Identification of acoustic sources with uncertain data

Abstract

In inverse acoustic problems where attempting to identify the vibratory velocities of sources at the origin of an acoustic radiated field, we have the measured radiated field (called objective) on an antenna with numerous sensors and a propagation model. If both are erroneous, misidentification follows. Here, the problem is formulated in the frequency domain and solved in the least mean square sense. An impaired objective including an unstructured error has virtually no chance of satisfying the propagation equation. Accordingly, with an accurate radiation model, we cannot identify source velocities able to generating this objective. With the same model but now with unknown parameters (in the case of only one parameter it could be the speed of sound within the medium), it is expected intuitively that the parameter value aiming at the perturbed objective does not reach it but ultimately generates a pressure satisfying the wave equation, with a value near the correct pressure. The error in the model is structured in the sense that the model keeps a form satisfying the equations of physics. Currently, it is reported that this intuitive expectation is observed quantitatively through the geometric interpretation of over-determined inverse problems dealt with in L2. © 2013 Acoustical Society of America.