The quantification of structure-borne transmission paths by inverse methods. Part 1: Improved singular value rejection methods

Structure-borne sound from installed machinery is often transmitted into a receiver structure via many connection points and several co-ordinate directions at each of them. In order to quantify the contributions from the various connection points, the operational forces at the interfaces, or an equivalent set of forces at some other locations, should be determined. These forces may be combined with measured transfer functions to determine their contributions to the sound at the receiver locations. Inverse methods are becoming widely used, in which a matrix of measured accelerances is inverted at each frequency and used with operational acceleration data to find the forces. Due to poor conditioning of this matrix, however, the results can often be unreliable. In this paper, using both simulations and measurements, an assessment is made of the success and failure of various strategies for dealing with the problems of ill conditioning, in particular over-determination and singular value rejection. In each case the test structure is a rectangular plate, and a wide frequency range is covered to include regions of both low and high modal overlap. Critical for the rejection of singular values is a suitable threshold. It is established that previously used thresholds, based on estimates of error in either accelerances or operational responses, cannot be used universally. An alternative approach is developed in which the accelerance matrix is perturbed by a different amount for each sample of the operational responses. Based on this approach a more robust strategy is proposed which takes account simultaneously of the effect of errors in both the accelerances and operational responses.