边界元法循环平稳近场声全息理论研究

循环平稳声场是工程中经常遇到的一种特殊非平稳声场,声压信号受到调制作用,导致频谱出现边带现象,经典的近场声全息技术重建得到的声场无法反映声场的调制特性.在平面循环平稳近场声全息基础上,提出一种边界元法的循环平稳近场声全息技术,用二阶循环统计量理论代替传统的傅里叶分析,并以声压的循环谱密度取代其频谱及功率谱密度作为重建量,可用于循环平稳声场中具有复杂表面声源的辐射声场.由于循环谱密度对循环平稳信号具有解调功能,用该方法重建得到的循环谱密度能有效地反映调制和载波信号的信息.仿真分析与实验表明了本理论的有效性和精度能满足工程要求.     

单层传声器阵列信号空间重采样的声波分离方法

为了重构非自由声场中目标声源的声场响应,提出单层传声器阵列信号空间重采样的声波分离方法.以球面波函数为基函数,建立由系列球面波函数叠加表达的声场数学模型.基于近场声全息原理,利用单层传声器阵列面上空间重采样形成的两组声压测量信号,求解基函数系数,并重构出传声器阵列两侧声源各自的声场响应,实现声波分离.使用脉动球和振动球共同作用的非自由声场,检验了数学模型以及传声器信号信噪比、传声器阵列形状和面积、声源中心位置、频率等关键参数对声波分离精度的影响,并在全消声室内进行了实验验证.最后,对单层传声器阵列重采样的声波分离方法的实施给出了建议.     

适用于循环平稳声场的基于波叠加法的近场声全息技术

在原有的平面循环平稳近场声全息基础上,提出一种基于波叠加法的循环平稳近场声全息技术,可以对具有复杂表面的声源进行全息重建,重建的声源表面声压谱相关密度函数能反映出调制信号的信息.声源表面声压谱相关密度函数全息图形象地反映了调制信号在表面的强弱分布情况,可由此确定调制信号源的产生位置.仿真分析和实验验证表明,基于波叠加法的循环平稳近场声全息技术可以更准确地反映循环平稳声场的调制特性.该方法继承了波叠加法的优点,无需计算边界奇异积分,计算效率高、精度好. 关键词： 近场声全息 循环平稳信号 波叠加     

适用于循环平稳声场的基于波叠加法的近场声全息技术

在原有的平面循环平稳近场声全息基础上，提出一种基于波叠加法的循环平稳近场声全息技术，可以对具有复杂表面的声源进行全息重建，重建的声源表面声压谱相关密度函数能反映出调制信号的信息.声源表面声压谱相关密度函数全息图形象地反映了调制信号在表面的强弱分布情况，可由此确定调制信号源的产生位置.仿真分析和实验验证表明，基于波叠加法的循环平稳近场声全息技术可以更准确地反映循环平稳声场的调制特性.该方法继承了波叠加法的优点，无需计算边界奇异积分，计算效率高、精度好.     

循环平稳声场近场声全息理论与实验研究

提出一种用于分析循环平稳声场的近场声全息技术。此类声场信号的调制现象非常严重,频谱上存在着明显的边频带,由于无法有效地分离调制和载波信息,以往近场声全息技术的全息图会在边频带处出现虚假的能量。本技术用二阶循环统计量理论代替传统的傅里叶分析,并以声压的谱相关密度函数取代其频谱及功率谱密度做为重建物理量。由于谱相关密度函数可以对循环平稳信号进行解调处理,使得该技术的全息图上不会因为边频带的存在出现虚假能量。仿真分析及实验研究表明,本技术可以更准确地提取循环平稳声场的调制和载波信息。     

循环平稳声场的声源定位研究

旋转机械产生的辐射声场具有循环平稳特性,传统的平面近场声全息技术无法准确反映其调制特性,往往在边频带上出现虚假的能量的分布. 采用循环谱密度取代功率谱密度作为重建物理量,则可准确提取循环平稳声场的调制和载波信息. 考虑到循环谱密度的计算量以及特征提取的准确性,提出了循环谱密度组合切片分析法,并分析了加性白噪声对重建的影响. 仿真分析及实验结果表明,此方法有较强的噪声抑制能力,全息重建的结果可准确反映声源的位置. 关键词： 循环平稳声场 近场声全息 噪声源定位     

弹性力学的复变量无网格局部 Petrov-Galerkin 法

复变量移动最小二乘法构造形函数, 其优点是采用一维基函数建立二维问题的试函数, 使得试函数中所含的待定系数减少, 从而有效提高计算效率. 文章基于复变量移动最小二乘法和局部Petrov-Galerkin弱形式, 采用罚函数法施加边界条件, 推导相应的离散方程, 提出弹性力学的复变量无网格局部Petrov-Galerkin法. 数值算例验证了该方法的有效性.     

