Numerical experiments prove the robustness of this method by reconstructing spatial and temporal profiles of multiple dynamic moving body forces in a one-dimensional heterogeneous solid bar. The sources create stress waves propagating through the bar. The guessed source functions are spatially discretized by using linear shape functions with an element size of 1m at discrete times with a time step of 0.001s. Thus, the total number of control parameters in this example is 100,000 (i.e., 100 (in space) by 1000 (in time)). The convergence toward the target in the numerical examples is excellent, reconstructing the spatial and temporal footprints of the sources.
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Stephen F. Lloyd, Chanseok Jeong, "Reconstruction of moving acoustic sources in heterogeneous elastic solid," Proc. SPIE 9803, Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2016, 98033L (20 April 2016);