COMPUTATIONAL INVERSE SOLUTION STRATEGIES FOR VISCOELASTIC MATERIAL CHARACTERIZATION USING VIBROACOUSTIC METHODS
Vibroacoustic testing methods are those in which a fluid immersed solid is excited by a remote force, while the resulting acoustic emission in the surrounding fluid is measured. The particular method studied herein consists of measuring the acoustic pressure amplitudes in the fluid surrounding a solid being vibrated to a steady-state with a harmonic pressure. These techniques are currently under development for use in nondestructive and noninvasive imaging of biological soft tissues. However, there is significant potential to extend these methods for quantitative characterization of tissue properties. Furthermore, viscoelastic material properties carry information about stiffness and damping of materials, both of which are significantly affected by the presence of disease. Therefore, approaches to extract these rate dependent properties will have considerable implications in the diagnosis and treatment of disease. Computational techniques were developed and analyzed to characterize the viscoelastic properties of solids using vibroacoustic tests. The techniques presented involve casting the inverse problem as a minimization problem which is then solved using a global nonlinear optimization algorithm. Through numerical and laboratory experiments, acoustic emissions are shown to hold sufficient information for quantifying both elastic and viscoelastic material behavior. In addition, a unique optimization algorithm is presented to account for the computational expense of numerical representations of biological systems along with the simulation demands of global optimization. The methodology, referred to as the Surrogate-Model Accelerated Random Search (SMARS) algorithm, is a non-gradient based iterative application of a random search algorithm and the surrogate-model method for optimization. Through simulated examples, the SMARS algorithm is shown to be both robust and efficient. In the cases examined, the SMARS algorithm is shown to outperform two traditional global optimization algorithms by attaining more accurate solutions with fewer function evaluations. Lastly, an approach is shown for incorporating the proper orthogonal decomposition (POD) technique for model reduction into the inverse solution strategy to further reduce the computational cost. The POD reduced-order modeling methodology is shown to be capable of generalizing over the viscoelastic material search domains for the inverse problems and identifying accurate estimates to the viscoelastic behavior of solids with minimal computational expense.
viscoelasticity; inverse problems; surrogate-model; random search; proper orthogonal decomposition; optimization
dissertation or thesis