Navier-Stokes方程的最小二乘等几何方法

基于Hermite多项式的C¹型单元构造复杂,限制了最小二乘有限元法的应用.引入高阶光滑的非均匀有理B样条作为基函数简化C¹型单元构造,提出求解黏性不可压流动Navier-Stokes方程的最小二乘等几何方法.用Newton法或Picard法对Navier-Stokes方程线性化,用线性化偏微分方程的余量定义最小二乘泛函,导出最小二乘变分方程,用NURBS构造高阶光滑的有限维空间来近似速度场和压力场.计算表明:本文方法计算的二维顶盖驱动流数值解能准确描述流动状况,计算的二维通道内圆柱绕流全局质量损失由最小二乘有限元法的6%降为0.018%,该方法可用于Navier-Stokes方程的求解,并且具有较好的质量守恒性.     

采用球面波叠加法还原自由声场的方法

为解决非自由声场中近场声全息重建时,干扰声在目标声源表面产生的散射影响,提出一种基于球面波叠加法的自由场还原技术。该技术首先采用基于球面波叠加法的声场分离技术获得向内和向外传播的声场,然后以目标声源的表面导纳作为边界条件,实现目标声源辐射声和散射声的分离,从而获得等效于自由声场的测量条件。该技术为准确实现非自由声场中的噪声源识别创造了条件。文中首先详细描述了该技术的基本原理,并提出一种最优球面波展开项数选取方法,最后通过数值仿真说明了该技术的有效性。结果表明:在频率较低时,散射声影响较小,采用声场分离技术和自由场还原技术效果相当;但随着频率升高,散射声影响逐步增强,必须采用自由场还原技术才能准确获得目标声源辐射声。      

单层传声器阵列重建相干声场的近场声全息方法研究

针对传声器阵列两侧存在相干声源的非自由声场重建问题,提出基于球面谐波函数扩展近场声全息理论的相干声场重建方法。该方法在已知测量面两侧声源几何位置时,使用单层传声器阵列获取测量面处的声压分布,通过最小二乘法获得与目标声源和干扰噪声源响应对应的最优球波函数扩展项数和最优系数向量,结合测点位置的空间坐标进行声波分解,并分别重建出各声源在测量面上的声压分布。为了验证方法的有效性,分别给出了相干噪声源为球形声源和非球形声源的仿真验证,并在全消声室内对双扬声器产生的相干声场的重建进行了实验验证。结果表明:该方法对球形声源和非球形声源干扰下的声场重建都具有较好的效果,球形声源干扰下的重建精度更高。      

Reconstruction of vibroacoustic fields in half-space by using hybrid near-field acoustical holography

In this paper we examine the accuracy and efficiency of reconstructing the vibroacoustic quantities generated by a vibrating structure in half-space by using hybrid near-field acoustic holography (NAH) and modified Helmholtz equation least squares (HELS) formulations. In hybrid NAH, we combine modified HELS with an inverse boundary element method (IBEM) to reconstruct a vibroacoustic field. The main advantage of this approach is that the majority of the input data can be regenerated but not measured, thus the efficiency is greatly enhanced. In modified HELS, we expand the field acoustic pressure in terms of outgoing and incoming spherical waves and specify the corresponding expansion coefficients by solving a system of equations obtained by matching the assumed-form solution to the measured acoustic pressure. Here the system of equations is ill conditioned and Tikhonov regularization is implemented through singular value decomposition (SVD) and the generalized cross-validation (GCV) method. Numerical examples of a dilating and oscillating spheres and finite cylinder are demonstrated. Test results show that hybrid NAH can yield a more accurate reconstruction than does a modified HELS, but a modified HELS is more efficient than is hybrid NAH [Work supported by NSF].     

