Formulations for acoustic inverse analysis based on the indirect boundary element method.

Abstract

New formulations for acoustic inverse analysis are developed based on the indirect boundary element method (IBEM). The numerical algorithms and extensive validation examples are presented for two different kinds of inverse analyses: acoustic field reconstruction and acoustic source reconstruction. IBEM is utilized to compute transfer functions between velocity boundary conditions on the surface of the acoustic source and the field points where the acoustic pressure data is prescribed. The presence of the obstacles adjacent to the vibrating source in the source reconstruction process is accounted for. Singular Value Decomposition (SVD) algorithm is employed for solving the resulting system of equations. The original acoustic field is considered to be prescribed at a limited number of field points. Thus, algorithms are developed to identify the optimal locations of a prescribed number of field points from a candidate set based on achieving the highest possible orthogonality for the basis of the range of the transformation matrix. The treatment of irregular frequencies encountered during the acoustic inverse analysis is also incorporated in the IBEM formulation. A new numerical formulation based on IBEM is developed for computing the sensitivity of the acoustic pressure with respect to the unequal acoustic impedance boundary conditions. The unequal acoustic impedance boundary conditions represent acoustic absorptive properties associated with each side of the surface of boundary element model and in general they are different from each other. Analytical solutions for the acoustic impedance sensitivity analysis considering plane waves traveling inside a rectangular duct are derived and utilized to validate the numerical results. A numerical vehicle pass-by noise simulation process is developed based on the acoustic field reconstruction formulation. Each major noise source is represented by a generic source in the computations. The generic sources for the main contributors of the pass-by noise are combined with a vehicle model for a complete pass-by noise simulation. The developed numerical techniques are validated through comparison between numerical results and test data for both component level and system level analyses.