Signal-to-Noise Ratio analysis for time-reversal based imaging techniques in bounded domains

Abstract

We consider the problem of localizing small material defects in rectangular bounded domains. The scalar acoustic equation is used to model wave propagation in this context. Our data is the scattered field collected at one or more receivers and due to impulsive excitations at one or more source positions. To localize the defect we use an imaging method that consists in back-propagating the recorded field in the domain of interest. The back-propagation is performed numerically using a model for the Green's function in the bounded medium. For the source localization problem this imaging technique is equivalent to computational Time Reversal (TR). We study in this paper the quality of imaging in terms of the Signal to Noise Ratio (SNR) both for the source and the defect localization problems. SNR here is defined as the value of the image at the true source (defect) location, divided by the maximal value of the image outside a small region around the true source (defect) location. Our theoretical analysis carried out for the simpler one-dimensional case allows us to correctly predict the performance of the method. Our results indicate that for the source localization problem the SNR increases linearly with the number of receivers while for the defect localization its maximal value is 2 and can only be attained by

A Numerical Study on Computational Time Reversal for Structural Health Monitoring

“…The plots indicate an almost linear relation with respect to the receivers' number with deviations that occurred because of ghost superposition or cancellation. For the case of axial motion, the case of the left plot in Figure 7a, the factor of the linear evolution with the number of receivers is that of two as it was expected [36], while in the case of transverse and rotational motion depicted in the plot of Figure 7b, the corresponding coefficient is smaller.…”

“…Following previous work [33,36], our choice here is to assumef of zero values components or units when it corresponds to some u r component. Evolutionf (t) = u(t * ) is the reversed in time component of vector u, actually being the solution of the forward problem of Equation (18).…”

“…The presence of ghosts is due to the bounded range of the domain and their location depends on the location of the receiver and boundary conditions. An in depth investigation has been presented in the literature [36] for the case of the acoustic field. In the current work, in the following section we present further results for the case of a beam and frame structures.…”