Nonparametric identification of asymmetric nonlinear vibration systems with the Hilbert transform

The objective of the paper is presenting a simple and more accurate technique for precise identification of nonlinear elastic force functions acting in asymmetric vibration systems. The identification procedure based on the Hilbert transform is a nonparametric one; it does not require a priori information about the system structure or its parameters. The examples of the identification of asymmetric classic vibration nonlinear models – the Helmholtz and the double-well Duffing oscillators – are investigated.

► The Hilbert transform decomposes a solution into harmonics and aperiodic components.
► Their combination forms a congruent envelope and an instantaneous frequency.
► The congruent functions present two skeleton curves of an asymmetric system solution.
► They also build precisely initial nonlinear elastic force characteristics.
► Two models are investigated: the Helmholtz and the Duffing–Holmes oscillators.