The term "coherent phase line enhancer" (CPLE) refers to a dual-transform method of spectral analysis that enhances the detection of periodic and quasi-periodic signals buried in wide-band noise. The CPLE is particularly useful for increasing the signal-to-noise ratios of spectral peaks ("lines") that represent periodic and quasi-periodic components of measurements of vibration, dynamic strain, and/or dynamic pressure in a turbine or other rotating machine. The purpose of such measurements, spectral analysis, and enhancement of spectral peaks is to assess machine performance and identify spectral signatures of bearing or gear-train defects.

Other machine-diagnostic spectral-analysis methods related to the CPLE have been described in several prior articles in NASA Tech Briefs. The need for the CPLE and those other methods arises, in part, because in conventional spectral displays, peak patterns are frequently difficult to assess in cases in which peaks are at or below the amplitude of wide-band noise. ["Conventional spectral displays" as used here denotes those produced by fast-Fourier-transform (FFT) processing of digitized signals.] In such displays, periodic signals may not be separated from wide-band noise because the phase information needed to show the peaks for these signals is missing after FFT processing. The CPLE involves a second transformation that restores the needed phase information. In addition, in the CPLE, the discreteness of each spectral component is quantified by a bandwidth coherence value.

The traditional method of estimating the auto power spectral density (PSD) function involves ensemble processing of the FFT amplitude of each segmented data block and discarding the FFT phase information. The resulting "ensemble amplitude averaging" PSD function is widely used in many commercial test and measurement products. For the purpose of separating a periodic signal from noise, additional signal-enhancement capability can be achieved by including phase-correlated information in the ensemble processing. After the original signal is transformed from the time domain to the frequency domain, the spectral record consists of an ensemble of blocks. In the CPLE, a second transform converts each spectral component along the ensemble direction into an "equivalent" wave-number domain, in which signal components are enhanced by virtue of their coherent phase relationships among the ensemble segments.

In comparison with spectrum obtained by FFT processing only, a CPLE spectrum provides a more accurate estimate of the frequency of a periodic signal. Moreover, the difference between the coherent phase characteristic of a periodic signal and the random phase of wide-band noise is more apparent in the wave-number domain. As a result, in comparison with a conventional power spectrum, a CPLE spectrum enables better detection of periodic signals. Unlike some other filtering techniques (e.g., adaptive filter, adaptive line enhancer, and the like) used to enhance signals, the CPLE can be the basis of a relatively simple and stable approach that can be easily implemented in the frequency domain along with the FFT.

The quasi-periodicity (as distinguished from pure periodicity) of the vibration signal from a typical rotating machine poses a major obstacle to the direct application of the CPLE to analysis of these signals. The rotation-speed-related components of the signal (e.g., synchronous harmonics and subharmonics, bearing signatures, gear signatures, and the like) are all quasi-periodic because rotation tends to momentarily accelerate or decelerate as the load on the machine varies. A direct application of the CPLE to the signal does not provide any enhancement because only weak (if any) coherent phase relationships exist among the ensemble segments. However, one can obtain the desired enhancement by following either or both of the following two approaches:

The first approach is called "CPLE/OT" (where "OT" signifies "Order Tracking method"). This method requires an additional pulse tachometer (key-phasor) signal. Measurement of the time between the pulses yields an instantaneous value of the rotation period once per revolution. On the basis of this measurement, the original digital signal, which is sampled at uniform intervals of time, is then resampled with a fixed number of samples during each revolution. The resampling involves the use of either linear interpolation or (in the case of large variations of speed) spline-curve-fit interpolation. The resampling is utilized in the conventional synchronous timer averaging (STA) method. STA enhances a waveform through direct time averaging of the resampled waveform over many revolutions. Within the resampled signal, all the speed-related components are periodic. Therefore, CPLE spectral analysis is applicable to speed-related signal enhancement.

The second approach is called "CPLE/PSEM" (where "PSEM" denotes "phase synchronized enhancement method"). This method does not require the key-phasor signal. The PSEM involves a phase-to-time conversion algorithm that transforms the instantaneous phase of a reference component of the signal into the desired resampling time for synchronization. (The reference component is selected by the user and is typically synchronous with either the rotation or a harmonic thereof.) Within the resulting PSEM signal, both the reference component and all its coherently correlated components become periodic. Consequently, when CPLE spectral analysis is applied to the PSEM signal, enhanced results are obtained.

This work was done by Jen-Yi Jong of AI Signal Research, Inc., for Marshall Space Flight Center. For further information, please contact the company at or (256) 551-0008.

Inquiries concerning rights for the commercial use of this invention should be addressed to

the Patent Counsel
Marshall Space Flight Center; (256) 544-0021.

Refer to MFS-31426.

NASA Tech Briefs Magazine

This article first appeared in the July, 2001 issue of NASA Tech Briefs Magazine.

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