Distinguishing geometrically identical instruments: Possibilistic identification of material parameters in a parametrically model order reduced finite element model of a classical guitar

Abstract

The identification of material parameters of classical guitars is particularly interesting as the orthotropic material parameters of wood vary largely and lead to hearable differences even in seemingly identical instruments. Identification methods intended to achieve this task commonly try to fit, e.g., finite element models to experimental data by minimizing a given objective function, and typically return precise parameter values. However, such one-point estimators do not contain much information with respect to the uncertainty that may remain regarding the true values – irrespective of whether such a ground truth can be assumed at all. Model updating techniques that also intend to quantify these uncertainties typically require the practitioner to specify a statistical model of the experiment, which is not easily formulated. Moreover, virtually all uncertainty quantification techniques require a high number of model evaluations, which is diametrically opposed to the long evaluation times of high-fidelity finite element models. In this contribution, an alternative technique for uncertainty quantification based on possibility theory is proposed and applied to a classical guitar. Only requiring the practitioner to specify an objective function, which may be identical to the one used to find point estimates, it is readily accessible and straightforward to apply. Great emphasis is put on the construction of a high-fidelity guitar model and the construction of suitable surrogate models via parametric model order reduction based on Krylov subspace methods, which drastically reduces the number of degrees of freedom in the surrogate model of the finite element model while maintaining the parameter dependency. In this manner, model order reduction allows for significant speedups of the model evaluations and, more importantly here, facilitates the uncertainty quantification in the first place. It is demonstrated how this scheme is able to find regions of plausible parameter values of the guitar and how one may distinguish quasi-identical instruments with great confidence, e.g., due to the disjointness of such regions, compared to the moderate confidence implied by more or less disagreeing point estimates. Although motivated by the material parameter identification of guitars, the presented method yields great potential for applicability to inverse problems tackled with finite element models in general.