Enhancing the reconstruction of in-duct sound sources using a spectral decomposition method
Simulated variations of the mean-squared error (dB), , for the reconstruction of an in-duct wall-mounted monopole over a ring of equivalent sources, assuming a SNR of 20 dB, as a function of the standoff distance and the nondimensional frequency.
Relationships between field-source variables in the spatial and spectral domains.
Close-up of the microphone traverse system used for the reconstruction of the strength of volume velocity sources in the UTC circular duct acoustic facility.
Modulus (top) and phase (bottom) of the volume velocity of a compression driver: true (thick) and reconstructed (a) without regularization (thin) and with Tikhonov regularization (GCV: dotted; L-curve: dashed); (b): using the ESM with Tikhonov-L-curve regularization over a ring of equivalent sources, with an eventual shift angle (dashed:; dotted:; and dash-dotted:).
Variations of the relative error (%) on the pressure field, when recomposed at from an increasing number of field points versus the number of iterations used in the modal decomposition.
Cross-sectional distributions of the acoustic pressure field at , (a) measured and (b) recomposed after 17 iterations, and corresponding imaging of the axial acoustic velocity [(c) and (d)].
Variations with of the number of selected modal components used for reconstruction at (a) and (b) : theoretical criterion (bold), Tikhonov L-curve criterion (dashed), and number of cut-on modes (thin).
Variations with of the (a) radial and (b) angular resolution obtained for the reconstruction at (gray) and (black) from direct imaging (bold line) and after iterations (dotted). The resolution obtained with cut-on modes only (thin line).
Cross-sectional imaging of the axial acoustic velocity (modulus in ) reconstructed after modal iteration at (top row), (mid row), and (bottom row) from in-duct pressure data acquired at from the source section for one source at (left column), two correlated sources respectively at and 120° (mid column), and at and −60° (right column).
Cross-sectional imaging of the axial acoustic velocity (modulus in ) reconstructed at from in-duct pressure data measured at from the source section which comprises two correlated drivers wall-mounted at 0° and −60°: (a) direct imaging from raw pressure; (b) imaging after 20 iterations for the pressure modal decomposition.
Layout of the UTC rectangular flow duct facility used for in-duct acoustic imaging from wall-pressure data.
Cross-sectional imaging of the axial acoustic velocity (modulus in ) reconstructed at [(a) and (b)] and [(c) and (d)] from wall-pressure measurements using the FSDM: [(a) and (c)]stopping criterion; [(b) and (d)] L-curve criterion.
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