Use of the Teager Kaiser Energy Operator to estimate machine speed

Robert B. Randall and Wade A. Smith
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phmec_16_043.pdf528.23 KBJune 27, 2016 - 6:37am

For diagnostics of variable speed machines such as wind turbines, it is essential to have a measure of instantaneous speed, preferably extracted from the response signal to avoid the need for a tacho signal. The Teager Kaiser Energy Operator (TKEO) was first proposed by Teager, and refined by Kaiser. It is analogous to the total (kinetic and potential) energy of a simple oscillator. A discrete version of the TKEO can be estimated from three adjacent samples of a signal, so it is very efficient to calculate from a sampled time record in real time. It can be used to obtain estimates of amplitude and frequency modulation. A previous paper showed it can also be calculated simply as the squared envelope of the derivative of a signal, using Hilbert transform techniques via the frequency domain. The differentiation can be very efficiently performed by j operations in the frequency spectrum, at the same time as the bandpass filtration, which can be achieved with ideal, zero phase shift filters, using FFT techniques. It cannot then be done in real-time, but this is rarely a problem in machine condition monitoring where information is typically being sought days, weeks or months in advance. The TKEO equals the product of the squared envelope of the signal and the square of the instantaneous frequency, so the latter can be obtained by dividing the squared envelope of the derivative by the squared envelope of the signal. In this paper it is shown that this can be applied to the determination of the instantaneous speed of a machine, as long as a harmonic of one of the shaft speeds is isolated in the frequency domain from interference by adjacent components. This approach is applied to a couple of practical cases, and in particular compared with the results from another more complicated approach on a wind turbine signal, based on phase demodulation of the same carrier, followed by phase unwrapping and differentiation. Virtually the same results were obtained. In both cases the differentiation gave some high frequency noise, but this could easily be smoothed using various techniques.

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Submission Keywords: 
variable speed
speed determination
Teager Kaiser Energy Operator
Wind turbine condition monitoring
Submission Topic Areas: 
Model-based methods for fault detection, diagnostics, and prognosis
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