Inverse boundary element calculations based on structural modes

The inverse problem of calculating the flexural velocity of a radiating structure of a general
shape from measurements in the field is often solved by combining a Boundary Element
Method with the Singular Value Decomposition and a regularization technique. In their standard
form these methods solve for the unknown normal velocities of the structure at the relatively
large number of nodes in the numerical model. Efficiently the regularization technique smoothes
the solution spatially, since a fast spatial variation is associated with high index singular values,
which is filtered out or damped in the regularization. Hence, the effective number of degrees of
freedom in the model is often much lower than the number of nodes in the model. The present
paper deals with an alternative formulation possible for the subset of radiation problems in
which a (structural) modal expansion is known for the structure. The inverse problem is
formulated in terms of modal amplitudes rather than of nodal velocities. The size of the inverse
problem and the built-in regularization can be controlled by choosing the number of modes
accounted for in the model.