A source sensitivity approach for source localization in steady-state linear systems

Localizing sources in physical systems represents a class of inverse problems with broad scientific and engineering applications. This paper is concerned with the development of a non-iterative source sensitivity approach for the localization of sources in linear systems under steady-state. We show that our proposed approach can be applied to a broad class of physical problems, ranging from source localization in elastodynamics and acoustics to source detection in heat/mass transport problems. The source sensitivity field introduced in this paper represents the change of a cost functional caused by the appearance of an infinitesimal (or point) source in a given domain (or its boundary). In order to extract macroscopic inferences, we apply a threshold to the source sensitivity field in a way that parallels the application of the topological derivative concept in shape identification. We establish precise formulas for the source sensitivity field using a direct approach and a Lagrangian formulation. We show that computing the source sensitivity field entails just obtaining the solution of a single adjoint problem. Hence, the computational expense of obtaining the source sensitivity is of the same order as that of solving one forward problem. We illustrate the performance of the method through numerical examples drawn from the areas of elastodynamics, acoustics, and heat/mass transport. Our results show that our proposed approach could be used on its own as a source detection tool or to obtain initial guesses for more quantitative iterative gradient-based minimization strategies. © 2013 IOP Publishing Ltd.

Duke Scholars

Author Wilkins Aquino Thomas Lord Department of Mechanical Engineering and Materia ...