Huancai Lu

Reconstruction of transient acoustic radiation from a sphere

Transient near-field acoustical holography (NAH) formulation is derived from the Helmholtz equation least squares (HELS) method to reconstruct acoustic radiation from a spherical surface subject to transient excitations in a free field. To facilitate derivations of temporal solutions, we make use of the Laplace transform and expansion in terms of the spherical Hankel functions and spherical harmonics, with their coefficients settled by solving a system of equations obtained by matching an assumed-form solution to the measured acoustic pressure. To derive a general form of solution for a temporal kernel, we replace the spherical Hankel functions and their derivatives by polynomials, recast infinite integrals in the inverse Laplace transform as contour integrals in a complex s-plane, and evaluate it via the residue theorem. The transient acoustic quantities anywhere including the source surface are then obtained by convoluting the temporal kernels with respect to the measured acoustic pressure. Numerical examples of reconstructing transient acoustic fields from explosively expanding, impulsively accelerating, and partially accelerating spheres, and that from a sphere subject to an arbitrarily time-dependent excitation are depicted. To illustrate the effectiveness of HELS-based transient NAH formulations, all input data are collected along an arbitrarily selected line segment and used to reconstruct transient acoustic quantities everywhere.

Study on suppression of background noise using near-field acoustic holography with single layer microphone array

A study was carried out to suppress background noise in non-free field generated by target sound source and noise source based on near-field acoustic holography with single layer microphone array. The acoustic pressures in non-free field are expressed as superposition of incoming and outgoing spherical wave functions. The coefficients of those spherical wave functions are determined based on the principle of Helmholtz Equation Least-Squares (HELS) method. The sound field was then separated once both the coefficients of incoming and outgoing spherical wave functions obtained. The error incurred in the process of inverse calculation was minimized via least-squares method as utilized in HELS. Numerical simulations were conducted to validate the approach, in which the non-free field was generated by different sound sources with analytical solutions, such as dilating sphere, oscillating sphere, and vibrating simply-supported thin plate. Those sound sources perform as target source and background noise source a...

RECONSTRUCTING ACOUSTIC RADIATION PATTERNS OF AN ELONGATED, BAFFLED PLATE AT HIGH FREQUENCIES WITH THE NYQUIST SPATIAL SAMPLING RATE SIGNIFICANTLY RELAXED

Traditionally, high-accuracy full-sphere polar measurements require dense sampling of the sound field at very-fine angular increments, particularly at high frequencies. The proposed HELS (Helmholtz equation least squares) method allows this restriction to be relaxed significantly. Using this method, far fewer sampling points are needed for full and accurate reconstruction of the radiated sound field. Depending on the required accuracy, sound fields can be reconstructed using only 10% to 20% of the number of sampling points required by conventional techniques. The HELS method allows accurate reconstruction even when the Nyquist spatial sampling rate is violated in certain directions. This paper examines the convergence of HELS solutions via theory and simulation for reconstruction of the acoustic radiation patterns generated by a rectangular plate mounted on an infinite rigid flat baffle. In particular, the impact of the number of expansion terms and that of measurement points as well as errors imbedded in the input data on the resultant accuracy of reconstruction is analyzed.

On vibroacoustic modal analysis of arbitrarily shaped vibrating structures.

Vibroacoustic modal analysis based on Helmholtz least squares method (HELS) is presented in this paper to explore the inherent dynamic characteristics and correlation of structural vibration and sound radiation of arbitrarily shaped vibrating structures. A series of mutually orthogonal vibroacoustic components is established by decomposing the normal velocity and normal acoustic intensity, which are reconstructed on source surface using HELS, in an orthogonal space through singular value decomposition (SVD). By further analyzing the vibration efficiency and radiation efficiency, the contribution of each of individual modal components to the resultant structural vibration and sound radiation can then be quantified. Therefore one is allowed to identify the vibroacoustic modal components that are most responsible for resultant structural vibration and sound radiation. The test object is a clamped and baffled thin rectangular steel plate, which was excited by a shaker and tested in a semianechoic chamber. The...

Reconstruction of Normal Surface Velocities of a Simply-Supported Baffled Plate Using Helmholtz Equation Least Square Method

The normal surface velocities of highly a non-spherical object are reconstructed based on the measurement of field acoustic pressures using Helmholtz equation least-squares (HELS) method. The objectives of this study are to numerically examine the feasibility and accuracy of reconstruction and the impacts of various parameters involved in reconstruction of vibro-acoustic responses using HELS. The vibrating object is a simply-supported and baffled thin plate. The reasons for selecting this object are that plate is the most challenging source geometry for HELS method, and it represents a class of structures that cannot be exactly described by the spherical Hankel functions and spherical harmonics, which are primarily embedded in the HELS formulation, yet the analytic solutions to vibro-acoustic responses of a baffled plate are readily available so the accuracy of reconstruction can be checked in detail. The Rayleigh integral is used to generate the input field acoustic pressures for reconstruction. The Euler’s equation is employed to establish the system model of reconstruction of vector velocities. Regularization associated with the truncated singular value decomposition is utilized to compromise the resultant accuracy and stability of the vector velocity reconstruction. The reconstructed normal surface velocities are validated against the benchmark values, and the out-of-plane vibration patterns at several natural frequencies are compared with the natural modes of a simply-supported plate. The impacts of various parameters such as the measurement points, measurement distance, the location of origin of coordinate system, microphone spacing, and ratio of measurement aperture size to the area of source surface of reconstruction on the resultant accuracy of reconstruction are examined.Copyright

