated test plate and the model. The application of the method to the experimental data demonstrated that the updated model provided a slight improvement of the nominal model. A new metric for comparing the error between the model and the test data based on the matrix 2-norm is presented.