Reconstructing blockages in a symmetric duct via quasi-isospectral horn operators

This paper proposes a new method for the reconstruction of the blockage area function in a symmetric duct by resonant frequencies under a given set of end conditions, i.e., open–open or closed–closed ends. The analysis is based on the explicit determination of quasi-isospectral ducts, that is duct profiles which have the same spectrum as a given duct with the exception of a single eigenfrequency which is free to move in a prescribed interval. The analytical reconstruction was numerically implemented and tested for the detection of blockages. Numerical results show that the accuracy of identification increases with the number of eigenfrequencies used and that the reconstruction is rather stable with respect to the shape, the size and the position of the blockages.