High‐frequency reconstruction of radiation patterns from a rectangular baffled plate using the Helmholtz equation least squares method

The Audio Engineering Society (AES) Standards require that full‐sphere polar measurements of a sound field be taken at a very fine angular increment (1 deg) to ensure the accuracy in describing high‐frequency radiation patterns of a source. This super fine angular resolution coupled with a far‐field measurement requirement leads to an excessive number of measurements. For example, at 1 m and 1 degree angular resolution we would need more than 64 000 measurement points. To alleviate this difficulty, the HELS (Helmholtz Equation Least Squares)‐based near‐field acoustical holography is used to reconstruct the radiation patterns. It is shown that HELS can provide accurate reconstruction of radiation patterns for dimensionless frequencies up to ka=25 based on the sound field sampled on a spherical surface at a rate lower than that required by AES Standards. HELS allows for accurate reconstruction even for sample spacing that violates the Nyquist spatial sampling rate in certain directions. In this paper, the convergence of HELS solutions is examined by comparing reconstructed radiation patterns with the analytic solution for a rectangular baffled plate. In particular, the impacts of the number of expansion terms in HELS and measurement points, and that of errors imbedded in the input data on the accuracy of reconstruction are analyzed.

Reconstruction of vibro‐acoustic response of a plate using Helmholtz equation least‐squares method

A numerical investigation of reconstructing the vibro‐acoustic responses of an arbitrary structure subject to vibration excitations based on the Helmholtz equation least‐squares (HELS) method is presented. It is emphasized that in many engineering applications, the exact solution to a general vibrating structure does not exist, and the HELS method is one way of getting approximate solutions in a cost‐effective manner. In this study, the test object is a simply supported, unbaffled thin plate. The reason for selecting this simply supported plate is that the analytic solutions to the plate vibrations are readily available. The field acoustic pressures generated by the Rayleigh integral are taken as input to HELS algorithms to reconstruct the normal velocity and normal acoustic intensity on the plate surface using Tikhonov regularization associated with generalized cross‐validation methods. The reconstructed normal surface velocities are compared with the benchmark values, and the out‐of‐plane vibration patt...

Reconstructing transient acoustic field resulting from an explosion

Generalized Helmholtz equation least squares (HELS) formulations for reconstructing transient acoustic radiation from an arbitrary object subject to arbitrarily time‐dependent excitations are developed. Laplace transform is employed to build a transfer matrix for a multi‐input multi‐output system and reconstructed signals are obtained using convolution with respect to the input data in the time domain directly. Stability of solutions is realized by controlling the pole‐residue locations in the Laplace domain. To facilitate calculations of the poles and residues, ztransform is utilized. To validate this general transient HELS formulation, the reconstructed pressure histories are compared with those measured by pressure sensors at the same locations. Space‐time tomography resulting from different charges is produced, and the acoustic pressure distribution over the entire time record is reconstructed. It is interesting to notice that this transient HELS formulation enables one to trace time histories of blas...

Helmholtz equation least squares method for transient nearfield acoustic holography

The generalized Helmholtz equation least squares (HELS) formulations for reconstructing transient acoustic radiation from an arbitrary object subject to an arbitrary time‐dependent excitation are derived. To facilitate the derivations, the Laplace transform is employed and the vibro‐acoustic quantities on the source surface are solved explicitly in terms of the acoustic pressures measured on a conformal surface around the source at close range multiplied by transfer functions in the Laplace domain first. The vibro‐acoustic responses in the time domain can then be expressed as convolution integrals of the measured acoustic pressure signals over temporal kernels. Replacing the spherical Hankel functions in the transfer functions with polynomial expressions, we can recast the infinite integrals in the inverse Laplace transform as contour integrals and evaluate the temporal kernels by using residue theorem. Once the temporal kernels are determined, the vibro‐acoustic quantities anywhere in the field, includin...

Prediction of acoustic radiation via 3D particle velocity measurements

It has been shown [Wu and Hu, J. Acoust. Soc. Am. 103, 1763–1774 (1998)] that one can use an explicit integral formulation to predict acoustic radiation from a vibrating object based on a particle velocity distribution over a hypothetical surface enclosing this object. The advantages of this integral formulation are that solutions thus obtained are unique and the efficiency of numerical computations is high. The challenge is how to acquire 3D particle velocities when measurements are taking place in the air, in which seeding particles are hard to control and the signal to noise ratio is low. Here we use laser Doppler Anemometry (LDA) to accomplish this task. Two LDA probes are utilized to measure two components of the particle velocities simultaneously, and the third component is obtained by rotating one probe 90° and measuring again. A traverse system is adopted to sweep the LDA probes over a measurement plane to enhance efficiency. Once particle velocities are specified on all nodes of the enclosing mea...