An Innovation In Real-Time Acoustic Holography

这个GOALI项目是与福特汽车公司高级工程中心合作进行的。本研究的目标有两个：(1)开发一种创新的方法来准确而经济地重建声压场；(2)将这种方法扩展到产生实时声全息，使人们能够可视化瞬时声压分布及其随时间变化的演变。该方法的新颖之处在于，声压是通过声学模态的扩展或亥姆霍兹方程的一组特解来重建的。与这些声学模型相关的系数是通过要求假设形式解满足测点的压力边界条件来确定的。采用最小二乘法对误差进行了最小化处理。该方法的意义在于得到的解是唯一的，数值计算效率高。这是因为所采用的声学模式代表了满足亥姆霍兹方程的特征函数的完整集合。声学模态的数量决定了测量点的数量，当考虑到源几何形状时，选择合适的坐标系时，测量点的数量很小。因此，数值计算是快速和有效的。此外，声压被写为声模态的显式形式。因此，时域信号可以通过直接傅里叶反变换得到。这使得实时声全息术的产生成为可能。该调查将为诊断结构和空气噪声源提供一个有效的工具。使用该工具，设计工程师可以更好地了解噪声产生机制，经济有效地评估复杂机器的噪声性能，并制定有效的措施来规避振动和噪声问题。该工具还将显著提高课堂教学的有效性。它将使学生“看到”声波的辐射、反射和衍射，从而使复杂声学概念的学习更容易、更有趣和有效。

This GOALI project is being carried out in collaboration with the Advanced Engineering Center of Ford Motor Company. The objectives of this investigation are two-fold: (1) to develop an innovative methodology to reconstruct the acoustic pressure fields accurately and cost-effectively, and (2) to extend this methodology to producing real-time acoustic holography that enables one to visualize the instantaneous acoustic pressure distributions and their evolution as the excitation forces change with time. The novelty of the methodology lies in the fact that the acoustic pressures are reconstructed through an expansion of acoustic modes, or a set of particular solutions to the Helmholtz equation. The coefficients associated with these acoustic models are determined by requiring the assumed form solution to satisfy pressure boundary conditions at measurement points. The errors incurred in this process are minimized by using the least squares method. The significance of this methodology is that solutions thus obtained are unique and the efficiency of numerical computations is high. This is because the acoustic modes employed represent a complete set of eigenfunctions that satisfy the Helmholtz equation. The number of acoustic modes determines the measurement points, which is small when a right coordinate system is selected for the source geometry under consideration. Hence numerical computations are fast and efficient. Moreover, the acoustic pressure is written as an explicit form of the acoustic modes. Therefore the time-domain signals can be obtained by taking a direct inverse Fourier transformation. This makes the generation of real-time acoustic holography possible. The investigation will yield an effective tool for diagnosing both structure and airborne noise sources. Using this tool, the design engineers can acquire a better understanding of the noise generation mechanisms, assess the noise performance of a complex machine cost-effectively, and develop effective measures to circumvent vibration and noise problems. This tool will also significantly enhance the teaching effectiveness in classroom education. It will enable students to `see` the radiation, reflection, and diffraction of sound waves, thus making the learning of complex acoustic concepts easier, and more interesting and effective.