Inverse viscoelastic material characterization using POD reduced-order modeling in acoustic–structure interaction

A strategy is presented for applying the proper orthogonal decomposition (POD) technique for model reduction in computational inverse solution strategies for viscoelastic material characterization. POD is used to derive a basis of optimal dimension from a selection of possible solution fields which are generated through a traditional acoustic–structure interaction finite element model for a given vibroacoustic experiment. The POD bases are applied with the Galerkin weak-form finite element method to create a reduced-order numerical model with decreased computational cost, but which still maintains accuracy close to that of the original full-order finite element model. The reduced-order model is then combined with a global optimization technique to identify estimates to the viscoelastic material properties of a fluid immersed solid from vibroacoustic tests. A strategy is also presented to select the viscoelastic parameters of the initial full-order analyses used to create the POD bases. The selection process is shown through an example to maximize the generalization capabilities of the reduced-order model over the material search space for a minimal number of full-order analyses. Two examples are then presented in which the parameters of rheological viscoelastic models are identified for solids immersed in water, which are subject to a steady-state harmonic pressure while the acoustic response is measured at a point in the surrounding fluid. The POD reduced-order models were able to generalize over the material search domains for the inverse problems. Therefore, the reduced-order solution strategy was capable of identifying accurate estimates to the viscoelastic behavior of the solids with minimal computational expense.