Parametric and nonparametric identification of nonlinearity in structural dynamics
The work described in this thesis is concerned with procedures for the identification of nonlinearity in structural dynamics. It begins with a diagnostic method which uses the Hubert transform for detecting nonlinearity and describes the neccessary conditions for obtaining a valid Hubert transform. The transform is shown to be incapable of producing a model with predictive power. A method based on the identification of nonlinear restoring forces is adopted for extracting a nonlinear model. The method is critically examined; various caveats, modifications and improvements are obtained. The method is demonstrated on time data obtained from computer simulations. It is shown that a parameter estimation approach to restoring force identification based on direct least—squares estimation theory is a fast and accurate procedure. In addition, this approach allows one to obtain the equations of motion for a multi—degree—of—freedom system even if the system is only excited at one point. The data processing methods for the restoring force identification including integration and differentiation of sampled time data are developed and discussed in some detail. A comparitive study is made of several of the most well—known least—squares estimation procedures and the direct least —squares approach is applied to data from several experiments where it is shown to correctly identify nonlinearity in both single— and multi—degree--of—freedom systems. Finally, using both simulated and experimental data, it is shown that the recursive least—squares algorithm modified by the inclusion of a data forgetting factor can be used to identify time—dependent structural parameters.