A Formulation for Updating Finite Element Models Through Consistent Use of Laser Vibrometer Data
Siethoff, Eric Ten
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This thesis suggests a formulation for updating physically meaningful parameters in analytical finite element(FE) models using scanning laser Doppler vibrometer(SLDV) dynamic response data. The update formulation is demonstrated in several computer simulations. The formulation is the result of incorporating an analytical FE model into an experimental model. The experimental model efficiently utilizes SLDV data to fully exploit the instrument's capability to automatically make measurements at many locations. The data in the experimental model is posed in a manner consistent with an analytical FE model's representation for harmonic response, simplifying comparison between the two. The experimental model, which uses finite element shape functions as a basis for a least squares fit to the data, can be solved to give a velocity field based only on that data. The function resulting from inserting the analytical model into the experimental model is an expression of the prediction error of the FE model as compared to the test data. This function is minimized using a quasi-Newton optimization routine, reducing the error and resulting in an updated model. Computer simulations of the update algorithm indicate that: 1. Analytically supplied derivatives and variable scaling are required by the optimization routine to consistently converge, 2. The percentage error of updated parameters falls within two standard deviations of the data's percentage error, 3. Error in the position of the laser results in the update algorithm's failure, and, 4. Error in the parameters not included in the update will appear as error in the updated parameters' solution.
- Masters Theses