Adjoint equation-based inverse-source modeling to reconstruct moving acoustic sources in a one-dimensional heterogeneous solid

S. F. Lloyd, C. Jeong

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish
Article number04018089
JournalJournal of Engineering Mechanics
Issue number9
StatePublished - Sep 1 2018


  • Acoustic source inversion
  • Addressing solution multiplicity
  • Identification of moving wave sources
  • Recovery of spatial and temporal variables of sources
  • State-adjoint-control-equation-based minimization


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