A method for non-parametric identification of non-linear vibration systems with asymmetric restoring forces from a resonant decay response

•Zero-crossing method for systems with asymmetric restoring forces (ZCA) is proposed.•Backbones, damping curves, and asymmetric non-linear restoring forces can be identified.•The proposed method is applied to both simulated and experimental data.•A detailed comparison with the Hilbert vibration decomposition is made.•The proposed method exceeds the Hilbert vibration decomposition in many aspects. A method for non-parametric identification of systems with asymmetric non-linear restoring forces is proposed in this paper. The method, named the zero-crossing method for systems with asymmetric restoring forces (ZCA), is an extension of zero-crossing methods and allows identification of backbones, damping curves and restoring elastic and dissipative forces from a resonant decay response. The validity of the proposed method is firstly demonstrated on three simulated resonant decay responses of the systems with off-centre clearance, bilinear and quadratic stiffness. Then, the method is applied to experimental data from a micro-electro-mechanical resonator in order to quantify its non-linear damping and stiffness effects. Throughout the paper the proposed method is also compared with the Hilbert vibration decomposition to demonstrate that the ZCA yields more accurate results with much less effort.