Reconstruction of Transient Vibro-acoustic Fields Using BEM-based NAH and Fourier Analysis

Abstract

This study is on the identification of extended sources by reconstructing the transient vibro-acoustic fields using the nearfield acoustical holography (NAH) based on the boundary element method (BEM) and Fourier analysis. The research is motivated by two principal reasons. First, the transient analysis is a very important topic in noise control and acoustic design. There are many situations where transient sound source is encountered in engineering problems as most of vibrating structures are subject to impulsive or time-varying excitations. Transient wave field also contains a lot of information that can be used to investigate the characteristic of the propagation medium. The fact that the BEM-based NAH is a robust, well defined frequency domain method for reconstructing an arbitrarily shaped sound source becomes the second reason. Naturally, it is desirable to extend the application not only to the time harmonic cases, but also to the transient problems. A procedure of implementing the BEM-based NAH efficiently for transient problems is proposed, in which spectral analysis using short time Fourier transform is employed to link data representation in time domain and the inverse calculation in frequency domain. Although the concept looks quiet straightforward, a number of difficulties have to be resolved in the realization. Calculation error can arise from the aliasing in time and frequency, spectral leakage, and Gibbs phenomenon. It is because the measured input data and the calculated transfer function are only given in a finite discrete range. Besides, the ill-posedness of inverse problem makes the system very sensitive to the noise. These difficulties would lead to a very poor reconstruction of source parameters. Therefore, an appropriate procedure in the signal processing and regularization techniques should be applied for obtaining a precise end result. In this work, the problems of spectral leakage, aliasing in frequency and in time were overcome by...