Adjoint Equation-Based Inverse-Source Modeling to Reconstruct Moving Acoustic Sources in a One-Dimensional Heterogeneous Solid
Publication: Journal of Engineering Mechanics
Volume 144, Issue 9
Abstract
The need to reconstruct moving acoustic sources arises in many real-world applications—for example, smart highways for detecting the motions and weights of vehicles, and underwater acoustic forensics. Despite the usefulness of acoustic source inversion (ASI), to date, few papers have shown the feasibility of identifying unknown signal amplitudes and time-varying positions of moving acoustic sources of an arbitrary number within or on complex media without any prior knowledge about the sources. To fill this gap, this paper introduces a new computational framework for reconstructing spatial and temporal profiles of moving acoustic sources from wave responses measured at sparsely distributed sensors. To reconstruct acoustic source profiles without a priori knowledge of the sources, the presented ASI method employs discretization of source functions in space and time. The value of each discretized parameter is estimated at every iteration in the inversion procedure. Because of the high resolution of the discretization, the number of inversion parameters ranges in the hundreds of thousands in the presented numerical examples. To tackle such a large-scale inverse problem, a state-adjoint-control-equation-based optimization technique is employed. The finite-element method (FEM) is used to obtain wave responses in state and adjoint problems. Numerical experiments, in one-dimensional (1D) undamped heterogeneous solids, prove the robustness of this method by reconstructing spatial and temporal profiles, i.e., speeds, locations, frequencies, and magnitudes, of multiple dynamic moving loads. The accuracy of convergence toward the target in the numerical examples is excellent, reconstructing the spatial and temporal footprints of the sources.
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Acknowledgments
This work was supported by the Burns Faculty Fellowship from the School of Engineering and the Grant-in-Aid program from the Office of the Graduate Studies at The Catholic University of America. This support is gratefully acknowledged.
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Published In
Journal of Engineering Mechanics
Volume 144 • Issue 9 • September 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Dec 3, 2017
Accepted: Apr 4, 2018
Published online: Jul 6, 2018
Published in print: Sep 1, 2018
Discussion open until: Dec 6, 2018
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