Acoustic spinning-mode analysis by an iterative threshold method

Abstract

Spinning-mode analysis methods are commonly used for studying the spatial structure of the acoustic field inside ducts. In some applications, the background noise is very high, so that the acoustic modes may be overwhelmed by spurious modes in the modal spectra. The problem may be solved by methods that greatly reduce the background noise. Four methods studied in a previous work are briefly summarized in this article. The method providing the best reduction of the background noise is inaccurate in certain cases. An iterative threshold technique is proposed to eliminate this drawback. It is compared to the four other methods using numerical simulations and mode measurements in the nozzle of a Turbomeca TM333 turboshaft engine. Nomenclature/ = frequency G, = gain in signal to noise ratio of method / = 10 log[(S/N) OUT /(S/N) IN ] / = unit matrix Im[w(/, m)] = imaginary part of o>(/, m) J = number of microphones L = number of data blocks M N = set of noise modes M s = set of acoustic modes, signal m = angular wave number of spinning mode order N(f, 0) = frequency Fourier transform of Ai(r, 0) n(t, 6) = background noise Re[o>(/, m)] = real part of w(f, m) 5(/, 0) = frequency Fourier transform of s(f, 0) s(t, 0) = acoustic pressure, signal T Vmin = the smallest power spectral density on a noise mode Tr[V(f)] = trace of matrix T(/) t = time y(/, 0) = frequency Fourier transform of y(t, 0) y(t, 0) = time history of acoustic pressure (signal -+ noise) measured by a microphone at angle 0 T/v(/) = cross-spectral matrix of N(f, 0) r s (/) = cross-spectral matrix of S(f, 0) r y (f) = cross-spectral matrix of Y(f, 0), see Eq. (3) 8 = Kronecker symbol 0 = angle 6j = location angle of microphone y [ = 277(y -!)//],/= 1,2, . . . ,7 cr 2 (/) = noise power spectral density <£,(/, m) = wave number spectrum at frequency/by method / o>(/, m) = angular Fourier transform of Y(f, 0) * = complex conjugate + = transposed complex conjugate Presented as Paper 92-02-041 at

Compressive sensing based spinning mode detections by in-duct microphone arrays

“…The conventional mode detection methods (for the azimuthal mode decompositions in particular) [4,[6][7][8][9][10] conduct spatial Fourier series decompositions by using circular sensory arrays [3,4,[11][12][13][14], which usually consist of a large number of equally spaced microphones to satisfy the famous Shannon-Nyquist sampling theorem, i.e. the array should have at least 2m microphones to capture an azimuthal mode of the mth order.…”