Parameter Estimation and Effect of Gravity on a Multiple Degree of Freedom Nonlinear System under Random Excitation

Nonlinearity affects many dynamical systems under operating conditions and recent literature demonstrates that accurate models should be developed to account for nonlinearity, in order to preserve good prediction capability. In this paper a nonlinear model for a particular multiple degree-of-freedom system (MDOF) is developed and the effects of gravity are discussed. These effects are concerned both with the disruption of the symmetry and the dependence of the natural frequencies on the acceleration due to gravity. Analytical models with increasing complexity are developed to account for these effects and to investigate them in a practical system. An important task towards a better understanding of the system behavior is the extraction of the physical parameters from experimental measurements. In the present case this can be achieved by performing nonlinear subspace identification (NSI). Although some features of nonlinear systems may be masked by random excitation, it has been shown recently that such an excitation is suitable for nonlinear system parameter identification. In this paper it is shown how NSI, used in conjunction with the rational fraction polynomial (RFP) method, can be applied for estimating the physical parameters (including masses) without any a priori knowledge of the nonlinear system. This new method exploits the fact that the equations of motion are coupled also via the nonlinearity.