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

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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.