Sherman P.

Noise and vibration processes often include both random and tonal components. Coherence analysis cannot be readily applied to the tonal components, since the coherence between two tones having the same frequency is unity. Thus, for example, two independent engines operating at the same speed will exhibit unity coherence at harmonics of the operating speed. For this reason, noise source identification using coherence analysis has typically ignored the near-unity coherence associated with narrow spectral lines. However, those spectral lines not only often times dominate the spectrum, and so it is reasonable to question whether there is, indeed, information in them that would allow one to use them to quantify the level of correlation between tonal noise sources. The answer to this question is the focus of this paper. It is affirmative, and based on the fact that two independent machines will never operate at exactly the same speed. Furthermore, the machine speed always entails minor speed fluctuations. By tracking the amplitude and frequency fluctuations associated with a given tonal component using an extended Kalman filter (EKF) one can extract amplitude and frequency time series that can quantify the level of correlation between two tones having the same nominal frequency. We present the structure of our EKF, investigate its sensitivity to critical EKF parameters, and offer novel measures for quantifying the correlation between two tones. These measures range from statistical correlations between amplitude/frequency paired random variables, to cross correlation functions of these processes. Many methods for tracking time varying tones have been proposed. Those methods have been evaluated in high SNR settings (>10dB). The EKF method presented in this work is shown to work well at much lower SNRs (e.g. -3 dB). This is important, since many machinery applications entail a notable amount of random noise/vibration.