Finite element model tuning using automated structural optimization system software

A method of adjusting analytical finite element models to measured data is presented. The algorithm uses a mathematical optimization strategy to minimize deviations between measured and analytical modal frequencies and partial mode shapes. A mode tracking algorithm is used to identify and account for mode switching during the optimization process. The algorithm was successfully implemented using the Automated Structural Optimization System Software. Experimental results are presented for tuning a lightly damped 6-m flexible frame structure. The results demonstrate excellent agreement between the tuned model and measured data and illustrate the importance of off-nominal validation before accepting a model for simulation purposes. CCURATE prediction and simulation of the dynamic behav- ior of large flexible space structures require analytical models that agree with measured data. Unfortunately, uncertainty in a finite element model (FEM) implies less than perfect correlation between analytical and measured data. When the disagreement is deemed unacceptable, it is necessary for the design engineer to make ad- justments to the FEM. For large problems the number of potential parameters to adjust, such as elemental areas, elastic moduli, inertia moments, etc., quickly becomes overwhelming. Thus a systematic method is required to ensure the adjustments produce the desired results. To this end, a method is introduced that poses a numerical optimization problem, namely, given a set of measured eigenvalues and partial eigenvectors, determine the values of selected physical parameters of the model that minimize the weighted deviations from the analytical eigenvalues and eigenvectors. Numerous techniques and goals of model tuning, also referred to as model refinement or model identification, have appeared in the literature. The common attribute of these techniques is that they at- tempt to minimize the required modification to the analytical mass and stiffness matrices, assuming the FEM is a reasonable approxi- mation to the physical structure. Sensitivity based approaches have been presented in the literature that adjust the matrices by estab- lishing an objective function based on the difference between the experimental and analytical model data.1"5 An advantage of those methods is that the updated models are consistent with the FEM formulation, and thus the connectivity is preserved. An alternative method employing an optimal matrix update has been developed by Berman and Nogy6 and Baruch.7 In this method, a perturbation mass, damping, or stiffness matrix is determined that, when added to the analytical matrices, produces the measured result. The advantage of this method is a tuned analytic model that exactly reproduces the experimental data. Its shortcoming is that it does not guarantee the closeness to unmeasured modes not used in the tuning process. This is a result of potentially unrealistic changes in the stiffness matrix, such as the introduction of load paths that physically do not exist. To overcome some of the shortcomings of Baruch's method of stiff- ness matrix adjustments, Kabe8 and Kammer9 introduced objective functions that ensure stiffness terms are corrected in a manner such that the connectivity of the analytical model is preserved. Similar