Model Order Reduction Using Basis Expansions for Near field Acoustic Holography

The identification/localization of propulsion noise in turbo machinery plays an important role in its design and in noise mitigation techniques. Near field acoustic holography (NAH) is the process by which all aspects of the sound field can be reconstructed based on sound pressure measurements in the near field domain. Identification of noise sources, particularly in turbo-machinery applications, efficiently and accurately is difficult due to complex noise generation mechanisms. Backward prediction of the sound field closer to the source than the measurement plane is typically an unstable “ill-posed” inverse problem due to the presence of measurement noise. Therefore regularized inversion techniques are typically implemented for noise source reconstruction. Another major source of ill-posedness in NAH inverse problems is a larger number of unknowns (sources) than available pressure measurements. A model reduction technique is proposed in this paper to address this issue. Under this paradigm, the NAH inverse problem is reformulated through an expansion of the (unknown) source distribution in terms of a suitable basis set. The problem is then reduced to determining the (typically) small number of expansion coefficients from the measurements. In this study, spatially local Gaussian basis functions are used in the expansion. Preliminary results indicate that the expansion of sources in terms of local basis functions provides higher accuracy in acoustic source identification and reconstruction.