Hybrid near-field acoustic holography

Hybrid near-field acoustical holography (NAH) is developed for reconstructing acoustic radiation from an arbitrary object in a cost-effective manner. This hybrid NAH is derived from a modified Helmholtz equation least squares (HELS) formula that expands the acoustic pressure in terms of outgoing and incoming waves. The expansion coefficients are determined by solving an overdetermined linear system of equations obtained by matching the assumed-form solution to measured acoustic pressures through the least squares. Measurements are taken over a conformal surface around a source at close range so that the evanescent waves can be captured. Next, the modified HELS is utilized to regenerate as much acoustic pressures on the conformal surface as necessary and take them as input to the Helmholtz integral formulation implemented numerically by boundary element method (BEM). The acoustic pressures and normal velocities on the source surface are reconstructed by using a modified Tikhnov regularization (TR) with its regularization parameter determined by generalized cross validation (GCV) method. Results demonstrate that this hybrid NAH combines the advantages of HELS and inverse BEM. This is because a majority of the input data are regenerated but not measured, thus the efficiency of reconstruction is greatly enhanced. Meanwhile, the accuracy of reconstruction is ensured by the Helmholtz integral theory and modified TR together with GCV method, provided that HELS converges fast enough on the measurement surface. Numerical examples of reconstructing acoustic quantities on the surface of a simplified engine block are demonstrated. [Work supported by NSF.]     

Combined Helmholtz equation-least squares method for reconstructing acoustic radiation from arbitrarily shaped objects

A combined Helmholtz equation-least squares (CHELS) method is developed for reconstructing acoustic radiation from an arbitrary object. This method combines the advantages of both the HELS method and the Helmholtz integral theory based near-field acoustic holography (NAH). As such it allows for reconstruction of the acoustic field radiated from an arbitrary object with relatively few measurements, thus significantly enhancing the reconstruction efficiency. The first step in the CHELS method is to establish the HELS formulations based on a finite number of acoustic pressure measurements taken on or beyond a hypothetical spherical surface that encloses the object under consideration. Next enough field acoustic pressures are generated using the HELS formulations and taken as the input to the Helmholtz integral formulations implemented through the boundary element method (BEM). The acoustic pressure and normal component of the velocity at the discretized nodes on the surface are then determined by solving two matrix equations using singular value decomposition (SVD) and regularization techniques. Also presented are in-depth analyses of the advantages and limitations of the CHELS method. Examples of reconstructing acoustic radiation from separable and nonseparable surfaces are demonstrated.     

Partial field decomposition of multi-source cyclostationary sound field

The cyclostationary sound field is a kind of special non-stationary field which has obvious modulation phenomena. Conventional planar near-field acoustic holography (PNAH) technique cannot exactly reflect its modulation characteristics. If the cyclic spectral density (CSD) instead of the complex sound pressure is adopted as the reconstruction variable, the modulating wave and carrier wave components of the cyclostationary sound field can be extracted effectively. A new technique called cyclostationary PNAH utilizing the CSD is proposed in this paper. Based on this technique, the problem of partial field decomposition by singular value decomposition (SVD) of multiple incoherent cyclostationary sound sources is researched. The results of numerical simulation and experiments show that the CPNAH technique and SVD decomposition method are effective.     

On the choice of expansion functions in the Helmholtz equation least-squares method

This paper examines the performance of Helmholtz equation least-squares (HELS) method in reconstructing acoustic radiation from an arbitrary source by using three different expansions, namely, localized spherical waves (LSW), distributed spherical waves (DSW), and distributed point sources (DPS), under the same set of measurements. The reconstructed acoustic pressures are validated against the benchmark data measured at the same locations as reconstruction points for frequencies up to 3275 Hz. Reconstruction is obtained by using Tikhonov regularization or its modification with the regularization parameter selected by error-free parameter-choice methods. The impact of the number of measurement points on the resultant reconstruction accuracy under different expansion functions is investigated. Results demonstrate that DSW leads to a better-conditioned transfer matrix, yields more accurate reconstruction than both LSW and DPS, and is not affected as much by the change in measurement points. Also, it is possible to obtain optimal locations of the auxiliary sources for DSW, LSW, and DPS by taking an independent layer of measurements. Use of these auxiliary sources and an optimal combination of regularization and error-free parameter choice methods can yield a satisfactory reconstruction of acoustic quantities on the source surfaces as well as in the field in the most cost-effective manner.     

