Combined Helmholtz equation–least squares method for reconstructing acoustic radiation from arbitrarily shaped objects

A combined Helmholtz equation-least squares (CHELS) method is developed for reconstructing acoustic radiation from an arbitrary object. This method combines the advantages of both the HELS method and the Helmholtz integral theory based near-field acoustic holography (NAH). As such it allows for reconstruction of the acoustic field radiated from an arbitrary object with relatively few measurements, thus significantly enhancing the reconstruction efficiency. The first step in the CHELS method is to establish the HELS formulations based on a finite number of acoustic pressure measurements taken on or beyond a hypothetical spherical surface that encloses the object under consideration. Next enough field acoustic pressures are generated using the HELS formulations and taken as the input to the Helmholtz integral formulations implemented through the boundary element method (BEM). The acoustic pressure and normal component of the velocity at the discretized nodes on the surface are then determined by solving two matrix equations using singular value decomposition (SVD) and regularization techniques. Also presented are in-depth analyses of the advantages and limitations of the CHELS method. Examples of reconstructing acoustic radiation from separable and nonseparable surfaces are demonstrated.