The Theoretical And Experimental Study On Near-Field Acoustic Holography For Arbitrary Sources In The Cyclostationary Sound Field

Identification of the noise source is the first step of the noise control. Visualizing the acoustic field will offer more information for the location of the source and its physical mechanism. Among the different methods, nearfield acoustic holography (NAH) is one important tool for analyzing sound field due to its high resolution. The high resolution is obtained from the closely measuring that the sound field information is reserved ultimately in the sampling data including the evanescent wave. NAH method is developed to be suitable for the arbitrarily-shaped source from the simple geometries such as plane, cylinder and sphere. The sound field including the pressure, normal velocity and sound power is recon- structed after building the spatial transformation between the source and the hologram. NAH method is widely applied to the industry such as NVH analysis in the auto-mobile industry, locating noise sources, structure modal analysis. The progress of NAH methods attracts researchers'attention in the recent three decades. The most research on the NAH focused on the stationary sound field and the non-stationary sound field is involved less.In the industry, there is a kind of non-stationary signal named cyclostationary signal whose cyclic statistics is with characteristics to decompose the carrier wave and modulation wave solely. The cyclostationary sound field excited by some machines is often observed in the industry, such as the internal combustion engines and rolling-bearings, especially when they run under ill conditions. The cyclic statistics theory has been utilized to detect machinery faults, and the main parameters are the second-order statistics which are researched deeply and understood relatively clearly. The periodical and modulation components can be decomposed by cyclostationary spectrum density (CSD) by nonlinear transform and cyclic factor. According to the cyclostatinary theories, the 3-dimensional graphics of the cyclostationary signal with the variance of the cyclic frequency and frequency, or its slice at the proper cyclic frequency, will supply the information of the modulation wave and carrier wave. The common spectrum analysis can't realize the decomposition.Since the spectrum or PSD distribution of sound pressure displayed in the original NAH hologram can't show the statistical information of sound energy varying with time, the conventional NAH is not suitable for cyclostationary sound field. The method named cyclostationary nearfield acoustic holography (CYNAN) is developed to analyze the cyclostationary sound field whose hologram shows the energy distribution of the modulation wave components at the appropriate cyclic frequency. The reconstruction of the cyclostation- ary sound by CYNAH will help understand the physical mechanism and sound field characteristics. Because the objects are limited to be planar or close to planar that is impossible for most cases in the industry, it is necessary to modify the planar CYNAH to adapt to the arbitrarily-shaped objects by combining with other numerical methods.There are three kinds of CYNAH methods are presented in this dissertation, combining with boundary element method (BEM), wave superposition algorithm (WSA) and Helmholtz equation least square (HELS), respectively. The second-order cyclic statistics is used as the variables for reconstruction of sound field in the place of the velocity or pressure in the common NAH. All of three methods can be used to analyze the sources with complicated profiles that are often encountered in practice. In the dissertation, their theories are derived and factors affecting the reconstruction accuracy are analyzed, the experiments are also described in details. The project in present dissertation is aided financially by National Natural Science Foundation of China (granted No. 10674096).The main contents of dissertation are as follows:(1) The progress of NAH is reviewed firstly. The NAH methods are described in classes due to their combined numerical methods. The techniques of hologram data sampling, reconstructed algorithm and engineering application are summarized. The non-stationary sound field is less concerned in the former research. CYNAH methods suitable for arbitrarily-shaped objects are advised on the basis of the planar CYNAH for both the academic and engineering viewpoints.(2) CYNAH method based on BEM is derived where the second-order cyclic statistics take the place of velocity and pressure as the variance. Comparing with the common BEM- based NAH, the reconstruction of the cyclostationary sound field by BEM-based CYNAH shows the velocity or pressure CSD distribution which will help to understand the characteristics of the sound field. The factors affecting the accuracy are analyzed by the numerical simulations.(3) WSA-based CYNAH is employed to reconstruct the cyclostationary sound field, which is assumed to be generated by a series of cyclostationary virtual sources inside of the objects. After the cross-CSDs between the virtual sources and the rigid reference are determined by an inverse procedure, the CSD at anywhere of the whole sound field can be calculated. Numerical simulations supply some guides for the application of WSA- based CYNAH to the objects such as spatial ratio, regularization, background noise, etc.(4) The third CYNAH method suitable for the objects with complicated profiles is related with the HELS method. The coefficients of every basis function are supposed to vary cyclostatioinarily with time. The optimal number of the basis functions and relative cross CSD vector between coefficients and rigid reference are obtained by least square method. Then the reconstruction of the CSD can be realized. Some numerical simulations are also done for understanding the HELS-based CYNAH.(5) The research on the comparison of these three CYNAH methods above whose objects are arbitrarily-shaped is carried out. The advantages and disadvantages of every method are concluded which are beneficial for researchers to choose the right one under different conditions.(6) The validities of the methods above are illustrated by experiments finished in an semi-anechoic chamber. The experiment objects are a cubic sound box and a dodecahedron loudspeaker. The objects are driven by the cyclostationary signal. A rigid reference microphone is set around the objects at a close distance and the signals on the hologram are scanning-sampled by a scanning equipment. All the three methods are applied to analyze the same objects and the comparison is done.