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

A number of methods for non-linear system identification in the time and frequency domain have been developed in the past. These methods have been applied to many systems, ranging from micro-scale devices to macro-scale systems, sometimes with uncertain results. The aim of this paper is to assess the efficiency of a subset of methods and understand their range of usability. The methods considered in this study are the restoring force surface (RFS), Hilbert transform (HT), zero-crossing (ZC), direct quadrature (DQ), short-time Fourier transform (SFT) and zero-crossing for asymmetric systems (ZCA). The accuracy and robustness of the methods against measured noise were evaluated using simulated data from a SDOF system. The application of the selected methods to a simulated non-linear MDOF system was also investigated. It could be shown that under certain conditions these methods may still provide reliable results for MDOF systems although generally their use should be avoided. The methods were also applied to data from a micro-electro-mechanical-systems (MEMS). Unfortunately, due to lack of symmetry in the experimental data, only the RFS and ZCA could have been used, leading to the finding that the MEMS device may be modelled using quadratic stiffness.