Strategic improvements to the inverse boundary element method in acoustics

A noise source identification technique using the inverse boundary element method (BEM) has been developed in recent years. The Inverse BEM results in an underdetermined and ill-posed problem and, therefore, had been considered to be impractical and can produce an erroneous surface vibration reconstruction. This study identifies several major problems with the inverse BEM. An approach to determine the field point configuration necessary for an accurate reconstruction was developed. The field point grid has to satisfy the uniqueness, completeness, and field point density criteria. The uniqueness criterion is based on the condition number of the acoustics transfer matrix (ATM) and serves as a bound to the reconstruction error. The completeness criterion measures how complete the source information is being captured by the field points. The field point density criterion provides information on the minimum reconstruction rank required. This new approach is shown to work better than the current Tickonov regularization using the L-curve, which can result in a low reconstruction rank, as an effort to regularize the ill-conditioning nature of the ATM. This newly developed approach insures sufficient reconstruction rank while maintaining a well-conditioned transfer matrix. As examples, a simple vibrating plate and a more complicated engine cover reconstruction are presented.;The inverse BEM is computationally expensive, particularly for large models. An alternative approach to calculate the acoustic transfer matrix using the Rayleigh integral or the high frequency boundary element approximation was developed. The field reconstruction is shown to have a comparable accuracy to the inverse BEM.;This study also evaluates the use of the inverse BEM for complex sources where the acoustic particle velocity is reconstructed on an imaginary surface, such as the discharge plane of a fan or the opening of a duct. Potential application of this approach includes the numerical prediction of flow generated noise. It is shown that the measurement surface does not need to be conformal to the reconstruction surface and, therefore, for cases involving flow, the measurement of sound pressure can be done outside of the flow field. A numerical prediction of a classic vortex shedding noise problem is presented as an illustration.;Keywords. inverse boundary element method, acoustic holography, noise source identification, BEM, acoustic source reconstruction...