Application of the Energy Operator Separation Algorithm (EOSA) for the Instantaneous Amplitude and Frequency Calculation of Nonlinear Dynamic Systems Response

A number of non-linear dynamic responses require analysis with an increased resolution in their time domain representation, especially the ones presenting abrupt changes, such as those caused by the introduction of cracks, gaps, and slip. Typical technological applications include bearings or gears with localized defects. Since the time resolution of well-known time-frequency analysis tools (such as Wavelet-Transform) presents limitations, the Energy Operator Separation Algorithm (EOSA) is considered. The algorithm is based on the Teager-Kaiser nonlinear differential energy operator and leads to the calculation of the instantaneous amplitude and frequency of the response. Compared to the Hilbert transform, it leads at least to the same estimation errors, but in addition presents smaller computational complexity and faster adaptation, due to its instantaneous nature. The EOSA is applied on responses of a nonlinear Van der-Pol oscillator, on signals simulating the dynamic response of defective rolling element bearings and on three signals measured at industrial installations, resulting from defective bearings. In all cases the algorithm leads to the efficient calculation, mainly of the instantaneous amplitude of the signals. However, certain improvements are necessary in order to increase the smoothness, mainly of the resulting instantaneous frequency time waveforms.Copyright © 2009 by ASME