L1 generalized inverse beam-forming algorithm resolving coherent/incoherent, distributed and multipole sources

Abstract

To resolve coherent/incoherent, distributed/compact, and multipole aerodynamic-sound sources with phased-array pressure data, a new source-detection algorithm is developed based on L 1 generalized inverse techniques. To extract each coherent signal, a cross spectral matrix is decomposed into eigenmodes. Subsequently, the complex source-amplitude distribution that recovers each eigenmode is solved using generalized inverse techniques with reference solutions which include multipoles as well as a monopole. Namely, the source distribution consisting of pre-defined source types is solved as an L 1 norm problem using iteratively re-weighted least squares (IRLS). The capabilities of the proposed algorithm are demonstrated using various benchmark problems to compare the results with several existing beam-forming algorithms, and it is found that distributed sources as well as dipoles with arbitrary orientation can be identified regardless of coherency with another source. The resolution is comparable to existing deconvolution techniques, such as DAMAS or CLEAN, and the computational cost is only several times more than that of DAMAS2. The proposed algorithm is also examined using previous model-scale test data taken in an open-jet wind-tunnel for a study on jet–flap interaction, and some indication of dipole radiation is discerned near the flap edge.