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### Minimum Sensor Density for Quantitative Damage Imaging

#### Abstract

Quantitative information regarding the size and severity of structural damage is required for structural integrity assessment. In the context of structural health monitoring using distributed sensors, several imaging algorithms have been developed recently. However, a large number of sensors is needed to meet the correct sampling requirements for accurate image reconstruction, the number being dictated by the size of the prescribed imaging domain. It is shown here that this requirement can be greatly reduced, based on an understanding of the mathematical structure and properties of the multistatic data matrix. The concepts of bandwidth and rank of the data matrix are defined and their relevance for the required number of sensors is discussed. An approximate translation theorem is proposed, and on that basis it is shown that a twopass imaging procedure can be implemented, in which the required number of sensors is dictated by the size of the damage, which is generally much smaller than the imaging domain. In particular, it is shown that, provided the insonifying wavelength is selected to be approximately equal to the damage size, one can obtain sufficiently accurate images for the purposes of safety prognostics by using only six or seven sensors. This considerably enhances the prospects for a practical implementation of in situ imaging of structural damage in plate-like structures, at least in the absence of geometrical complexities such as stiffeners or cut outs. The influence of such complexities is currently being investigated.