ITR/ACS :Collaborative Research: Advanced Algorithms for Visualizing Sources of Noise and Vibrations of Complex Structures

该项目的目标是开发先进的算法，用于基于简单的声压测量来可视化复杂振动结构的噪声和振动源。开发的软件将提供一个有效的，强大的，用户友好的工具，实践工程师关心的识别和控制的噪声和振动。 例如，这将允许飞机设计师减少飞机客舱内的噪音量，或制造更安静的汽车。这个项目将解决数学，计算和工程相关的问题，从振动结构，也被称为声全息寻找声辐射源。该过程涉及基于来自结构附近的麦克风阵列的简单声压测量来确定结构中的振动模式。声全息术的数学部分是一个反问题，直接问题是确定流体介质中的辐射声压场，给定结构的振动响应。像这样的逆问题是不适定的，因此需要有效的正则化技术作为过滤器。在这个项目中，研究人员将汇集他们在先进的计算科学，数学分析和机械工程方面的专业知识和经验，将声全息技术提升到更高的水平，以具有成本效益的方式解决工程噪声和振动问题。算法和正则化技术将牢固地建立在数值线性代数，数学分析和工程实践的当前工作的基础上。将开发迭代方法，为单层和Helmholtz-Kirchhoff积分方程方法提供快速计算技术。将建立稳定性和准确性的估计，为亥姆霍兹方程最小二乘（HELS）方法和组合HELS（CHELS）方法的最佳正则化策略、测量位置和展开函数的数量提供指导。该方法的实验验证将在飞机机舱和车辆前端的内部和外部区域进行。

The goal of this project is to develop advanced algorithms for visualizing the sources of noise and vibrations of complex vibrating structures based on simple measurements of acoustic pressures. The software developed will provide an efficient, robust, and user-friendly tool to practicing engineers concerned with identification and control of noise and vibration. For example, this will allow aircraft designers to reduce the amount of noise inside the passenger cabin of an airplane, or make quieter cars. This project will address mathematical, computational, and engineering issues related to finding the source of acoustic radiation from a vibrating structure, also known as acoustic holography. This process involves determining the vibrational patterns in a structure based on simple acoustic pressure measurements from an array of microphones near the structure. The mathematical part of acoustic holography is an inverse problem, the direct problem being to determine the radiated acoustic pressure field in the fluid medium, given the vibration responses of the structure. Inverse problems such as this are ill-posed, thus requiring effective regularization techniques as filters. In this project, the researchers will pool their expertise and experience in advanced computational science, mathematical analysis, and mechanical engineering to elevate the acoustic holography to a higher level for solving engineering noise and vibration problems in a cost-effective manner. The algorithms and regularization techniques will be firmly based on current work in numerical linear algebra, mathematical analysis, and engineering practice. Iterative methods will be developed to provide fast computational techniques for both the single layer and Helmholtz-Kirchhoff integral equation methods. Estimates of stability and accuracy will be established to provide guidance for optimal regularization strategies, measurement locations, and number of expansion functions for the Helmholtz Equation Least Squares (HELS) method and combined HELS (CHELS) method. Experimental validation of the methods will be carried out for both interior and exterior regions on an aircraft cabin and a vehicle front end.