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

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.

[1]  Jeffrey Hilton Miles Core Noise Diagnostics of Turbofan Engine Noise Using Correlation and Coherence Functions , 2010 .

[2]  ShouYan Wang,et al.  Exact confidence interval for magnitude-squared coherence estimates , 2004, IEEE Signal Processing Letters.

[3]  A. Nuttall,et al.  An approximation to the cumulative distribution function of the magnitude-squared coherence estimate , 1981 .

[4]  R. Lerch,et al.  Flow-Induced Sound of Wall-Mounted Cylinders with Different Geometries , 2008 .

[5]  P. Welch The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms , 1967 .

[6]  J. Gosselin Comparative study of two-sensor(magnitude-squared coherence) and single-sensor(square-law) receiver operating characteristics , 1977 .

[7]  V. Benignus Estimation of the coherence spectrum and its confidence interval using the fast Fourier transform , 1969 .

[8]  G. Carter Receiver operating characteristics for a linearly thresholded coherence estimation detector , 1977 .

[9]  Rory A. Fisher,et al.  The general sampling distribution of the multiple correlation coefficient , 1928 .

[10]  M. Foster,et al.  THE COEFFICIENT OF COHERENCE: ITS ESTIMATION AND USE IN GEOPHYSICAL DATA PROCESSING , 1967 .

[11]  N. R. Goodman ON THE JOINT ESTIMATION OF THE SPECTRA, COSPECTRUM AND QUADRATURE SPECTRUM OF A TWO-DIMENSIONAL STATIONARY GAUSSIAN PROCESS , 1957 .

[12]  Pavel Sovka,et al.  Approximation of statistical distribution of magnitude squared coherence estimated with segment overlapping , 2007, Signal Process..

[13]  H. Freund,et al.  Cortico‐muscular synchronization during isometric muscle contraction in humans as revealed by magnetoencephalography , 2000, The Journal of physiology.

[14]  T. G. Sofrin,et al.  Axial Flow Compressor Noise Studies , 1962 .

[15]  T. Teichmann,et al.  The Measurement of Power Spectra , 1960 .

[16]  John F. Stein,et al.  subthalamic nucleus , 2004 .

[17]  J. Bendat,et al.  Random Data: Analysis and Measurement Procedures , 1971 .

[18]  A. Piersol Time delay estimation using phase data , 1981 .

[19]  Jeffrey Hilton Miles Separating Turbofan Engine Noise Sources Using Auto- and Cross Spectra from Four Microphones , 2008 .

[20]  D. G. Watts,et al.  Spectral analysis and its applications , 1968 .

[21]  Jeffrey Hilton Miles,et al.  Time Delay Analysis of Turbofan Engine Direct and Indirect Combustion Noise Sources , 2009 .

[22]  A M Amjad,et al.  A framework for the analysis of mixed time series/point process data--theory and application to the study of physiological tremor, single motor unit discharges and electromyograms. , 1995, Progress in biophysics and molecular biology.

[23]  D. B. Preston Spectral Analysis and Time Series , 1983 .

[24]  Samuel D. Stearns,et al.  Signal processing algorithms using Fortran and C , 1992 .

[25]  G. Carter Coherence and time delay estimation , 1987, Proceedings of the IEEE.

[26]  J. Chung Rejection of flow noise using a coherence function method , 1977 .

[27]  J. Miles Restricted Modal Analysis Applied to Internal Annular Combustor Autospectra and Cross-Spectra Measurements , 2007 .

[28]  A. Nuttall Invariance of distribution of coherence estimate to second-channel statistics , 1981 .

[29]  Malcolm J. Crocker,et al.  Measurement of frequency responses and the multiple coherence function of the noise‐generation system of a diesel engine , 1975 .

[30]  Julius S. Bendat,et al.  Engineering Applications of Correlation and Spectral Analysis , 1980 .

[31]  Luca Faes,et al.  Surrogate data analysis for assessing the significance of the coherence function , 2004, IEEE Transactions on Biomedical Engineering.

[32]  Jeffrey Hilton Miles Separating Direct and Indirect Turbofan Engine Combustion Noise Using the Correlation Function , 2010 .

[33]  Jeff M. Mendoza,et al.  Source Separation from Multiple Microphone Measurements in the Far Field of a Full Scale Aero Engine , 2008 .

[34]  Barry G. Quinn,et al.  The Estimation and Tracking of Frequency , 2001 .

[35]  Charles L. Byrne,et al.  Signal Processing: A Mathematical Approach , 1993 .

[36]  G. Carter,et al.  Estimation of the magnitude-squared coherence function via overlapped fast Fourier transform processing , 1973 .

[37]  M. J. Crocker,et al.  Reply to ’’Comments on ’Measurement of frequency response and the multiple coherence function of the noise generation system of a diesel engine’ ’’ [J. Acoust. Soc. Am. 60, 951–952 (1976)] , 1976 .