Comparison of Nonlinear System Identification Methods for Free Decay Measurements with Application to MEMS Devices

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

“…The coefficients are not exactly the same for all cases, but they have the same order of magnitude. They also correspond to the quadratic stiffness coefficient estimated by the RFS in [23]. The coefficients identified using the ZCA are slightly lower than those identified by the HVD, which is in line with the previous observation of weaker non-linear behaviour estimated by the ZCA in Fig.…”

“…This observed asymmetry suggested that the restoring forces might be asymmetric. The presence of the asymmetry was also confirmed by the restoring force surface method in [23]. This asymmetry is more significant at higher amplitudes and almost disappears at lower amplitudes of vibration.…”

“…Therefore, it can be concluded that the elastic restoring force of the MEMS can be modelled using quadratic stiffness. This observation was also confirmed in [23] by the use of the restoring force surface (RFS) method. As discussed in [24] many different sources of non-linearities exist in MEMS -mechanical (kinematic or material), electrostatic and thermal.…”

“…It can be seen that the natural frequency f 0 is more or less the same for all initial amplitudes and both methods. It corresponds to the natural frequency that was estimated using the ZC in [14,24] and by the restoring force method in [23]. The same natural frequency can also be visually identified in Fig.…”

“…For the identification of systems with symmetric restoring forces, the well-known Freevib algorithm [12] which is based on the Hilbert transform has been used for a long time. However, there are several numerical problems while using the Hilbert transform so the alternative procedures based on zero-crossing methods were developed in [13,[21][22][23]. The key difference between the Freevib and zero-crossing methods is that the zero-crossing times are used to obtain the instantaneous amplitude and frequency instead of the Hilbert transform.…”