This paper discusses a novel, robust, computational framework for reconstructing spatial and temporal profiles of moving vibrational sources in a heterogeneous, elastic, damped, truncated one-dimensional solid using sparsely measured wave responses. We use the finite element method to obtain wave solutions because of its flexibility and robustness for heterogeneous media. To reconstruct wave source profiles without a priori knowledge of the sources, we employ high-resolution discretization of source functions in space and time. Because of such dense discretization, the order of magnitude of the number of inversion parameters could range up to hundreds of thousands. To identify such a large number of control parameters, an adjoint-gradient-based source inversion approach is used within a context of discretization-then-optimization (DTO). Numerical experiments prove the robustness of this method by reconstructing spatial and temporal profiles of multiple dynamic moving body forces in a heterogeneous, damped solid bar. The numerical experiments show that using the conjugate gradient method gives improved results over the steepest descent method. The inversion performance is not affected by the acceleration, frequency, or amplitude of targeted moving dynamic distributed loads. While inversion performance is not affected by the damping or wave speed in the domain when the model is homogeneous, a mismatch in acoustic impedance for materials in a heterogeneous solid bar leads the inversion to converge more slowly. The inversion is sensitive to noise, but filtering the noise from the measured data help reduce the inversion error.
- Inverse problem
- absorbing boundary condition
- discretize-then-optimize (DTO) approach
- moving wave source inversion