Inverse determination of structure-borne sound sources

Abstract

Structure-borne sound from installed machinery is often transmitted into the receiver structure via many connection points and several coordinate directions at each of them. In order to quantify the contributions from the various connection points and directions, the operational forces at the interfaces should be determined. If these are determined indirectly, two sets of measurements are required: the operational responses at a series of positions and a set of frequency response functions (FRF's). A matrix of measured FRF's has to be inverted at each frequency in order to obtain the forces. The indirect force determination is prone to errors. The forces can contain large errors introduced by the combination of errors in the measurement of operational responses and FRF's and ill-conditioning of the FRF matrix at certain frequencies.

The relative performance of different FRF estimators has also been studied in this thesis. Out of five estimators considered, the conventional H\ estimator has been found to be more reliable under all conditions of measurement noise considered.

The resampling of the accelerance matrix has been proposed which is then implemented practically by a perturbation of the accelerance matrix. This method has been found to take account of FRF errors reliably. But it is sensitive to the errors in responses measured. The concept of rejecting perturbed singular values has been developed to take account of shortcomings in matrix perturbation and the singular value rejection. This method has been found to be robust against any level of noise in the measurements of operational responses and the FRF's.

Two regularization techniques, iterative inversion and Tikhonov regularization, have been explored in the next stage. Although these are not new, they have not previously been applied to structural dynamics problems rigorously. A direct comparison is made of Tikhonov regularization and singular value rejection. Initially the regularization parameter is selected based on ordinary cross validation (OCV). The performance of OCV for structural dynamics problems is analysed. A new method called selective cross validation (SCV) for selecting the regularization parameter is then proposed. To take of account of large condition numbers at resonances in conjunction with small response errors, modifications referred to as biased OCV and SCV are proposed to limit the error amplification.

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