A combined model reduction/SVD approach to nonlinear model updating

We consider the updating of nonlinear structural dynamics models for which the mathematical form of the nonlinearity is known ahead of time. Free vibration data from the actual structure are compared to model simulated data, and selected coefficients in the model are to be updated based on this comparison. We present two versions of model reduction based updating: 1) an exact for the linear case model reduction is first applied to produce a reduced order nonlinear model that is used to simulate the measured data; the full model parameters are updated using a standard least squares optimization to minimize the error between the experimental and simulated coordinate histories (or coordinates and velocities); 2) the same reduced nonlinear model as in method 1) is used, but the updating optimization is performed by minimizing the error in the singular value decompositions of the simulated and measured responses; in this second method the approach of Hasselman, et al [5] is used to alter the model coefficients by minimizing the squared error between the parameters comprising the SVD's of the data and the simulation The two approaches have been applied to simulated data in low order toy problems. The results are the following: 1) both methods produce an acceptable updating, 2) updating is reasonably successful in both linear and nonlinear versions of the system analyzed, which has an isolated, static cubic nonlinearity, 3) the method requires a model reduction to be performed at each parameter perturbation stage, and a more efficient method for accomplishing this is needed in order to render the approach useful from a practical standpoint.