Use of nonsingular boundary integral formulation for reducing errors due to near-field measurements in the boundary element method based near-field acoustic holography

The advantage of using the normal component of the particle velocity rather than the sound pressure in the hologram plane as the input of conventional spatial Fourier transform based near field acoustic holography ͑NAH͒ and also as the input of the statistically optimized variant of NAH has recently been demonstrated. This paper examines whether there might be a similar advantage in using the particle velocity as the input of NAH based on the equivalent source method ͑ESM͒. Error sensitivity considerations indicate that ESM-based NAH is less sensitive to measurement errors when it is based on particle velocity input data than when it is based on measurements of sound pressure data, and this is confirmed by a simulation study and by experimental results. A method that combines pressure-and particle velocity-based reconstructions in order to distinguish between contributions to the sound field generated by sources on the two sides of the hologram plane is also examined.

Section: Introductionmentioning

confidence: 99%

Near field acoustic holography based on the equivalent source method and pressure-velocity transducers

Zhang

Jacobsen

et al. 2009

“…A modified boundary element formulation based on Helmholtz integral equation has been reported to overcome such problems. 30,31 In our case the minimum distance between field points and source surface for BEM calculations is set to one-half an element length. Expressed in matrix-vector form, the discretized problem becomes…”

Section: A Formation Of the Inverse Bem Transfer Matrixmentioning

confidence: 99%

Sound source reconstruction using inverse boundary element calculations

Schuhmacher¹,

Hald²,

Rasmussen

et al. 2003

130

Whereas standard boundary element calculations focus on the forward problem of computing the radiated acoustic field from a vibrating structure, the aim in this work is to reverse the process, i.e., to determine vibration from acoustic field data. This inverse problem is brought on a form suited for solution by means of an inverse boundary element method. Since the numerical treatment of the inverse source reconstruction results in a discrete ill-posed problem, regularization is imposed to avoid unstable solutions dominated by errors. In the present work the emphasis is on Tikhonov regularization and parameter-choice methods not requiring an error-norm estimate for choosing the right amount of regularization. Several parameter-choice strategies have been presented lately, but it still remains to be seen how well these can handle industrial applications with real measurement data. In the present work it is demonstrated that the L-curve criterion is robust with respect to the errors in a real measurement situation. In particular, it is shown that the L-curve criterion is superior to the more conventional generalized cross-validation ͑GCV͒ approach for the present tire noise studies.

“…In addition to the classical NAH technique based on spatial discrete Fourier transforms, 1-3 many alternative methods have been developed in the past years, e.g., the inverse boundary element method, [4][5][6] the statistically optimized method, 7,8 the Helmholtz equation least-squares method, 9,10 and the equivalent source method. [11][12][13] Among all these techniques NAH based on spatial Fourier transforms is the easiest to implement and also the most computationally efficient because of the use of the fast Fourier transform algorithm.…”

Section: Introductionmentioning

confidence: 99%

Patch near field acoustic holography based on particle velocity measurements

Zhang

Jacobsen²,

Bi³

et al. 2009

Patch near field acoustic holography ͑PNAH͒ based on sound pressure measurements makes it possible to reconstruct the source field near a source by measuring the sound pressure at positions on a surface that is comparable in size to the source region of concern. Particle velocity is an alternative input quantity for NAH, and the advantage of using the normal component of the particle velocity rather than the sound pressure as the input of conventional spatial Fourier transform based NAH and as the input of the statistically optimized variant of NAH has recently been demonstrated. This paper examines the use of particle velocity as the input of PNAH. Because the particle velocity decays faster toward the edges of the measurement aperture than the pressure does and because the wave number ratio that enters into the inverse propagator from pressure to velocity amplifies high spatial frequencies, PNAH based on particle velocity measurements can give better results than the pressure-based PNAH with a reduced number of iterations. A simulation study, as well as an experiment carried out with a pressure-velocity sound intensity probe, demonstrates these findings.