Experimental Identification of Nonlinear Continuous Vibratory Systems Using Nonlinear Principal Component Analysis

In identifying machines and structures, one sometimes encounters cases in which the system should be regarded as a nonlinear continuous system. The governing equations of motion of a nonlinear continuous system are described by a set of nonlinear partial differential equations and boundary conditions. Determiming both of them simultaneously is a quite difficult task. Thus, one has to discretize the governing equations of motion, and reduce the order of the equations as much as possible. In analysis of nonlinear vibratory systems, it is known that one can reduce the order of the system by using the nonlinear normal modes preserving the effect of the nonlinearity accurately. The nonlinear normal modes are description of motion as nonlinear functions of the coordinates for analysis. In identification, if and can express the data as nonlinear functions of the coordinates for identification, it is expected that accurate mathematical model with minimum degree of freedom can be determined. Based on this idea, this research proposes an identification technique which uses nonlinear principal component analysis by a neural network. Applicability of the proposed technique is confirmed by numerical simulation.