Yong-Bin Zhang

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

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 (NAH) 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 (ESM). 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.

Transient nearfield acoustic holography based on an interpolated time-domain equivalent source method

Transient nearfield acoustic holography based on an interpolated time-domain equivalent source method (ESM) is proposed to reconstruct transient acoustic fields directly in the time domain. Since the equivalent source strengths solved by the traditional time-domain ESM formulation cannot be used to reconstruct the pressure on the source surface directly, an interpolation function is introduced to develop an interpolated time-domain ESM formulation which permits one to deduce an iterative reconstruction process. As the reconstruction process is ill-conditioned and especially there exists a cumulative effect of errors, the Tikhonov regularization is used to stabilize the process. Numerical examples of reconstructing transient acoustic fields from a baffled planar piston, an impulsively accelerating sphere and a cube box, respectively, demonstrate that the proposed method not only can effectively reconstruct transient acoustic fields in the time domain, but also can visualize acoustic fields in the space domain. And, in the first numerical example, the cumulative effect of errors and the validity of using the Tikhonov regularization to suppress the errors are described.

Sound source identification and sound radiation modeling in a moving medium using the time-domain equivalent source method

Planar near-field acoustic holography has been successfully extended to reconstruct the sound field in a moving medium, however, the reconstructed field still contains the convection effect that might lead to the wrong identification of sound sources. In order to accurately identify sound sources in a moving medium, a time-domain equivalent source method is developed. In the method, the real source is replaced by a series of time-domain equivalent sources whose strengths are solved iteratively by utilizing the measured pressure and the known convective time-domain Greens function, and time averaging is used to reduce the instability in the iterative solving process. Since these solved equivalent source strengths are independent of the convection effect, they can be used not only to identify sound sources but also to model sound radiations in both moving and static media. Numerical simulations are performed to investigate the influence of noise on the solved equivalent source strengths and the effect of time averaging on reducing the instability, and to demonstrate the advantages of the proposed method on the source identification and sound radiation modeling.

Patch near field acoustic holography based on particle velocity measurements

Patch near field acoustic holography (PNAH) 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.

Sound field reconstruction using compressed modal equivalent point source method

The accuracy, resolution, and economic cost of near-field acoustic holography (NAH) are highly dependent on the number of spatial sampling points. Generally, higher accuracy and resolution require more spatial sampling points, which may increase the workload of measurement or the hardware cost. Compressive sensing (CS) is able to solve the underdetermined problems by utilizing the sparsity of signals, and thus it can be applied to NAH to reduce the number of spatial sampling points but at the same time provide a high-resolution reconstruction image. Based on the CS theory, this paper proposes a compressed modal equivalent point source method (CMESM). In the method, a sparse basis that is obtained from the eigen-decomposition of the power resistance matrix is introduced to compress the equivalent point source strengths, and the ℓ1-norm minimization is used to promote sparse solutions. Both numerical simulation and experimental results demonstrate the validity of the proposed CMESM and show its advantage over the existing methods when the number of spatial sampling points is reduced.

Acoustic design sensitivity analysis based on wave superposition approach.

Research on the acoustic design sensitivity is significant for its ability to provide the optimized orientation for low noise design of radiating structures. In this paper, the wave superposition approach (WSA) is employed to calculate acoustic design sensitivity. The sensitivity formulations based on the wave superposition are presented in a direct differentiation way, by which the sensitivity of acoustic quantities with respect to the design variables such as structural parameters or physical properties can be obtained. This method is suitable for both shape and sizing sensitivity analysis of arbitrary shaped sources. Compared with the conventional direct differentiation boundary element method, the proposed method has improved accuracy and speed of computation, and has no inherent problem of singular integration which will make numerical processing more complicated. Numerical experiments are demonstrated to show the validity and feasibility of the proposed method.

Stability analysis of inverse time domain boundary element method for near-field acoustic holography

Stability of the inverse time domain boundary element method (ITBEM) for near-field acoustic holography is investigated. An eigenvalue system is built by reformulating the ITBEM to an iterative format. Through the analysis of the eigenvalue system, a stabilization criterion is derived. Then the stabilization criterion is utilized to reveal the stabilization mechanism of the TSVD method which plays an important role in the ITBEM. Furthermore, a method for properly choosing the ratio of truncated singular values to ensure the stability is provided. Although stability can be managed by using the TSVD method, the accuracy of the results cannot always be guaranteed. To overwhelm this difficulty, an averaging technique is further introduced, and its stabilization mechanism is investigated by incorporating it into the ITBEM formulations. Numerical simulations are carried out to validate the stabilization criterion, and the stabilization mechanisms of TSVD and averaging are shown specifically with extensive eigenvalue analyses.

Suppressing the onset of instabilities in the time-domain equivalent source method using a multistep approach

Numerical instability is an important issue that should be addressed in the time-domain equivalent source method (TESM). This study proposes a multistep method to stabilize TESM when using the measured acoustic pressure data to optimize equivalent source strengths. Unlike the conventional single-step method that solves each time step in the time-marching process of TESM, the proposed method performs a one-time solution for several time steps. The multistep solution can potentially reduce the accumulation rate of error, and improves filtering effects by changing the structure of the matrix that needs to be inverted when the truncated singular value decomposition or Tikhonov regularization is used in the time-marching process. Numerical simulations with three examples demonstrate the effectiveness of the multistep method in improving the stability of solutions compared with the single-step method. Effects of the number of merged time steps on the solutions are also discussed to guide the selection process. Finally, the sensitivity of the multistep method to numerical parameters is investigated to demonstrate its consistency under different configurations of numerical parameters.