Woodwind instrument design optimization based on impedance characteristics with geometric constraints

Augustin Ernoult, Christophe Vergez, Samy Missoum, Philippe Guillemain, Michael Jousserand

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Computational optimization algorithms coupled with acoustic models of wind instruments provide instrument makers with an opportunity to explore new designs. Specifically, they enable the automatic discovery of geometries exhibiting desired resonance characteristics. In this paper, the design optimization of woodwind instruments with complex geometrical features (e.g., non-cylindrical bore profile and side holes with various radii and chimney heights) is investigated. Optimal geometric designs are searched so that their acoustic input impedance has peaks with specific target frequencies and amplitudes. However, woodwind instruments exhibit complex input impedance whose features, such as resonances, might have non-smooth evolution with respect to design variables, thus hampering gradient-based optimization. For this reason, this paper introduces new formulations of the impedance characteristics (resonance frequencies and amplitudes) using a regularized unwrapped angle of the reflection function. The approach is applied to an illustrative instrument subjected to geometric constraints similar to the ones encountered by manufacturers (a key-less pentatonic clarinet with two-registers). Three optimization problems are considered, demonstrating a strategy to simultaneously adjust several impedance characteristics on all fingerings.

Original languageEnglish (US)
Pages (from-to)2864-2877
Number of pages14
JournalJournal of the Acoustical Society of America
Issue number5
StatePublished - Nov 1 2020

ASJC Scopus subject areas

  • Arts and Humanities (miscellaneous)
  • Acoustics and Ultrasonics


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