Non-linear system identification based on Lie series solutions

A direct method of system identification and parameters monitoring is introduced for a general class of non-linear systems. The only requirement is that the system characteristics must be modelled by analytic or sufficiently smooth functions of the state variables, including the time parameter. The approach is based on the operator Lie representations and the corresponding Lie series solutions. This kind of solutions can be obtained for a general class of non-linear systems in the form of analytical power series including the system parameters. Despite the local characterisation of such solutions, the corresponding information carried by the solutions appears to be sufficiently complete and provides precise estimates of the system parameters. A non-linear vertical cantilever beam, excited at its support, is considered as a sample problem. Both constant and relaxation stiffness parameters are determined at every sample point, and thus the stiffness relaxation curves are recovered from the phase space dynamics. The method is found to be stable with respect to artificially introduced noisy components of the numerically simulated data and an increase in the number of degrees of freedom.