Theoretical And Experimental Study On Transient Sound Field Holographic Reconstruction Based On The Time-domain Equivalent Source Method

A lot of transient phenomena exist in the practical engineering, such as metal riveting, vehicles or compressors start and stop, friction squeal, etc., which usually produce transient radiation noise. Such transient noise not only directly affects people’s subjective evaluation of product noise and comfort experience, but also can cause hearing impairment to the on-site workers. For controlling noise, a variety of sound source localization techniques and characteristic analysis approaches have been developed. Thereinto, the near-field acoustical holography(NAH) is provided with the most precise positioning capability, the relatively high imaging resolution and the excellent reconstruction accuracy. The NAH for the steady sound sources is mainly performed in the frequency domain and has been successfully applied in many fields through nearly thirty-year development.Visualized reconstruction for the transient sound source contributes to understanding the working mechanisms and changing process of the transient sound field, thus providing an effective analysis procedure for controlling the transient noise radiation and reducing the vibration impact. Different from the steady-state sound field, the frequency characteristics of the transient sound field are time-varying and even have a complicated randomness. Therefore, the acoustic characteristics at a certain frequency are unable to describe the whole acoustic field. Since the direct application of the frequency-domain NAH to the transient sound field fails to meet the reconstruction requirements, researchers have developed the time-domain NAH methods. By conducting the reconstruction through all time, the time-domain NAH is used to obtain the time-changing rule of the sound field to effectively predict or reconstruct the transient sound field.As one of the time-domain NAH methods, the time-domain equivalent source method(TDESM) is adaptable to the sound source with arbitrary profile, and its computation is the most simple and efficient. As such, the TDESM has attracted more and more attention recently. Nevertheless, the study and application of TDESM is currently at the initial stage. There are still many problems which require more in-depth studies and analysis, and the method itself also has some limitations. Such issues can limit the practical application and extension of the TDESM. This work explores the deficiencies of the present TDESM, whereby the corresponding solutions are proposed and the research is performed on the transient sound field holographic reconstruction based on the TDESM. This dissertation investigates the influence of some important factors on the sound field reconstruction based on the interpolated TDESM(ITDESM). Moreover, a hybrid approach to reconstruct transient sound field by combining the free-field time reversal method(TRM) and ITDESM, an extended ITDESM based on the image theory, and two half-space ITDESMs based on the transient half-space Green’s functions are proposed in the dissertation, respectively. The study aims to reduce the cost of the measurement and computation involved in the transient sound field reconstruction, to improve the reconstruction accuracy and imaging resolution, to expand the applications of the TDESM and to improve the applicability of TDESM to the practical engineering problems, thus achieving the further perfection and development of the transient sound field reconstruction and visualization technique. The work is supported by the National Natural Science Foundation of China(No. 11104182), and follows the research route of combining the theoretical modeling, numerical simulations and experimental verifications together. The main contents of the dissertation are summarized as follows:(1) The significance of the subject is first expounded. The development and state of art of the frequency-domain NAH and the time-domain NAH are then introduced, and the applicability and limitations of each method are clearly stated. Thus, the TDESM is determined to be the most adaptable, simple but effective method for rebuilding the transient sound field holographically. By analyzing the advantages and limitations of the present TDESM, the research contents of the dissertation are established.(2) With the TDESM as a starting point, the reason for that the TDESM cannot realize the transient sound field reconstruction is pointed out, and the reconstruction formulation based on the ITDESM are derived. The validity of the ITDESM are demonstrated by the numerical simulations, and several factors influencing the reconstruction results are analyzed, e.g., the hologram position, the equivalent source plane, the grid spacing and the measurement error. According to the simulation results, some reasonable suggestions on how to choose the related parameters are given, which can guide the practical application of the ITDESM. The feasibility of ITDESM in reconstructing the transient sound field is experimentally verified by an impacted plate.(3) A hybrid approach is developed to reconstruct the transient sound field radiated from the two-dimensional sources with unknown locations and sizes, by combing the free-field TRM and the ITDESM. This approach allows placing the equivalent sources only near the real sound sources to save the microphone number while guaranteeing a high imaging resolution of the sound field. The hybrid approach provides a simple, effective way to collocate the equivalent sources for the ITDESM. A dual-planar-piston model is studied by numerical simulation for feasibility demonstration. Experimental verification using two baffled loudspeakers shows that higher reconstruction accuracy and resolution can be achieved by using the developed hybrid scheme than the original ITDESM with relatively the same number of sampling channels.(4) An extended ITDESM based on the image theory is proposed to reconstruct the semi-free transient sound field directly in the time domain. The method places the equivalent sources in the vicinity of both the real sound sources and their images. The derived reconstruction formulation expresses the acoustic contribution from each virtual equivalent source with the strengths of the corresponding real equivalent source, thereby saving the computational cost. Numerical simulations demonstrate the superiority of the extended ITDESM relative to the original ITDESM. The applicability of proposed method to different reflection conditions and its robustness to the measurement error are also examined. A loudspeaker conducted on the ground and an acoustic material is, respectively, used to further validate the proposed extended ITDESM.(5) Two half-space ITDESMs are proposed to model the transient sound propagation over a mass-like plane and a pure absorbing plane, respectively. By replacing the free-space transient Green’s function in the original ITDESM with two half-space transient Green’s functions in closed form, the sound reflection effect can be fully considered. Numerical simulations demonstrate the effectiveness of both the half-space ITDESMs. It is proved that modeling by the half-space ITDESM for a mass-like plane is more accurate than that resulting from the rigid plane model and the free-field model. In addition, the half-space ITDESM for a pure absorbing plane has good adaptability to the background noise and the microphone positioning error. The feasibility and validity of both the half-space ITDESMs are experimentally verified via an impacted steel plate.