Publications

Improved Expansion Results Using Regularized Solutions

Beale, Chris; Schultz, Ryan S.; Fowler, Deborah

Traditional expansion techniques utilize a modal projection wherein modal response is estimated based on a generalized inverse of measurements at a sparse set of degrees of freedom. Those modal response estimates are then used to project out to a larger set of degrees of freedom, resulting in predicted responses at more points or even full- field. As with any generalized inverse problem, the results are sensitive to noise and conditioning of the inverted matrix. While much has been done to improve numerics of matrix inversion problems in the context of input estimation or source identification problems, little has been done to improve the numerics of inverse solutions in expansion problems. This work presents numerical correction or regularization techniques applied to expansion problems using both simple and complex example structures. The effects of degree of freedom selection and noise are explored. Improved expansion results are obtained using straightforward regularization techniques, meaning higher accuracy responses can be obtained at expansion degrees of freedom with no change in the sparse set of measurements.