Visualization of acoustic radiation from a vibrating bowling ball.

This paper presents visualization of acoustic radiation from a vibrating bowling ball using the Helmholtz equation least squares (HELS) method. In conducting the experiments, the ball is excited by a vibration shaker using stationary random signals. The radiated acoustic pressures are measured using two microphones and taken as input to the HELS formulations. The reconstructed acoustic pressures on the bowling ball surface are compared with those measured at the same locations. Also shown are comparisons of the reconstructed and measured acoustic pressure spectra at various locations on the bowling ball surface. Results demonstrate that the accuracy of reconstruction based on measurements over a conformal surface is much higher than that over a finite planar surface. This is because the latter often extends beyond the near-field region, making the accuracy of measurements inconsistent. Nevertheless, satisfactory reconstruction of acoustic pressure fields over the entire bowling ball surface can still be obtained based on the measurements taken over a finite planar surface on one side of the source. In a similar manner, the normal component of the surface velocity is reconstructed. Once these acoustic quantities are determined, the time-averaged acoustic intensity is calculated. Also presented are the formulations for estimating a priori the numbers of expansion functions and measurements required by the HELS method and the guidelines for determining the reconstruction error and optimum measurement locations, given the overall dimensions of the source and the highest frequency of interest in reconstruction.     

循环平稳声场的声源定位研究

旋转机械产生的辐射声场具有循环平稳特性,传统的平面近场声全息技术无法准确反映其调制特性,往往在边频带上出现虚假的能量的分布.采用循环谱密度取代功率谱密度作为重建物理量,则可准确提取循环平稳声场的调制和载波信息.考虑到循环谱密度的计算量以及特征提取的准确性,提出了循环谱密度组合切片分析法,并分析了加性白噪声对重建的影响.仿真分析及实验结果表明,此方法有较强的噪声抑制能力,全息重建的结果可准确反映声源的位置.     

Reconstructing the vibro-acoustic quantities on a highly non-spherical surface using the Helmholtz equation least squares method

This paper presents helpful guidelines and strategies for reconstructing the vibro-acoustic quantities on a highly non-spherical surface by using the Helmholtz equation least squares (HELS). This study highlights that a computationally simple code based on the spherical wave functions can produce an accurate reconstruction of the acoustic pressure and normal surface velocity on planar surfaces. The key is to select the optimal origin of the coordinate system behind the planar surface, choose a target structural wavelength to be reconstructed, set an appropriate stand-off distance and microphone spacing, use a hybrid regularization scheme to determine the optimal number of the expansion functions, etc. The reconstructed vibro-acoustic quantities are validated rigorously via experiments by comparing the reconstructed normal surface velocity spectra and distributions with the benchmark data obtained by scanning a laser vibrometer over the plate surface. Results confirm that following the proposed guidelines and strategies can ensure the accuracy in reconstructing the normal surface velocity up to the target structural wavelength, and produce much more satisfactory results than a straight application of the original HELS formulations. Experiment validations on a baffled, square plate were conducted inside a fully anechoic chamber.     

利用声辐射模态重构任意目标的散射声场

水下目标散射声场的重构可以作为水下目标散射特性的研究基础。本文主要利用声辐射模态对水下目标进行散射声场重构研究。首先,在借助声传递矩阵给出的任意结构声辐射模态的流体域求解方法基础上,通过理论证明了目标的散射声压与声辐射模态具有函数关系。其次,借助声场分布模态的概念,同时考虑到声场分布模态病态及声压测量易受噪声污染,提出基于声辐射模态的正则化散射声场重构算法。仿真结果表明,波数越低,重构所需声辐射模态阶数越少,在较高波数时仅需总模态数的大约20%即可对声场进行重构。与基于边界元的声场重构算法相比,计算量减小了至少80%,且克服了赫姆霍兹积分方程最小二乘法仅对球壳结构的重构效果较好而不适用于长条形结构重构的缺陷。