Biomedical Applications of Vibration and Acoustics in Imaging and Characterizations
4 Computational Inverse Problem Techniques in Vibroacoustics
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This chapter describes state-of-the-art numerical methods for the solution of direct and inverse vibroacoustic problems. Particular emphasis is placed on current and emerging techniques for the characterization of material properties through the use of vibroacoustic experiments. Numerical techniques such as the weak-form Galerkin finite element method and the boundary element method are presented as tools for solving the boundary-value and initial boundary-value problems occurring in coupled acoustic-structure interaction problems. Then, emerging model-updating techniques for the solution of inverse problems that use the aforementioned numerical methods coupled with classical and novel optimization and machine learning tools are presented. An example problem is presented which applies these inverse problem techniques for the characterization of viscoelastic and elastic properties of a solid using vibroacoustic testing methods. Advantages, disadvantages, and the relevance of the described methods in medical applications will be addressed throughout the chapter.