Estimation of signal coherence threshold and concealed spectral lines applied to detection of turbofan engine combustion noise

Abstract

Combustion noise from turbofan engines has become important, as the noise from sources like the fan and jet are reduced. An aligned and un-aligned coherence technique has been developed to determine a threshold level for the coherence and thereby help to separate the coherent combustion noise source from other noise sources measured with far-field microphones. This method is compared with a statistics based coherence threshold estimation method. In addition, the un-aligned coherence procedure at the same time also reveals periodicities, spectral lines, and undamped sinusoids hidden by broadband turbofan engine noise. In calculating the coherence threshold using a statistical method, one may use either the number of independent records or a larger number corresponding to the number of overlapped records used to create the average. Using data from a turbofan engine and a simulation this paper shows that applying the Fisher z-transform to the un-aligned coherence can aid in making the proper selection of samples and produce a reasonable statistics based coherence threshold. Examples are presented showing that the underlying tonal and coherent broad band structure which is buried under random broadband noise and jet noise can be determined. The method also shows the possible presence of indirect combustion noise.

Statistical evaluation of coherence estimated from optimally beamformed signals

“…The use of segment overlapping has potential to make MSC estimates even more precise; however, it also makes the analytical derivation of the MSC distribution very difficult to trace. In fact, for the special case of the MSC estimated between two signals, the explicit formula for the MSC statistical distribution is known only for the segmentation without overlapping; for the overlapped segmentation only approximations are available [23,33,34]. Still, for this MSC estimate, the analytic formula for the non-overlapped case has become a good basis for the approximation of the statistical distribution of the MSC estimated with segment overlapping.…”

Spatial correlation in the ambient core noise field of a turbofan engine

“…Note that the higher statistical confidence interval based on the number of independent records (n d ¼ 128) is a more conservative estimate of the measured coherence threshold for the Honeywell TECH977 turbofan engine. Miles 13 previously found that with a 50 percent overlap the higher statistical confidence interval based on the number of independent records is a more conservative estimate of the measured coherence threshold for measurements made in the Pratt & Whitney PW4098 turbofan engine. Miles 13 showed that for a Gaussian distribution and using a 50 percent overlap to reduce the variance, a coherence threshold calculated with n o ¼ 2ns did work well.…”

“…Miles 12,13 shows that instead of relying on the confidence interval given by Eq. (2), which is based on a statistical theory, to obtain a threshold value forĉ 2 nn ðn s Þ, one can use a deliberately unaligned time history to create the threshold value.…”

“…where this formula determines a P-percent threshold confidence interval using the number of independent data segments/blocks, n s , used in the Welch's periodogram method spectral estimator (see Miles 12,13 ). The 95 percent confidence interval based on n s ¼ 128 independent samples is 0.0233.…”

“…Experimental studies of indirect combustion noise from a Pratt & Whitney PW4098 (East Hartford, CT) turbofan engine using an aligned and purposely nonaligned coherence procedure on acoustic measurements in the engine combustor and in the far field are discussed by Miles. 12,13 Experimental studies of indirect combustion noise from a Honeywell TECH977 (Phoenix, AZ) turbofan engine using cross-spectra and correlation function procedures to estimate the post-combustion (postflame) residence time from acoustic measurements in the engine combustor and in the far field are discussed by Miles. [14][15][16][17] The post-combustion (post-flame) residence time is the time taken for an entropy disturbance to travel in the combustor from the flame to the turbine entrance at the flow velocity.…”