Scientific Article

Full waveform inversion for bore reconstruction of woodwind-like instruments

¹ Project-team Makutu, INRIA Bordeaux-Sud Ouest, Universite de Pau et des Pays de l’Adour, E2S UPPA, CNRS, 200 avenue de la vieille Tour, 33405 Talence Cedex, France
² University of Bordeaux, CNRS, Arts et Metiers Institute of Technology, Bordeaux INP, INRAE, I2M Bordeaux, 33400 Talence, France
³ HUMEAU Factory, 24700 Montpon-Ménestérol, France

^* Corresponding author: augustin.ernoult@inria.fr

Received: 21 May 2021
Accepted: 19 September 2021

Abstract

The internal geometry of a wind instrument can be estimated from acoustic measurements. For woodwind instruments, this involves characterizing the inner shape (bore) but also the side holes (dimensions and location). In this study, the geometric parameters are recovered by a gradient-based optimization process, which minimizes the deviation between simulated and measured linear acoustic responses of the resonator for several fingerings through an observable function. The acoustic fields are computed by solving a linear system resulting from the 1D spectral finite elements spatial discretization of the wave propagation equations (including thermo-viscous effects, radiation and side holes). The “full waveform inversion” (FWI) technique exploits the fact that the gradient of the cost function can be computed by solving the same linear system as that of the direct problem but with a different source term. The gradient is computed with better accuracy and less additional cost than with finite-difference. The dependence of the cost function on the choice of the observed quantity, the frequency range and the fingerings used, is first analyzed. Then, the FWI is used to reconstruct, from measured impedances, an elementary instrument with 14 design variables. The results, obtained in about 1 minute on a laptop, are in excellent agreement with the direct geometric measurements.